1. 2025
3. GeoGT

Dehn Functions of Coabelian Subgroups — Pratit Goswami <pratit.goswami-1@ou.edu>

The study of Dehn functions has developed into a major area of research in geometric group theory mainly because the growth types of these functions are quasi-isometry invariants of finitely presented groups. The Dehn function of a finitely presented group G is also connected to the complexity of solving the word problem in G namely, a finitely presented group has solvable word problem if and only if the Dehn function for a finite presentation is recursive. In this talk, we will discuss new methods for computing the precise Dehn functions of coabelian subgroups of direct products of groups, that is, subgroups which arise as kernels of homomorphisms from the direct product onto a free abelian group. This is joint work with Noel Brady and Rob Merrell.

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1. 2024
3. STDC2024-GTop

"Shake slice conjecture" and "Smooth 4-D Poincaré conjecture" — Eylem Yıldız <eylem.yildiz@duke.edu>

In this talk, we will address two conjectures. Firstly, we will present the proof of "0-shake slice knots are slice", which was a collaborative effort with Selman Akbulut. Secondly, we will discuss how the progress made in the first problem can assist in tackling the "Smooth 4-D Poincaré conjecture". If time allows, we will delve into this further.

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1. 2026
3. Continua
5. Plenaries

$R^i$-sets in continua and hyperspaces — Patricia Pellicer-Covarrubias <paty@ciencias.unam.mx>

$R^1$, $R^2$ and $R^3$-continua were defined by S. T. Czuba in 1980, in particular he showed that the existence of any one of these sets in a continuum $X$ implies the noncontractibility of $X$. Also, $R^i$-continua have proved to be useful when studying noncontractibility of hyperspaces. In this talk we recall these concepts and we present some relations between them in continua and hyperspaces.

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1. 2025
3. GeoTop

3-Manifolds, Isotopy, and Group Actions — Trent Lucas <trent_lucas@brown.edu>

Suppose a finite group acts on a closed manifold M. Given two equivariant homeomorphisms of M, if we know that they are isotopic, can we conclude that they are equivariantly isotopic? An important theorem of Birman-Hilden and MacLachlan-Harvey says the answer is "yes" if M is a hyperbolic surface; Margalit-Winarski asked whether the same is true when M is a 3-manifold. We answer Margalit-Winarski's question for a wide class of group actions on 3-manifolds; this includes a 3-manifold analog of the hyperelliptic involution, which we can understand particularly well via a connection with geometric group theory.

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1. 2026
3. GeoGT

A Combination Theorem for Relatively Hyperbolic Groups — Darius Alizadeh <daliza2@uic.edu>

Given a group $G$ acting cocompactly on a suitable simply connected cell complex $X$ with relatively hyperbolic cell stabilizers, we show $G$ itself is relatively hyperbolic. Building on work of Dahmani and Martin, the proof constructs a model for the Bowditch boundary by gluing together the boundaries of cell stabilizers. More generally, any cocompact action on a cell complex $X$ induces an algebraic \emph{complex of groups} decomposition which generalizes Bass--Serre theory in the case where $X$ is 1--dimensional. This model connects this algebraic decomposition with a topological decomposition of the boundary which we hope will be useful for answering other questions.

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1. 2025
3. Continua

A Dendrite Equivalence Relation on Loop Space — Spencer Arnesen <spencer.arnesen@mathematics.byu.edu>

This talk will discuss how to turn a loop space into a group by factoring through dendrites. Inspired by the fact that group homomorphisms between fundamental groups of one-dimensional spaces induce, up to conjugation, a continuous map, and that path homotopies on one-dimensional spaces factor through a dendrite we show that homotopy through a dendrite is an equivalence relation and induces a group structure on a subset of loops. This group is always locally free.

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1. 2025
3. Set-Theoretic

A Forcing Axiom for Preserving a Lindelöf Space — Thomas Gilton <tdgilton@gmail.com>

A topic of continued interest in set-theoretic topology is the question of which topological properties are preserved under which forcings. In recent work, the speaker and Holshouser have shown that strongly proper forcings preserve a wide variety of covering properties (including Lindelöf), generalizing work of Dow, Iwasa, and Kada. In this talk, we will give an overview of yet further work done by the speaker on this topic. Namely, we discuss how to create forcing axioms for proper posets that preserve a given Lindelöf space. This uses Neeman's two-type side conditions machinery in combination with the earlier work of Gilton and Holshouser.

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1. 2026
3. Applied & Data

A Medial-Axis-Based Measure of District Compactness — Greg Malen <gmalen@skidmore.edu>

An essential question for democracy is how to rigorously determine the likelihood that a congressional map has been gerrymandered. A number of state constitutions require districting plans to be "compact," yet no technical legal definition of compactness exists in this context, leaving us to contend with the oft-cited sentiment that "you know it when you see it." In this talk, I will introduce a novel compactness measure based on a geometric structure known as the medial axis. This skeleton-like structure has been shown to have strong ties to the science of how the human brain perceives and processes complex shapes, thus offering a mathematically rigorous version of “the eye test.” I will explain the construction of this metric in detail, and then compare it to a recent machine-learning-based compactness metric introduced by Kaufman, King, and Komisarchik (2021). Specifically, in this work we examine the performance of our measure and theirs in several case studies, including two states whose districting plans were especially contentious and the entire 2016 congressional district map. This is joint work with Ellen Gasparovic at Union College, and Jason D’Amico and Mushan Zhong, who were undergraduates at Union College at the time of their contributions.

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1. 2026
3. Applied & Data

A Schauder Basis for Multiparameter Persistence and Persistence Variants — Zachariah Ross <thomas.z@ufl.edu>

To help combine statistics and machine learning with multiparameter persistence, we would like to map signed barcodes to a Banach space or Hilbert space. We use iteratively refined triangulations to define a Schauder basis of compactly supported Lipschitz functionals. We prove that evaluation of these functionals embeds signed barcodes into sequence space via a map which is both linear, and Lipschitz with respect to the 1-Wasserstein distance. I will illustrate these results with examples for one-parameter persistence, two-parameter persistence, and the variant called mixup barcodes.

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1. 2024
3. STDC2024-STT

A bound for the density of any Hausdorff space — Nathan Carlson <ncarlson@callutheran.edu>

We show, in a certain specific sense, that both the density and the cardinality of a Hausdorff space are related to the "degree" to which the space is nonregular. It was shown by Sapirovskii that $d(X)\leq\pi\chi(X)^{c(X)}$ for a regular space $X$ and the speaker observed this holds if the space is only quasiregular. We generalize this result to the class of all Hausdorff spaces by introducing the nonquasiregularity degree $nq(X)$, which is countable when $X$ is quasiregular, and showing $d(X)\leq\pi\chi(X)^{c(X)nq(X)}$ for any Hausdorff space $X$. This demonstrates that the degree to which a space is nonquasiregular has a fundamental and direct connection to its density and, ultimately, its cardinality. Importantly, if $X$ is Hausdorff then $nq(X)$ is "small" in the sense that $nq(X)\leq\min\{\psi_c(X),L(X),pct(X)\}$. This results in a unified proof of both Sapirovskii's density bound for regular spaces and Sun’s bound $\pi\chi(X)^{c(X)\psi_c(X)}$ for the cardinality of a Hausdorff space $X$. A consequence is an improved bound for the cardinality of a Hausdorff space. We give an example of a compact, Hausdorff space for which this new bound is a strict improvement over Sun's bound.

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1. 2024
3. STDC2024-CT

A class of 1-dimensional continua: Shape Theory meets Dynamics — Krystyna Kuperberg <kuperkm@auburn.edu>

The notion of movability was introduced by K. Borsuk in 1967 as one of the basic notions in shape theory. A compactum X embedded in an absolute neighborhood retract (ANR), such as the Hilbert cube or the Euclidean space, is movable if for any neighborhood U of X there is a smaller neighborhood V of X such that V can be moved by a homotopy within U into any neighborhood W of X. Movability does not depend on the choice of the ANR or the embedding. A continuum that is locally homeomorphic to the Cartesian product of the Cantor set and an open interval is called a lamination. In this talk we consider movable and non-movable laminations appearing as invariant sets in aperiodic continuous dynamical systems, as well as the flow around them and the larger 1-dimensional invariant compacta containing the laminations. A non-movable invariant lamination in a 3-dimensional Euclidean space is often contained in an invariant compactum that is movable.

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1. 2024
3. STDC2024-Plenary

A classification of Hénon maps in the presence of strange attractors — Jan Boronski <jan.boronski@uj.edu.pl>

In my talk I shall present my work with Sonja Štimac on Hénon maps with strange attractors (Wang-Young parameters). First I shall explain a construction (inspired by a work of Crovisier and Pujals on mildly dissipative diffeomorphisms of the plane) of conjugacy of these maps to the shift homeomorphisms on inverse limits of dendrites with dense set of branch points, and a characterization of orbits of critical points in terms of these inverse limits. Then I will explain how this leads to a classification of conjugacy classes of such maps in terms of a single sequence of 0s and 1s. References: 1. Boronski J., Štimac S; Densely branching trees as models for Hénon-like and Lozi-like attractors, Advances in Mathematics 429 (2023) 109191 2. Boronski J., Štimac S; The pruning front conjecture, folding patterns and classification of Hénon maps in the presence of strange attractors, arXiv:2302.12568v2

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1. 2026
3. Dynamics

A complex dynamics approach to understanding birational maps of the plane arising from cluster algebra mutations — Krishna Chaitanya Kalidindi <kkalidin@iu.edu>

There is a family of birational self-mappings of the plane arising from the theory of cluster algebra mutations that was studied previously by Machacek-Ovenhouse from the perspective of real dynamics. We study this family of mappings from the perspective of complex dynamics and, in particular, show that is most cases there is no conserved quantity. No background on cluster algebras is expected from the audience. This is the joint-work with Andrei Grigorev, Andres Quintero and Roland Roeder.

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1. 2025
3. Applied

A discontinuous ham sandwich theorem — Matt Superdock <superdockm@rhodes.edu>

The "ham sandwich" theorem states that any $n$ finite Borel measures on $\mathbb{R}^{n}$ can be simultaneously bisected by a single hyperplane, provided each measure is absolutely continuous with respect to Lebesgue measure. In 1984, Cox & McKelvey showed that even for discontinuous measures, there exists a single hyperplane such that at most half of each measure lies on each side. In this talk, we consider the problem of minimizing the differences of the measures of the two open half-spaces determined by a chosen hyperplane, where the measures may be discontinuous. We show that if the dimension of $\mathbb{R}^{n}$ is much larger than the number of measures, then there exists a hyperplane that divides the measures more fairly than in Cox & McKelvey's result.

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1. 2026
3. Applied & Data

A discrete view of Gromov's filling area conjecture — Chris Wells <chris@mathematicaster.org>

In differential geometry, a metric surface $M$ is said to be an isometric filling of a closed metric curve $C$ if $\partial M=C$ and $d_M(x,y)=d_C(x,y)$ for all $x,y\in C$. Gromov's filling area conjecture from 1983 asserts that among all isometric fillings of the Riemannian circle, the one with the smallest surface area is the hemisphere. Gromov's conjecture has been verified if, say, $M$ is homeomorphic to the disk and in a few other cases, but it is still open in general. Admittedly, I'm not a differential geometer, so we consider instead a particular discrete version of Gromov's conjecture which is likely fairly natural to anyone who studies graph embeddings on arbitrary surfaces. We obtain reasonable asymptotic bounds on this discrete variant by applying standard graph theoretic results, such as Menger's theorem. These bounds can then be translated to the continuous setting to show that any isometric filling of the Riemannian circle of length $2\pi$ has surface-area at least $1.36\pi$ (the hemisphere has area $2\pi$). This appears to be the first quantitative lower-bound on Gromov's problem that applies to an arbitrary isometric fillings. (Based on joint work with Joe Briggs)

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1. 2025
3. GeoTop

A generalization of Cannon's conjecture for cubulated hyperbolic groups — Corey Bregman <corey.bregman@tufts.edu>

We show that cubulated hyperbolic groups with spherical boundary of dimension 3 or at least 5 are virtually fundamental groups of closed, orientable, aspherical manifolds, provided that there are sufficiently many quasi-convex, codimension-1 subgroups whose limit sets are locally flat subspheres. The proof is based on ideas used by Markovic in his work on Cannon's conjecture for cubulated hyperbolic groups with 2-sphere boundary. This is joint work with Merlin Incerti-Medici.

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1. 2026
3. General & ST

A glance at function spaces with a dense functionally countable subspace — Vladimir Tkachuk <vova@xanum.uam.mx>

We will present some results on existence of dense functionally countable subspaces in spaces $C_p(X)$. It will be shown, among other things, that there is a consistent example of a scattered Lindel\"of $P$-space $X$ for which $C_p(X)$ has no dense functionally countable subspace and that $\mathbb R^{\omega_1}$ has a dense functionally countable subspace of cardinality $\omega_2$ if and only if the Kurepa Hypothesis holds.

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1. 2025
3. Continua

A notable contractible dendroid — Alejandro Illanes <illanes@matem.unam.mx>

A dendroid is an arcwise connected continuum such that the intersection of any two of its subcontinua is connected. In 1985, Tadeusz Mackiowiak constructed a contractible non-selectible dendroid X. Through the years the originality of the structure of this dendroid has been useful to produce several counterexamples. In this talk we will mention some other important properties of X and some of the examples that have constructed using it, including a new one related to the hyperspace of subcontinua with empty interior of a continuum.

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1. 2026
3. Continua

A simple USC bonding function giving $D_m$ as its inverse limit space — Robert Roe <rroe@mst.edu>

We show how the Wa\.zewski universal dendrite of order $m$, for any positive integer $m$ greater than 2, can be obtain as the generalized inverse limit of a single set-valued upper semi-continuous bonding function on $[0,1]$ whose graph consists of exactly $m$ line segments. $D_m$ has been obtained previously as a generalized inverse limit of a single bonding function but in that case the bonding function was extremely complicated consisting of infinitely many line segments. This is joint work with Faruq Mena.

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1. 2025
3. GeoGT

A weak Tits alternative for groups acting on buildings — Chris Karpinski <christopher.karpinski@mail.mcgill.ca>

Buildings are highly symmetrical non-positively curved simplicial complexes introduced by Jacques Tits in the 1950s to study semisimple algebraic groups. Over the years, buildings have garnered interest among geometric group theorists due to their non-positively curved structure and close connections to Coxeter groups. We prove that groups acting properly and cocompactly on buildings satisfy an algebraic dichotomy, commonly encountered among groups with non-positive curvature features, known as the weak Tits alternative: either the group is virtually abelian or it contains a nonabelian free subgroup. This is joint work with Damian Osajda and Piotr Przytycki.

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1. 2024
3. STDC2024-CT

Accessible points of arc-like continua — Andrea Ammerlaan <ajammerlaan879@my.nipissingu.ca>

This talk will discuss the Nadler-Quinn problem. Posed in 1972, the problem asks if, given any arc-like continuum $X$ and any point $x \in X$, we can embed $X$ in the plane with $x$ accessible. In 2001, Minc constructed a particularly simple example of an arc-like continuum $X$ and point $p \in X$ for which it was not known whether $p$ could be made accessible in a plane embedding of $X$. In 2020, Anusic proved that $X$ can, in fact, be embedded with $p$ accessible. I will give an overview of this proof and briefly introduce a more recent approach to the problem.

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1. 2025
3. GeoGT

Acylindrical actions on trees and applications to the outer automorphism group of Baumslag-Solitar groups — Bratati Som <bratatis@buffalo.edu>

An acylindrical action generalizes proper and cobounded actions on hyperbolic spaces. Non-elementary acylindrical actions provide acylindrically hyperbolic groups, which includes most mapping class groups of punctured surfaces, 3-manifold groups, and $Out(F_n)$ for $n > 1$. In this talk, we will explore how acylindricity of a group action on a tree can be preserved under quotients by certain subgroups, and discuss the existence of a largest acylindrical action for some groups acting on trees. In addition, we will show when $Out(BS(p,q))$ is acylindrically hyperbolic for non-solvable Baumslag-Solitar groups, despite $BS(p,q)$ itself not being acylindrically hyperbolic, and explore further applications of these acylindricity results. This is a joint work with Daxun Wang.

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1. 2024
3. STDC2024-STT

Adding a continuous map by forcing — Akira Iwasa <akiraiwasa94@gmail.com>

We discuss in what circumstances forcing adds new continuous maps. We prove that if $X$ is scattered compact Hausdorff and $Y$ is discrete, then forcing does not add any continuous maps from $X$ to $Y$. On the other hand, if $X$ is not a zero-dimensional scattered pseudocompact space and $Y$ has more than one point, then ccc forcing adds a continuous map from $X$ to $Y$.

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1. 2025
3. Set-Theoretic

Adding an uncountable discrete subspace by forcing — Akira Iwasa <akiraiwasa94@gmail.com>

Suppose that a topological space $X$ has no uncountable discrete subspace. We discuss if $X$ can obtain an uncountable discrete subspace in forcing extensions. We prove that for any monotonically normal space $X$ which has no uncountable discrete subspace, $X$ can obtain an uncountable discrete subspace in some forcing extension if and only if $X$ is not separable.

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1. 2024
3. STDC2024-DS

Adic systems associated to multivariable polynomials — Sarah Frick <sarah.frick@furman.edu>

In this talk we will discuss adic systems on Bratteli diagrams associated to multivariable polynomials. While these diagrams are not stationary, they exhibit a self-similar structure that can be used to understand any resulting adic system. In particular, the structure alone implies the diagram is inherently expansive. Further, any diagram with multivariable polynomial shape will also be inherently expansive.

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1. 2025
3. Plenary

All is Rep-Tile — Alexandra Kjuchukova <akjuchuk@nd.edu>

An n-dimensional rep-tile is a PL n-manifold X, embedded in $\mathbb{R}^n$, which can be decomposed as the union of mutually isometric manifolds similar to X which have non-overlapping interiors. For one astonishing example, all knot exteriors are homeomorphic to rep-tiles, by a 2021 result of Blair, Marley and Richards. I will give an isotopy classification of rep-tiles in all dimensions. I will also outline our proof, which is based on a technique called ball swapping. This is joint work with Ryan Blair, Patricia Cahn and Hannah Schwartz.

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1. 2024
3. STDC2024-DS

Amorphic complexity and tameness of automatic systems — Elzbieta Krawczyk <ela.krawczyk7@gmail.com>

Amorphic complexity is a relatively new invariant of dynamical systems useful in the study of aperiodic order and low complexity dynamics. Tameness is a well-studied notion defined in terms of the size of the Ellis semigroup of the system. In the talk we will study amorphic complexity and tameness in the class of automatic systems (systems arising from constant length substitutions). We will present a closed formula for the complexity of any automatic system and show that tameness of automatic systems can be succinctly characterised using amorphic complexity: an automatic system is tame if and only if its amorphic complexity is one. The talk is based on a joint work with Maik Gröger.

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1. 2026
3. General & ST

An Adaptation of the Vietoris Topology for Ordered Compact Sets — Jared Holshouser <jholshouser1321@gmail.com>

We discuss a natural topology on powers of a space that is inspired by the Vietoris topology on compact subsets. We then place this topology in context with other product topologies; specifically, we compare this topology with the Tychonoff product, the box product, and Bell's uniform box topology. We identify a variety of topological properties for the specific case when the ground space is discrete. When the ground space is the Euclidean real line, we show that the resulting power is not Lindelöf, and hence, not Menger. This shows that, unlike the the Vietoris topology on unordered compact subsets, covering properties of the ground space need not transfer to the Vietoris power.

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1. 2026
3. GeoGT

An Improved Combination Theorem for A/QI Triples — Olu Olorode <oio3@cornell.edu>

Let $G$ be a group acting by isometries on a hyperbolic space $X$. Given geometrically natural subgroups $H$ and $K$ of $G$, it is natural to ask whether $ \langle H, K \rangle $ inherits the geometric properties of $H$ and $K$, and whether $ \langle H, K \rangle $ admits a nice algebraic structure. In a classical work of Gitik we receive an answer in the case where $G$ is a hyperbolic group, and $H$ and $K$ are quasiconvex. In more recent work of Martínez-Pedroza and Sisto, we receive an answer in the case where $G$ is relatively hyperbolic, and $H$ and $K$ are relatively quasiconvex. In this talk, I will discuss a generalization of a combination theorem of Abbot and Manning that covers a broader class of geometrically natural subgroups of such a group $G$. This is still a work in progress.

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1. 2025
3. Continua

An Uncountable Family of Generalized Inverse Limit Spaces Which are Pointwise Self Homeomorphic (Updated). — Faruq Mena <faruq.mena@soran.edu.iq>

In this talk, we will discuss how we found uncountable families of generalized inverse sequences on intervals and also on finite trees such that the inverse limit spaces of these sequences are pointwise self-homeomorphic. We give several examples of pointwise self-homeomorphic continua obtained in this manner including the dendrite $D_3$ and a dendrite containing $D_\omega$.

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1. 2026
3. GeoGT

An explicit section of the Laudenbach type exact sequence of the big mapping class group of $Map(M_Γ)$ — Jorge Andres Robinson Arrieta <jar064@uark.edu>

Brian Udall proved that there is a short exact sequence of the form: $$1 \xrightarrow{} Twist(M_{\Gamma})\xrightarrow{} Map(M_{\Gamma})\xrightarrow{\Psi} Map(\Gamma) \xrightarrow{}1,$$ where $Twist(M_{\Gamma})$ is the subgroup of $Map(M_{\Gamma})$ generated by sphere twists over sphere systems of $M_{\Gamma}.$ Udall also proved that this short exact sequence splits topologically. The purpose of this talk is to present an explicit formula for a section s of this short exact sequence.

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1. 2026
3. General & ST

An infinite library — KP Hart <k.p.hart@tudelft.nl>

We present an regular space that is not completely regular but only barely so: not only is it first-countable, but in addition all closed sets are $G_\delta$-sets and all points are zero-sets. This answers a question about how the lattice of zero-sets is situated in the lattice of all open sets. Some intermediate results on the Niemytzki plane make excellent homework exercises for a topology course.

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1. 2025
3. GeoGT

Anosov representations of cubulated hyperbolic groups — Theodore Weisman <tjwei@umich.edu>

An Anosov representation of a hyperbolic group $\Gamma$ is a representation which quasi-isometrically embeds $\Gamma$ into a semisimple Lie group - say, SL(d, R) - in a way which generalizes and imitates the dynamical behavior of a convex cocompact group acting on a hyperbolic metric space. It is unknown whether every linear hyperbolic group admits an Anosov representation. In this talk, after motivating the theory of Anosov representations from the perspective of geometric group theory, I will discuss joint work with Sami Douba, Balthazar Flechelles, and Feng Zhu which shows that every hyperbolic group acting geometrically on a CAT(0) cube complex admits a 1-Anosov representation into SL(d, R) for some d. The proof exploits the relationship between the combinatorial/CAT(0) geometry of right-angled Coxeter groups and the projective geometry of a convex domain in real projective space on which a Coxeter group acts by reflections.

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1. 2024
3. STDC2024-STT

Applications and Limitations of Strategic Translation in Selection Principles — Christopher Caruvana <chcaru@iu.edu>

We review various applications of strategic translations in topological selection games and also discuss some particular cases where direct applications fail.

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1. 2025
3. GeoTop

Arithmeticity and commensurability of links in thickened surfaces — Rose Kaplan-Kelly <rkaplank@gmu.edu>

In this talk, we will consider a generalization of alternating links and their complements in thickened surfaces. In particular, a family of generalized alternating links which each correspond to a Euclidean or hyperbolic tiling and have a right-angled complete hyperbolic structure on their complement. We will determine the arithmeticity of these links and find their pairwise commensurability. This is joint work with David Futer.

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1. 2026
3. GeoGT
5. Plenaries

Arithmeticity in Hyperbolic Geometry — Nick Miller <nicholas.miller@villanova.edu>

Arithmetic manifolds are hyperbolic manifolds constructed from number theoretic data. By their very definition, they exhibit a strong connection between algebraic invariants, such as trace fields, and geometric quantities like lengths of closed geodesics. Despite this, the geometry of these manifolds remains surprisingly mysterious. Nevertheless, a guiding philosophy is that arithmetic manifolds should be the most symmetric hyperbolic manifolds and therefore exhibit geometric phenomena that are rare or absent in generic hyperbolic manifolds. In this talk, I will survey arithmetic hyperbolic manifolds, likely focusing on low dimensions, and discuss several manifestations of this philosophy, both known and conjectural. I will then discuss new work furthering this philosophy by establishing finiteness of closed arithmetic surface bundles, resolving a conjecture of Bowditch, Maclachlan, and Reid.

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1. 2025
3. GeoGT

Asymptotic dimension of graphs of arcs and curves on infinite-type surfaces — Michael Kopreski <michaelkopreski@gmail.com>

In analogy to the curve complex and its role in the geometry of mapping class groups of finite-type surfaces, a number of authors have defined graphs whose vertices are arcs or curves on a given infinite-type surface S, and on which the mapping class group Map(S) acts by isometries. We show that for a broad class of such graphs, including the grand arc graph, the omnipresent arc graph, and all others defined comparably to Masur-Minsky, the asymptotic dimension is infinite. In particular, if one could construct a graph in this class admitting a Švarc-Milnor-type action of Map(S), then Map(S) would have infinite asymptotic dimension.

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1. 2026
3. GeoGT

Asymptotically rigid mapping class groups of infinite graphs — Thomas Hill <thill@math.utah.edu>

We introduce and study asymptotically rigid mapping class groups of certain infinite graphs. We determine their finiteness properties and show that these depend on the number of ends of the underlying graph. In a special case where the graph has finitely many ends, we construct an explicit presentation for the so-called \emph{pure graph Houghton group} and investigate several of its algebraic and geometric properties. Additionally, we show that the graph Houghton groups are not commensurable with other known Houghton-type groups, namely the classical, surface, braided, handlebody, and doubled handlebody Houghton groups, demonstrating that this graph-based construction defines a genuinely new class of groups. This is joint work with Sanghoon Kwak, Brian Udall, and Jeremy West.

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1. 2025
3. GeoTop

Automorphisms of the smooth fine curve graph — Katherine Booth <k.wbooth3@gmail.com>

The smooth fine curve graph of a surface is an analogue of the fine curve graph that only contains smooth curves. It is natural to guess that the automorphism group of the smooth fine curve graph is isomorphic to the diffeomorphism group of the surface. But it has recently been shown that this is not the case. In this talk, I will give several more examples with increasingly wild behavior and give a characterization of this automorphism group for the particular case of continuously differentiable curves.

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1. 2025
3. GeoGT

Automorphisms of the sphere complex of an infinite graph — Thomas Hill <thill@math.utah.edu>

For a locally finite, connected graph $\Gamma$, let $\operatorname{Map}(\Gamma)$ denote the group of proper homotopy equivalences of $\Gamma$ up to proper homotopy. Excluding sporadic cases, we show $\operatorname{Aut}(\mathcal{S}(M_\Gamma)) \cong \operatorname{Map}(\Gamma)$, where $\mathcal{S}(M_\Gamma)$ is the sphere complex of the doubled handlebody $M_\Gamma$ associated to $\Gamma$. We also construct an exhaustion of $\mathcal{S}(M_\Gamma)$ by finite strongly rigid sets when $\Gamma$ has finite rank and finitely many rays, and an appropriate generalization otherwise. This is joint work with Michael Kopreski, Rebecca Rechkin, George Shaji, and Brian Udall.

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1. 2026
3. Applied & Data

Bayesian Sheaf Neural Networks — Layal Bou Hamdan <lbouhamd@vols.utk.edu>

Equipping graph neural networks with a convolution operation defined in terms of a cellular sheaf offers advantages for learning expressive representations of heterophilic graph data. The most flexible approach to constructing the sheaf is to learn it as part of the network as a function of the node features. However, this leaves the network potentially overly sensitive to the learned sheaf. As a counter-measure, we propose a variational approach to learning cellular sheaves within sheaf neural networks, yielding an architecture we refer to as a Bayesian sheaf neural network. As part of this work, we define a novel family of reparameterizable probability distributions on the rotation group SO(n) using the Cayley transform. We evaluate the Bayesian sheaf neural network on several graph datasets, and show that our Bayesian sheaf models achieve leading performance compared to baseline models and are less sensitive to the choice of hyperparameters under limited training data settings.

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1. 2025
3. Applied

Bestvina-Brady discrete Morse theory and Vietoris-Rips complexes — Matthew Zaremsky <mzaremsky@albany.edu>

Bestvina-Brady discrete Morse theory is a topological tool that has historically been most useful in geometric group theory. In this talk I will discuss a version of Bestvina-Brady Morse theory that is particularly conducive to understanding topological properties of Vietoris-Rips complexes of metric spaces, and has applications not only to geometric group theory, but also to applied topology and topological data analysis. In particular I will discuss a recent short proof of a result of Virk, that says the metric space $\mathbb{Z}^n$ with the usual $L^1$ metric has contractible Vietoris-Rips complexes.

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1. 2026
3. Applied & Data

Beyond Persistent Homology: Commutative algebra neural network reveals genetic origins of diseases — JunJie Wee <weejunji@msu.edu>

Topological data analysis (TDA) has achieved remarkable success in molecular sciences over the past decade. Integrating TDA with deep learning has led to advances in drug design, materials discovery, protein engineering, and COVID‑19 research. However, many TDA tools rely heavily on persistent homology, which captures only limited aspects of the underlying algebraic and geometric structures. To move beyond these limitations, we develop new mathematical foundations that bridge pure mathematics with modern AI. Recently, we introduced a multiscale commutative algebra embedding that captures intrinsic physical and chemical interactions in molecular systems for the first time. Using Persistent Stanley–Reisner Theory, we extract algebraic invariants—including facet ideals and $f$‑vectors—to construct a Commutative Algebra Neural Network (CANet). Our approach integrates deep learning with rich algebraic information, producing AI models that are mechanistic, interpretable, and highly generalizable. I will present the mathematical framework of CANet and show how these descriptors reveal structural patterns underlying genetic disease–causing mutations, pushing TDA beyond persistent homology.

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1. 2025
3. Continua

Big and large continua — Teja Kac <teja.kac1@um.si>

We generalize the notion of generalized inverse limits of inverse sequences of closed intervals with upper semicontinuous bonding functions to inverse limits of inverse sequences over directed graphs. We show that under certain conditions such inverse limits contain big/large continua.

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1. 2024
3. STDC2024-GTop

Bilinear pairings on two-dimensional cobordisms and generalizations of the Deligne category — Radmila Sazdanovic <rsazdanovic@math.ncsu.edu>

The Deligne category of symmetric groups is the additive Karoubi closure of the partition category. It is semisimple for generic values of the parameter t while producing categories of representations of the symmetric group when modded out by the ideal of negligible morphisms when t is a non-negative integer. The partition category may be interpreted, following Comes, via a particular linearization of the category of two-dimensional oriented cobordisms. The Deligne category and its semisimple quotients admit similar interpretations. This viewpoint coupled to the universal construction of two-dimensional topological theories leads to multi-parameter monoidal generalizations of the partition and the Deligne categories, one for each rational function in one variable.

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1. 2025
3. Plenary

Bounded cohomology and displacement — Francesco Fournier-Facio <ff373@cam.ac.uk>

Bounded cohomology is a functional-analytic analogue of group cohomology that is central to rigidity theory, dynamics, geometric topology, and geometric group theory. A major drawback is the failure of excision, which renders even basic computations currently out of reach. One of the few cases where non-trivial computations are possible is transformation groups with certain displacement properties that are classically used in homology and stable commutator length. I will introduce a new algebraic criterion that captures this, is satisfied in many interesting settings, and implies vanishing in all degrees and with a large class of coefficients. Based on joint work with Caterina Campagnolo, Yash Lodha, and Marco Moraschini

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1. 2026
3. GeoGT

Boundedness of homeomorphism groups of portable manifolds — Megha Bhatt <mbhat@gradcenter.cuny.edu>

A group is said to be bounded if it has finite diameter with respect to every bi-invariant metric. This is a strong rigidity property for large groups, limiting the large-scale geometry of the group and the types of geometric actions it can admit. Building on ideas of Burago, Ivanov, and Polterovich, Rybicki proved that the identity component of the homeomorphism group of a portable manifold is bounded. In this talk, I will present a simplified proof of this result by constructing a uniform normal generator for the group.

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1. 2025
3. GeoTop

Bounding the Dehn surgery number by 10/8 — Beibei Liu <bbliumath@gmail.com>

In this talk, we provide new examples of 3-manifolds with weight one fundamental group and the same integral homology as the lens space $L(2k,1)$ which are not surgery on any knot in the three sphere. Our argument uses Furuta's 10/8-theorem, and is simple and combinatorial to apply. This is joint work with Piccirillo.

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1. 2026
3. GeoTop

Brackets of disk bundles and configuration space integrals — Robin Koytcheff <robin.koytcheff@louisiana.edu>

In joint work with Xujia Chen and Sander Kupers, we construct a bracket operation on the space of framed disk bundles of fiber dimension at least 4. Kontsevich used integrals over configuration spaces to produce graph homology classes from classes of disk bundles. We prove that our bracket operation is compatible with these Kontsevich characteristic classes via the bracket operation on graph homology. Applying our bracket to Watanabe’s bundles from Borromean surgery on trivalent graphs, we obtain new disk bundles, some of which are nontrivial.

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1. 2026
3. Continua

Bridging Closed Relations and Shift Systems: A Trichotomy of CR-Dynamical Properties — Judy Kennedy <kennedy9905@gmail.com>

Suppose $X$ is a compact metric space and $F$ is a closed relation on $X$. For a classical dynamical property $\mathcal{P}$, we introduce a natural trichotomy of CR-dynamical properties associated with a closed relation $F$: $CR-\mathcal{P}, CR-post\mathcal{P}, CR-pre\mathcal{P}.$ These three notions are designed so that $(X,F)$ satisfies $CR-\mathcal{P}$ exactly when the shift system $(X_F^+,\sigma_F^+)$ satisfies $\mathcal{P}$; whenever the shift system has property $\mathcal{P}$, the relation $F$ has $CR-post\mathcal{P}$; and whenever $F$ has $CR-pre\mathcal{P}$. the shift system has $\mathcal{P}$. We apply this to minimality, dense-orbit transitivity, and transitivity, establishing precise equivalences in each case. Our examples show that, in general, the three CR-versions of a property form a strict hierarchy, with none of the implications reversible without additional assumptions. This is joint work with Iztok Banic, Matevz Crepnjak, Goran Erceg, Ivan Jelic.

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1. 2025
3. Continua

Building $\mathbb R$-trees — Curtis Kent <curtkent@mathematics.byu.edu>

We discuss a natural way to build actions of the fundamental group of one-dimensional spaces (which might not have universal covers) on $\mathbb R$-trees. We will then discuss how the tools from the study of one-dimensional spaces can be adapted to more general spaces to build actions of locally free groups on $\mathbb R$-trees with prescribed orbit spaces.

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1. 2025
3. Plenary

Building Connections Between Topological Spaces With Games — Jared Holshouser <jholshouser1321@gmail.com>

We will examine three threads of inquiry in topology: convergence/compactness properties, spaces built out of other spaces (i.e. the space of real-valued continuous functions or the hyperspace of closed sets), and topological games. When a space is built out of another space, we can often translate the topological information from the first space to the second. For instance, open covers of the space can produce clustering sequences of real-valued functions. This topological information can be encoded through strategies in certain topological games. Working with Chris Caruvana and Steven Clontz, we have developed techniques for tying all of these threads together and have proven a wide array of connections between spaces and common constructions on those spaces. The general theory will be discussed and specific examples will be displayed.

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1. 2024
3. STDC2024-CT

Buried points of plane continua — David Lipham <dlipham@ccga.edu>

Sets on the boundary of a complementary component of a continuum in the plane have been of interest since the early 1920’s. Curry and Mayer defined the buried points of a plane continuum to be the points in the continuum which were not on the boundary of any complementary component. Motivated by their investigations of Julia sets, they asked what happens if the set of buried points is totally disconnected and non-empty. Curry, Mayer and Tymchatyn showed that in that case the continuum is Suslinian, i.e. it does not contain an uncountable collection of non-degenerate pairwise disjoint subcontinua. In an answer to a question of Curry et al, van Mill and Tuncali constructed a plane continuum whose buried point set was totally disconnected, non-empty and one-dimensional at each point of a countably infinite set. In this talk I will present proof that the van Mill-Tuncali example was the best possible in the sense that whenever the buried set is totally disconnected, it is one-dimensional at each of at most countably many points. I will also discuss a few related problems about plane continua and endpoints of dendroids. This talk is based on joint work with Jan van Mill, Murat Tuncali, Ed Tymchatyn, and Kirsten Valkenburg.

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1. 2026
3. General & ST

C-Spaces and Inverse Systems — Leonard Rubin <lrubin@ou.edu>

The concept of a C-space was introduced in 1978 by D. Addis and J. Gresham in order to provide a new class of spaces in dimension theory. We present an internal characterization for an inverse system $\mathbf{X}$ of compact Hausdorff spaces and maps that shows when its limit will be a C-space. This is precisely when $\mathbf{X}$ is a ``C-system,'' whose definition will be given in this presentation. We use this characterization to construct a C-system $\mathbf{Y}$ so that its inverse limit is a weakly infinite-dimensional, strongly countable-dimensional, metrizable compactum that is a C-space. Finally we introduce a new notion into topological game theory called a game-theoretic C-system.

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1. 2026
3. Dynamics

CANCELED -- Dynamics Arising from Group Actions on Primitive Elements — Pratyush Mishra <mishrap@wfu.edu>

There has been some substantial work on studying the structure of a group by analyzing the behavior of primitive elements, sometimes under strong assumptions by work of Platonov, Potapchik, Shpilrain and many others. We formulate and study a conjecture of Platonov and Potapchik for general group actions via analyzing the dynamics of primitive elements for a given action. Such studies led us to further afield to produce results that combines computational, dynamical, geometric, and purely algebraic viewpoints.

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1. 2025
3. GeoGT

CAT(0) geometry of complex curve complements and families — Kejia Zhu <kzhumath@gmail.com>

Motivated by the question of whether braid groups are CAT(0), we investigate the CAT(0) behavior of fundamental groups of plane curve complements and certain universal families. If $C$ is the branch locus of a generic projection of a smooth, complete intersection surface to $\mathbb{P}^2$, we show that $\pi_1(\mathbb{P}^2\setminus C)$ is CAT(0). In the other direction, we prove that the fundamental group of the universal family associated with the singularities of type $E_6$, $E_7$, and $E_8$ is not CAT(0). Other examples, both positive and negative, are discussed, with a special emphasis on rational 3-cuspidal curves. This is joint work with C. Bregman and A. Libgober.

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1. 2026
3. Dynamics

Calculating the Malaugh Operations — Forrest Hilton <fmhilton@uab.edu>

Connected Julia sets of a polynomial generally correspond to laminations, sets of chords of the unit disc that reflect the dynamics of the Julia set. If the circle is measured in revolutions and the polynomials studied are of degree $d$, then the dynamics on the lamination are given by the covering map $\sigma_d(t) := td \pmod 1$ where chords are mapped by their end points. Every lamination has at least one laminational invariant set, which is loosely an invariant complementary component of the lamination. That set has a significant impact on the shape of the Julia set. James Malaugh showed how to topologically transform a laminational invariant set in one degree into one in another degree, but he provided no way to execute these operations concretely. In this talk, we show how to calculate those operations.

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1. 2024
3. STDC2024-CT

Cantor Sets and Topological Entropy for Set-valued Functions on Countable Domains — James Kelly <james.kelly@cnu.edu>

We characterize when an inverse limit of a set-valued function is a Cantor set. Given a set-valued function $F\colon X\to 2^X$, we define the set $D(F)=\bigcap_{n=1}^\infty F^n(X)$. It is known that $\varprojlim F=\varprojlim F|_{D(F)}$, so we only need to consider the $F|_{D(F)}$. When $D(F)$ is finite, $\varprojlim F$ is a shift of finite type, so we focus on the case where $D(F)$ is infinite, and we give a characterization for $\varprojlim F$ to be a Cantor set for this context. We go on to examine the entropy of a set-valued function on a countable domain and how that relates to the inverse limit being a Cantor set. This includes joint work with L. Alvin and S. Greenwood.

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1. 2025
3. Continua

Cantor fences in plane continua — David Lipham <dlipham@ccga.edu>

David Bellamy constructed a surprising example of a smooth dendroid in the plane with a connected set of endpoints. In this talk, I will present the new result that any planable smooth dendroid with $1$-dimensional endpoint set must contain a Cantor fence (a copy of $2^\omega \times [0,1]$) or a Bellamy dendroid (a smooth dendroid whose endpoint set is connected). This is false outside the plane, and it is unknown whether every Bellamy dendroid contains a Cantor fence. More generally, a continuum is said to be non-Suslinian if it contains an uncountable family of pairwise disjoint, non-degenerate subcontinua. I will discuss some open problems about this property in Julia sets and other plane continua with rich dynamical structures. Among these are: If a plane continuum admits a mixing homeomorphism, then is it non-Suslinian? Is the Sierpiński carpet the only locally connected plane continuum that admits a mixing homeomorphism?

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1. 2025
3. GeoGT

Centers of Artin Groups Defined on Cones — MurphyKate Montee <mmontee@carleton.edu>

The Center Conjecture for Artin groups proposes that the center of any infinite type Artin group is trivial. This is known to hold for a wide class of Artin groups, but is not known in general. In this talk we will prove that the Center Conjecture passes to the Artin groups whose defining graphs are cones, if the conjecture holds for the Artin group defined on the set of the cone points. In particular, it holds for every Artin group whose defining graph has exactly one cone point. This is joint work with Kasia Jankiewicz.

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1. 2025
3. Plenary

Chaotic almost minimal actions — Van Cyr <van.cyr@bucknell.edu>

The joint action of $x\mapsto2x$ (mod 1) and $x\mapsto3x$ (mod 1) has a number of remarkable properties. Among them is that ever joint orbit is either finite or dense. Of course any minimal system has that property, but the x2,x3 system is special because it has a dense set of finite orbits that intermingle with dense orbits. In joint work with B. Kra and S. Schmieding, we abstract this property to what we call a chaotic almost minimal (CAM) system. I this talk I will discuss some properties of CAM systems, showing their similarities to and differences from the x2,x3 system.

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1. 2025
3. GeoGT

Characterizations of Stability via Morse Limit Sets — Jacob Garcia <jgarcia46@smith.edu>

An important example of Kleinian groups are the convex cocompact groups: every infinite order element of these groups is a loxodromic, and these groups are exactly the ones which admit Kleinian manifolds. A well known fact of convex cocompact groups is that they can be characterized exactly as the groups whose limit sets, on the visual boundary, are completely conical, or equivalently, completely horospherical. Convex cocompactness has been studied in the context of many non-hyperbolic spaces, such as mapping class groups, and has recently been generalized to the notion of subgroup stability. By using an analog of the visual boundary called the Morse boundary, a quasi-isometry invariant which "sees" hyperbolic directions for non-hyperbolic spaces, we show that subgroup stability is exactly classified by limit set conditions on the Morse Boundary which are analogous to the limit set conditions from the convex cocompact setting.

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1. 2025
3. Set-Theoretic

Characterizing Strong Infinite-Dimension, Weak Infinite-Dimension, and Dimension in Inverse Systems — Leonard Rubin <lrubin@ou.edu>

We present internal characterizations for an inverse system of compact Hausdorff spaces that show when its limit will be strongly infinite-dimensional, weakly infinite-dimensional, or have its dimension $n\in\mathbb{N}_{\geq0}$. Our main tool involves lifting the notion of an essential family into a parallel concept for inverse systems. In our presentation we plan to review the definitions of essential family, strong and weak infinite-dimensionality, finite dimensionality, and inverse systems. After doing that, we will state our main results but will not go into any proofs. The published paper with all details appears in *Rad Hazu. Matematičke Znanosti*, v. 29=564 (2025): 299-318.

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1. 2026
3. Continua

Characterizing local connectedness by non-cut sets in continua — Jorge Vega <vegacevedofc@ciencias.unam.mx>

In this talk we show that for a continuum X, the following conditions are equivalent: (i) the continuum X is locally connected, (ii) each non-cut set of X has arbitrarily small open neighborhoods whose complements are connected, (iii) each non-cut set of X has continuum-wise connected complement, (iv) the continuum X is aposyndetic with respect to each of its non-cut sets, and (v) the continuum X is aposyndetic with respect to each of its nonempty closed sets. Co-authors: Raúl Escobedo and Eduardo García-Muñoz.

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1. 2025
3. Applied

Circle Bundles For Data — Brad Turow <turow.b@northeastern.edu>

We introduce the notion of a discrete approximate circle bundle, as well as theory and algorithms to estimate characteristic classes. We apply these tools to study a benchmark optical flow dataset, where we confirm the toroidal model proposed by Adams et al. and discover larger spaces in other density regimes.

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1. 2025
3. Dynamics

Classification complexity of chaotic systems — Benjamin Vejnar <benvej@gmail.com>

The aim of this talk is first to briefly describe a natural way of measuring simplicity/complexity of classification problems by using Invariant Descriptive Set Theory and then to discuss recent applications in the context of topological dynamics. We mainly deal with the classification of transitive systems on the interval, on the Cantor set and on the Hilbert cube with respect to the topological conjugacy relation. At the end, we provide some attempts to identify the complexity of classification of minimal systems.

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1. 2025
3. GeoTop

Classifying holomorphic maps between spaces of polynomials — Peter Huxford <pjhuxford@uchicago.edu>

Let $\mathrm{Poly}_n\mathbb{C}$ be the space of monic, squarefree, degree $n$ polynomials in one variable over $\mathbb{C}$. Ferrari's solution to the quartic equation gives rise to a holomorphic map $R\colon\mathrm{Poly}_4\mathbb{C}\to\mathrm{Poly}_3\mathbb{C}$. We show that every holomorphic map $\mathrm{Poly}_n\mathbb{C}\to\mathrm{Poly}_m\mathbb{C}$ for $m\leq n$ is equivalent in a certain sense to a constant map, the identity map, or Ferrari's map $R$. This is joint work with Jeroen Schillewaert.

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1. 2025
3. Set-Theoretic

Closed copies of $\mathbb{N}$ in $\mathbb{R}^{\omega_1}$ — KP Hart <k.p.hart@tudelft.nl>

We investigate the existence of closed copies of the discrete space $\mathbb{N}$ of natural numbers in powers of the real line, in particular its $\omega_1$-power, that are not $C^\star$-embedded, or that are $C^\star$-embedded but not $C$-embedded. In the case of non-$C^\star$-embedding we find a whole family of new examples, based on Aronszajn trees and lines, and a combinatorial translation of the existence of such copies. In the case of $C^\star$- but not $C$-embedding we complement an earlier consistency result but showing in consistent with any desired cardinal arithmetic that $\mathbb{R}^{\omega_1}$ contains a closed copy of $\mathbb{N}$ that is $C^\star$- but not $C$-embedded.

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1. 2024
3. STDC2024-STT

Clustering Properties of Convex-Valued Upper Semicontinuous (CUSCO) Functions — Jared Holshouser <jholshou@norwich.edu>

We establish relationships between various topological selection games involving the space of minimal cusco maps into the real line and the underlying domain of those maps. These connections occur across different topologies, including the topology of pointwise convergence and the topology of uniform convergence on compacta. Full and limited-information strategies are investigated. The primary games we consider are Rothberger-like games, generalized point-open games, strong fan-tightness games, Tkachuk's closed discrete selection game, and Gruenhage's \(W\)-games.

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1. 2024
3. STDC2024-GTop

Coarse bottlenecking and coarse skeletons of graphs — Michael Bruner <mb225527@umconnect.umt.edu>

We introduce the concept of (coarse) n-point bottlenecking in graphs and study the coarse geometry of graphs in terms of bottlenecking in their coarse skeletons. We examine the connections of bottlenecking with coarse planarity. This is joint work with Atish Mitra and Heidi Steiger.

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1. 2026
3. GeoTop

Cohomology of Handlebody Torelli Groups — Annie Holden <aholden2@nd.edu>

We begin by introducing the Torelli subgroup of the mapping class group of a surface and outlining known results about its low-dimensional cohomology. We then present recent work extending these results to a Torelli subgroup of the mapping class group of a handlebody.

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1. 2024
3. STDC2024-GGT

Combinations of parabolically geometrically finite groups — Brian Udall <bu3@rice.edu>

We consider the collection of parabolically geometrically finite (PGF) subgroups of mapping class groups, which were defined by Dowdall-Durham-Leininger-Sisto. These are generalizations of convex cocompact groups, and the class of PGF groups contains all finitely generated Veech groups as well as certain free products of multitwist groups. We will see some basic motivations and properties of these groups, as well as discuss a combination theorem for PGF groups generalizing the combination theorem of Leininger-Reid for Veech groups. This allows one to build many more examples of PGF groups, including Leininger-Reid surface groups.

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1. 2026
3. General & ST

Combinatorial covering properties in countable and uncountable contexts — Michał Pawlikowski <michal-pawlikowski4@wp.pl>

Combinatorial covering properties as Rothberger’s, Hurewicz’s and Menger’s are procedures for generating a cover of a given topological space from a sequence of covers of this space. We present the most celebrated such properties together with the most important examples in a classical countable case. We also explore how these notions and examples extend to the uncountable context, where the initial sequence of covers has length $\kappa$ for some uncountable cardinal $\kappa$. In this generalized setting, we replace the Cantor space $2^\omega$ and the classical Baire space $\omega^\omega$ with the $\kappa$-Cantor space $2^\kappa$ and the $\kappa$-Baire space $\kappa^\kappa$, respectively. This is joint work with Piotr Szewczak and Lyubomyr Zdomskyy.

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1. 2026
3. General & ST

Comparative Topology of the Cantor Fan and the Cantor's Teepee — Manuel M. Aguilera <alex.martinez13@upr.edu>

The *Cantor's Fan* is a planar topological space in $\mathbb{R}^2$, constructed from the Cantor set in $[0,1]$ and inspired by the *Cantor's Teepee* introduced in 1921 by Bronisław Knaster and Kazimierz Kuratowski. In this paper, we determine which properties of the Cantor's Teepee persist in the Cantor's Fan; we restate the main properties in contemporary language, provide complete formal proofs, and include illustrative figures.

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1. 2025
3. Dynamics

Completely invariant sets and Lorenz maps — Piotr Oprocha <piotr.oprocha@osu.cz>

In this talk we will discuss relations between completely invariant sets and renormalizations of expanding Lorenz maps, that is maps $f\colon [0,1]\to [0,1]$ satisfying the following three conditions: 1. there is a critical point $c\in (0,1)$ such that $f$ is continuous and strictly increasing on $[0,c)$ and $(c,1]$; 2. $\lim_{x\to c^{-}}f(x)=1$ and $\lim_{x\to c^{+}}f(x)=0$; 3. $f$ is differentiable for all points not belonging to a finite set $F\subseteq [0,1]$ and $\inf_{x\not\in F} f'(x)>1$; with special emphasis on piecewise linear case. The talk is based on joint works with L. Cholewa.

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1. 2024
3. STDC2024-GTop

Complex Hyperbolic Gromov-Thurston Metrics — Barry Minemyer <bminemyer@commonwealthu.edu>

In 1987 Gromov and Thurston developed the first Riemannian manifolds that are not homotopy equivalent to a hyperbolic manifold but admit a Riemannian metric that is ϵ-pinched for any given ϵ>0. The manifolds that they construct are branched covers of hyperbolic manifolds, and to construct the metric they perform a sort of "geometric surgery" about the ramification locus. In 2022 Stover and Toledo proved the existence of similar branched cover manifolds built out of complex hyperbolic manifolds, and via a result of Zheng these manifolds admit a negatively curved Kahler metric. In this talk we will discuss how to construct a (not Kahler) Riemanain metric on these Stover-Toledo manifolds which is ϵ-close to being 1/4-pinched for any prescribed ϵ>0. These provide the first known examples of Kahler manifolds that are not homotopy equivalent to a complex hyperbolic manifold but admit a Riemannian metric that is ϵ-close to being 1/4-pinched.

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1. 2024
3. STDC2024-GTop

Computability of Immersions — Daniel Epelbaum <daniel@math.ucsb.edu>

Suppose we are handed a map of smooth manifolds and would like to know if it is homotopic to an immersion. In general this problem is undecidable, indeed even immersibility of an arbitrary manifold into $\mathbb{R}^n$ is undecidable. In this talk we will see how to use techniques from rational homotopy theory, and the h-principle of Hirsch and Smale to provide an algorithm for this problem whenever the codimension of the manifolds is odd.

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1. 2026
3. Dynamics
5. Plenaries

Computable Markov Partitions — Christian Wolf <cwolf@math.msstate.edu>

Computability in dynamical systems is a relatively young field that has attracted significant attention in recent years. One of its central questions is whether dynamically relevant objects can be algorithmically represented by a Turing machine. While this question has been extensively studied in symbolic dynamics, where computability results are known for various thermodynamical quantities such as entropy, pressure, equilibrium states and zero-temperature measures, a corresponding general theory for broader classes of topological and smooth dynamical systems is lacking. In this talk, we present an approach to bridging this gap by introducing the concept of computable Markov partitions. This framework allows us to establish far-reaching computability results for several classes of topological and smooth dynamical systems. The results presented in this talk are joint work with Michael Burr and Tamara Kucherenko.

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1. 2025
3. Applied

Computing the Bottleneck Distance from Every Direction — Elena Wang <wangx249@msu.edu>

One of the most common distances used to compare two persistence diagrams is the bottleneck distance. When the persistence diagrams of a shape in $\mathbb{R}^d$ are computed from every direction in $\mathbb{S}^{d-1}$, we obtain the persistent homology transform (PHT). An efficient way of comparing two PHTs remains unexplored. In this work, we develop a new kinetic data structure to compute the bottleneck distance between two PHTs obtained from shapes in $\mathbb{R}^2$ from every direction. We provide the events and necessary updates to maintain the distance between the diagrams using this structure. Our resulting algorithm runs in $O(n^2\log^2n)$. This is compared to the naive algorithm where $d_B$ is computed at a finite number of smartly chosen directions, which is $O(n^{7/2}\log n)$ complex. It is important to note that our algorithm provides an exact distance in every direction, while the latter is an approximation. Furthermore, we show that this data structure is not limited to the directional transform setting since the techniques apply to more general vineyard structures.

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1. 2025
3. Applied

Congruence of Planar Curves and the Signature Quiver — Irina Kogan <iakogan@ncsu.edu>

Deciding whether or not two curves are congruent under rotations and translations is a classical, but surprisingly subtle problem. In addition to its theoretical interest, this problem has numerous applications in computer vision and image processing, automated assembly,  signal processing, and more. To address this, as well as more general congruence problems, the signature curve parameterized by differential invariants was introduced by Calabi, Olver, Shakiban, Tannenbaum, and Haker (1998). While congruent curves have identical signatures, the converse is not true, as shown in Muso and Nicolodi (2009).  In a joint work with Eric Geiger (2021), we presented a mechanism for constructing non-congruent, non-degenerate curves with identical signatures. We also introduced a notion of the signature quiver and used it to formulate a congruence criterion for non-degenerate curves with non-simple signatures.

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1. 2026
3. GeoGT

Conjugator length in finitely presented groups — Francis Wagner <fw294@cornell.edu>

The conjugator length function of a finitely generated group is the function f so that f(n) is the minimal upper bound on the length of a word realizing the conjugacy of two words of length at most n. This function provides a measure for the complexity of a direct approach to the Conjugacy Problem for the finitely generated group. I will discuss what functions can be realized as the conjugator length function of a finitely presented group and the connection of this function with other important invariants of finitely presented groups.

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1. 2025
3. GeoGT

Connected components in Morse boundaries of right-angled Coxeter groups — Annette Karrer <annette.u.karrer@gmail.com>

Every finitely generated group G has an associated topological space, called a Morse boundary, that captures the hyperbolic-like behavior of G at infinity. It was introduced by Cordes generalizing the contracting boundary invented by Charney--Sultan. In this talk, we study subgroups arising from connected components in Morse boundaries of right-angled Coxeter groups and of such that are quasi-isometric to right-angled Coxeter groups. This talk is based on two projects. One is joint work with Bobby Miraftab and Stefanie Zbinden. The other one is joint work in progress with Matthew Cordes and Kim Ruane.

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1. 2025
3. GeoTop

Connectivity in the space of pointed hyperbolic 3-manifolds — Matthew Zevenbergen <zevenber@bc.edu>

I will show that the space of pointed infinite volume hyperbolic 3-manifolds is connected but not path connected. This space is equipped with the geometric topology, in which two pointed manifolds are close if they are almost isometric on large neighborhoods of their basepoints. The proof of connectivity will be an application of the density theorem for Kleinian groups. I will then use a combination of results on representations of Kleinian groups and Chabauty spaces of subgroups to construct an infinite family of path components of this space.

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1. 2026
3. GeoGT

Connectivity of Gromov boundary of the maximized hyperbolic space of right-angled Coxeter groups — Zhihao Mu <zmu@gradcenter.cuny.edu>

The maximized hyperbolic space of a right-angled Coxeter group (RACG) can be obtained from its Davis complex by coning off all standard flats. This space serves as the top-level hyperbolic space in the hierarchically hyperbolic structure of the RACG, analogous to the curve graph for mapping class groups. We provide a necessary and sufficient condition on the defining graph under which the Gromov boundary of the maximized hyperbolic space is connected.

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1. 2024
3. STDC2024-Plenary

Continuum Dynamics — Van Nall <vnall@richmond.edu>

Many of us remember when the Spring Topology Conference became the the Spring Topology and Dynamics conference in part because continua theorists were finding so many things they wanted to work on in dynamics. Classical Interval Dynamics is now a mature field with hundreds of articles and many books. Years ago continua theorists with considerable inspiration from Devaney’s accessible book began extending theorems in interval dynamics like the Sarkovski theorem to chainable continua, that is continua that are the inverse limit of interval functions. A favorite tool of continua theorists, inverse limits, have also been used in dynamical systems since whatever one might call the beginning. Inspired by Ethan Akin our group has been constructing continua and functions at the same time that have a variety of dynamical properties using what we call Mahavier products, also known as an inverse limit with a set valued function. Akin would probably call what we are doing the dynamics of closed relations. The dynamics are those of shift maps. In other words we extend from the now classic topic of dynamics of shift maps on inverse limits with a single bonding map to continua that cannot be expressed as an inverse limit with a single continuous function on a simpler space like an arc or a tree or a circle, but can be expressed as an inverse limit with a single closed relation. Specifically in this talk we look at various ways to express the Cantor fan and the Lelek fan as a Mahavier products . We obtain transitive homeomorphisms, mixing homeomorphisms, with and without a dense set of periodic orbits and with zero or positive entropy. This is joint work with Iztok Banic, Judy Kennnedy, Chris Mouron, and Goran Erceg.

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1. 2024
3. STDC2024-GTop

Corks for exotic diffeomorphisms — Terrin Warren <terrin@uga.edu>

In dimension 4, there exist simply-connected manifolds which are homeomorphic but not diffeomorphic; the difference between the distinct smooth structures can be localized using corks. Similarly, there exist diffeomorphisms of simply-connected 4-manifolds which are topologically but not smoothly isotopic. In this talk, I will discuss some preliminary results towards an analogous localization of this phenomena using corks for diffeomorphisms. This project is joint work with Slava Krushkal, Anubhav Mukherjee, and Mark Powell.

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1. 2025
3. Continua

Coselectibility regarding symmetric products — Patricia Pellicer-Covarrubias <paty@ciencias.unam.mx>

In this talk we consider a concept which is the dual to the concept of a selectible space, namely, a $\Lambda$-coselection space ($\Lambda$ may be any given hyperspace of a space $X$). We consider this concept when $\Lambda$ is the $n$th symmetric product $F_n(X)$. We present sufficient conditions for a continuum to be either an $F_2(X)$-coselection space or an $F_3(X)$-coselection space.

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1. 2026
3. Continua

Coselections on symmetric products — Veronica Martinez-de-la-Vega <vmvm@im.unam.mx>

Given metric continuum X we consider the n-th symmetric product, Fn(X) defined as the hyperspace of nonempty subsets with at most n elements. The continuum X is an Fn-coselection space (n≥2) if for each ε > 0, there exists a mapping gε : X →Fn(X) \F1(X) such that x ∈ gε(x) and diameter(gε(x)) <ε for each x∈X. Answering two questions by Patricia Pellicer-Covarrubias, in this talk we present two significant examples: (a) we prove that a Cook continuum is not an Fn-coselection space for any n ≥2, and (b) there exist two no homeomorphic compactifications of the ray [0,∞) with remainder a simple closed curve which are F2-coselection spaces.

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1. 2026
3. General & ST

Countable dense homogeneity in large products of Polish spaces — Andrea Medini <andrea.medini@tuwien.ac.at>

We will discuss joint work with Juris Steprāns concerning the countable dense homogeneity of products of Polish spaces, with a focus on uncountable products. Our main result states that a product of fewer than $\mathfrak{p}$ Polish spaces is countable dense homogeneous if the following conditions hold: (1) Each factor is strongly locally homogeneous, (2) Each factor is strongly $n$-homogeneous for every $n\in\omega$, (3) Every countable subset of the product can be brought in general position. For example, using the above theorem, one can show that $2^\kappa$, $\omega^\kappa$, $\mathbb{R}^\kappa$ and $[0,1]^\kappa$ are countable dense homogeneous for every infinite $\kappa<\mathfrak{p}$ (these results are due to Steprāns and Zhou, except for the one concerning $\omega^\kappa$). In fact, as a new application, we showed that every product of fewer than $\mathfrak{p}$ connected manifolds with boundary is countable dense homogeneous, provided that none or infinitely many of the boundaries are non-empty. This generalizes a result of Yang.

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1. 2024
3. STDC2024-DS

Counting Preimage Laminations — Forrest Hilton <fmhilton@uab.edu>

A lamination L is a closed set of chords of the unit disk so that no two chords intersect in the open disk. A lamination is d-invariant under the degree d covering map $\sigma_d:S\to S$ of the unit circle if it is forward invariant (for any chord $ab$ in L the chord $\sigma(a)\sigma(b)$ is also in $L$). In this talk we will discuss properties of d-invariant laminations that all contain a given forward invariant subset $P$ of chords (for example a given periodic chord). We count possible preimage laminations for n steps. i.e. the number of laminations that have a particular $P$ as their $\sigma_d^n$ image. In contrast to most laminations research, we do not specify critical cords (i.e., chords $ab$ so that $\sigma(a)=\sigma(b)$). We define what laminations should be included in our count. Particularly, we exclude critical and degenerate leaves from our laminations because they make the count immediately infinite. We also insist that each of the counted laminations are maximal, to avoid confluence, and have adequately many chords with the same image. This class of laminations has the added advantage that they are all realized by complex polynomials of degree d, giving us some hope that we can use our combinatorial model to assemble a model of polynomial parameter space. It is clear in the degree 2 case that the laminations which we generate in our count correspond to limbs outside the molecule of the connectedness locus, with exactly one exception for each n.

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1. 2024
3. STDC2024-Semi

Counting in a mapping class group orbit of triangulations — Tarik Aougab <taougab@haverford.edu>

We introduce the notion of a geodesic current with corners, a generalization of a geodesic current in which there are singularities (the ``corners'') at which invariance under the geodesic flow can be violated. Recall that the set of closed geodesics is, in the appropriate sense, dense in the space of geodesic currents; the motivation behind currents with corners is to construct a space in which graphs on S play the role of closed curves. Another fruitful perspective is that geodesic currents reside "at infinity'' in the space of currents with corners, in the sense that their (non-existent) corners have been pushed out to infinity. As an application, we count triangulations in a mapping class group orbit with respect to length, and we obtain asymptotics that parallel results of Mirzakhani, Erlandsson-Souto, and Rafi-Souto for curves. This represents joint work with Jayadev Athreya.

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1. 2026
3. General & ST

Covers, Stars, and Points, Oh My! — Jocelyn Bell <bell@hws.edu>

The proximal game, introduced in 2014, is a two-player infinite game played in a uniform space. It relies on the uniform structure in an inherent way: the first player chooses elements of the uniformity while the other selects points. A winning strategy for the first player implies the space has certain additional topological properties, which as such are independent of the particular uniform structure with which the game was played. So, is the uniform structure really necessary? I will discuss some recent progress in divorcing the proximal game from its reliance on a uniform structure, resulting in the creation of purely topological "point-star" games.

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1. 2026
3. GeoGT

Criterion for Finiteness of BMS Measure — Rou (Vicky) Wen <rwen5@wisc.edu>

In many useful settings, having a finite Bowen-Margulis-Sullivan (BMS) measure on a flow space allows people to normalize the BMS measure into a probability measure and facilitates powerful ergodic theoretic tools. This often leads to asymptotic estimates for counting orbital points and establishing equidistribution results. Hence, it is important to know when a dynamical system admits a finite BMS measure. In this talk, I will first introduce what is a BMS measure, and then state a criterion that detects the finiteness of BMS measure on a flow space associated to a discrete subgroup of higher rank semi-simple Lie group.

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1. 2026
3. Dynamics

Critical Orbit Relation Curves and Degenerations — Jan Kiwi <jkiwi@uc.cl>

Critical orbit relation curves of rational maps acting on the Riemann sphere are dynamically natural complex one-dimensional slices of moduli space. The aim of the talk is to review some known and new results (work in progress with Caroline Davis and Alex Kapiamba) about degenerations along these curves.

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1. 2025
3. Dynamics

Cubic polynomials and laminations — Nikita Selinger <nikita.selinger@gmail.com>

I will review the notion of laminations as introduced by W. Thurston and explain how laminations can be used to study parameter spaces of polynomials.

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1. 2026
3. Applied & Data

Cubical Persistent Homology of Hyperspectral Retinal Images — Desiree Paczay <dapaczay629@my.nipissingu.ca>

Topological Data Analysis (TDA) has emerged as a powerful framework for extracting meaningful structure from complex, high-dimensional data. In particular, persistent homology is widely used for its ability to quantify multiscale topological features while exhibiting robustness to noise. In this work, we apply persistent homology to hyperspectral images of retinal tissue in order to further investigate Spaceflight Associated Neuro-ocular Syndrome. Hyperspectral imaging captures vast spectral information, but its high dimensionality poses challenges for analysis and interpretation. For each spectral band, we treat pixel intensity as a scalar function and construct a sublevel set filtration of cubical complexes, which provide a natural cell-complex structure for image data. From the resulting persistence diagrams, we derive summary statistics including total persistence and feature counts in dimension 0. Preliminary results indicate that these persistence-based summaries distinguish between pigmented and albino retinal tissue. Ongoing work focuses on further interpretation of the detected topological structure and the implementation of additional persistence-based methods.

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1. 2024
3. STDC2024-STT

Cylinders as isoperimetric limits of Cayley graphs? — Joseph Briggs <jgb0059@auburn.edu>

Barber and Erde asked the following question: if $B$ generates $\mathbb{Z}^n$ as an additive group, then must the extremal sets for the isoperimetric inequality on the Cayley graph $(\mathbb{Z}^n,B)$ form a nested family? We answer this question negatively for both the vertex- and edge-isoperimetric inequalities, already when $n=1$. The key is to show that the structure of the cylinder $\mathbb{Z}\times(\mathbb{Z}/k\mathbb{Z})$ can be mimicked in certain Cayley graphs on $\Z$, leading to a phase transition. Based on joint work with Chris Wells.

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1. 2025
3. Plenary

Data Driven Homological Approaches for Detecting Changes in Dynamical System — Liz Munch <muncheli@msu.edu>

Persistent homology, the flagship method from the field of Topological Data Analysis, is a powerful tool for measuring shape and structure of data. In this talk, we explore methods for using this tool to detect homological changes in the underlying structure of dynamical systems.  As a first step, we can simplify a vineyard of persistence diagrams into a CROCKER plot to provide visual representations of qualitative shifts in the structure of examples such as the Lorenz and Rossler systems. We can also construct a "homological bifurcation plot" to enable the identification of qualitative shifts, namely P-type (phenomenological) bifurcations, within stochastic dynamical systems, defined by structural changes in the probability density functions (PDF) of the state variables. The talk will explore the successful application of this method to stochastic oscillators, showcasing its effectiveness in algorithmically detecting P-bifurcations. This talk is based on joint work with many collaborators, including Firas Khasawneh, İsmail Güzel, Sunia Tanweer, Sarah Tymochko, Audun Myers, and David Muñoz.

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1. 2024
3. STDC2024-GGT

Deciding when two curves are of the same type — Hanh Vo <thihanhv@asu.edu>

Let S be a compact orientable connected surface with negative Euler characteristic. Two closed curves on S are of the same type if their corresponding free homotopy classes differ by a mapping class of S. Given two closed curves on S, we propose an algorithm to detect whether they are of the same type or not. This is joint work with Juan Souto.

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1. 2026
3. Continua

Degree of homogeneity on some spaces — Alicia Santiago Santos <alicia@mixteco.utm.mx>

Given a positive integer n, a non-empty topological space is said to be 1/n-homogeneous provided there are exactly n orbits for the action of the group of homeomorphisms of the space onto itself, in which case we say that the degree of homogeneity of X, is n. In this talk, I will present our recent contributions to this lines of research.

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1. 2025
3. GeoTop

Dehn filling in semisimple Lie groups — Theodore Weisman <tjwei@umich.edu>

Thurston's Hyperbolic Dehn Filling Theorem is a seminal result in the theory of 3-manifolds. Given a single noncompact finite-volume hyperbolic 3-manifold M, the theorem provides a construction for a countably infinite family of closed hyperbolic 3-manifolds converging to M in a geometric sense. The theorem is a major source of examples of 3-manifolds admitting hyperbolic structures, and closely connects the topology of a 3-manifold to the analysis of the character variety of its fundamental group in PSL(2, C). In this talk, we discuss some analogs and generalizations of Thurston's theorem in the context of general (arbitrary-rank) semisimple Lie groups. We will explain how our results provide a way to construct new examples of Anosov and relatively Anosov representations into higher-rank Lie groups; time permitting, we will also discuss upcoming joint work with Jeff Danciger, which applies our results to construct exotic new examples of convex cocompact and geometrically finite groups acting on complex hyperbolic 3-space.

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1. 2025
3. GeoTop

Dehn twist and smooth mapping class group of 4-manifolds   — Anubhav Mukherjee <anubhavmaths@princeton.edu>

In this talk, I will present recent advancements in the study of smooth mapping class groups of 4-manifolds. Our work focuses on diffeomorphisms arising from Dehn twists along embedded 3-manifolds and their interaction with Seiberg-Witten theory. These investigations have led to intriguing applications across several areas, including symplectic geometry (related to Torelli symplectomorphisms), algebraic geometry (concerning the monodromy of singularities), and low-dimensional topology (involving exotic diffeomorphisms). This is collaborative work with Hokuto Konno, Jianfeng Lin, and Juan Munoz-Echaniz.

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1. 2024
3. STDC2024-CT

Dendrites and path-homotopies — Curtis Kent <curtkent@mathematics.byu.edu>

In a one-dimensional space, any nullhomotopic loop factors through a dendrite. Analogously, we can say that two paths $f$ and $g$, with the same endpoints, are equivalent if $f*\overline g$ factors through a loop in a dendrite, where $\overline g$ is the path $g$ traversed backwards. We will show that the equivalence relation generated by this relation is the same as the path-homotopy and discuss its consequences. This is joint work with Greg Conner, Jeremy Brazas, and Paul Fabel.

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1. 2026
3. GeoGT

Dense Conjugacy Classes in the Mapping Class Group of Graphs — Rocky Klein <klein@brandeis.edu>

The mapping class group of a locally finite graph Maps$(X)$ is the set of proper homotopy equivalences of $X$ up to proper homotopy. It is meant to be the analogue of the mapping class group of an infinite-type surface one dimension lower, but it also generalizes Out$(F_n)$ to a much larger class of possibly infinitely generated groups, establishing a "Big Out$(F_n)$." In this talk, I plan to define the mapping class group for a locally finite graph, discuss its topology, and give motivation. I will then discuss which locally finite graphs $X$ are such that Maps$(X)$ contains a dense conjugacy class. Along the way, we will discuss end spaces and their structures.

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1. 2025
3. Plenary

Diffeomorphisms of 3-manifolds with boundary — Corey Bregman <corey.bregman@tufts.edu>

Let M be a compact, connected, orientable 3-manifold with non-empty boundary. In this talk, we study the classifying space for the diffeomorphism group of M fixing the boundary pointwise, and show that it has the homotopy type of a finite CW complex. This parallels analogous results of Gramain and Earle-Schatz for surfaces, and confirms a conjecture of Kontsevich for orientable 3-manifolds. The proof will take us on a crash course in 3-manifold topology, and will feature a combination of results on geometrization of 3-manifolds with a topological poset parametrizing embedded spheres in M. This is joint work with Rachael Boyd and Jan Steinebrunner.

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1. 2025
3. Dynamics

Dimension of Lyapunov spectrum for non uniformly hyperbolic settings — Emma Dinowitz <emmad4867@gmail.com>

We study the Hausdorff dimension of the set of points with a fixed lyapunov exponent inside a family of subsets of a 3 dimensional flow with non uniform hyperbolicity properties. Recent work of Sarig, Lima, and others have constructed countable state markov partitions modeling these sets. Using their framework we prove upper bounds analogous to the uniformly hyperbolic situation.

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1. 2025
3. Set-Theoretic

Discrete density number — Alan Dow <adow@charlotte.edu>

A subset $D$ is a discretely dense subset of a space $X$ if every point of $X$ is in the closure of a discrete subset of $D$. The cardinal invariant, $Dd(X)$, was introduced by Juhasz and is the minimum cardinality of a discretely dense subset of $X$. We are reporting on some recent work with Juhasz and van Mill on results that improve upon the, seemingly only, obvious inequalities $d(X)\leq Dd(X)\leq |X|$. We also consider, $Fd(X)$, the free sequence density number.

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1. 2025
3. GeoGT

Distinguishing filling curve types via special metrics — Sayantika Mondal <smondal@gradcenter.cuny.edu>

In this talk, we look at filling curves on hyperbolic surfaces and consider its length infima in the moduli space of the surface as a type invariant. In particular, explore the relations between the length infimum of curves and their self-intersection number. For any given surface, we will construct infinite families of filling curves that cannot be distinguished by self-intersection number but via length infimum. I might also discuss some coarse bounds on the special metrics associated with these infimum lengths.

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1. 2026
3. General & ST

Do monotonically semi-neighborhood refining spaces have well-ordered neighborhood (F)? — Ted Porter <jporter@murraystate.edu>

In 1996, Stares introduced monotonically semi-neighborhood refining (MSNR) spaces and showed that well-ordered neighborhood (F) spaces are MSNR spaces. In this talk, the question of whether MSNR spaces have well-ordered neighborhood (F) is explored. We show that MSNR spaces have well-ordered (F) and hence are monotonically normal and hereditarily paracompact. MSNR spaces are also shown to be lob-spaces. The relationships between MSNR spaces with other monotone covering properties will also be explored.

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1. 2025
3. Plenary

Drilling and Filling in (relatively) hyperbolic groups — Jason Manning <jfmanning@cornell.edu>

Dehn surgery is a classical operation in which one converts one three-manifold to another by first removing a solid torus, and then gluing it back in in a different way. The first operation is called "drilling" and the second "filling". Both of these operations have group-theoretic interpretations in the world of hyperbolic and relatively hyperbolic groups. I will explain those interpretations and applications related to the Cannon conjecture (a special case of Wall's conjecture about $PD(n)$ groups). The most recent work is joint with Groves, Haïssinsky, Osajda, Sisto, and Walsh.

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1. 2024
3. STDC2024-STT

Dynamical Ideals of Topological Spaces — Justin Young <jyoung3@ufl.edu>

Joint work with J. Zapletal A dynamical ideal consists of a group acting on a set, along with an ideal that is invariant under the group action, and we can use dynamical ideals to obtain models of choiceless set theory. We focus on dynamical ideals where the underlying set is taken to be a topological space and the acting group is the group of homeomorphisms and look at how dynamical properties of the space correspond to fragments of AC in the associated model of set theory, along with particular examples.

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1. 2026
3. Dynamics

Dynamical approximation of post-singularly finite entire functions — Malavika Mukundan <mmukunda@bu.edu>

An entire map is said to be post-singularly finite if the forward orbit of its set of singular values is finite. Such maps play a crucial role in understanding natural families of entire maps. Motivated by previous work of Devaney, Goldberg and Hubbard, we ask the following question: _Given a post-singularly finite entire function f, can f be realized as the limit of a sequence of post-singularly finite polynomials?_ In joint work with Nikolai Prochorov and Bernhard Reinke, using techniques from Teichmüller theory, we show how we may answer this question in the affirmative.

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1. 2026
3. Dynamics

Dynamical systems as enriched functors — Suddhasattwa Das <iamsuddhasattwa@gmail.com>

A new advancement is presented in a broad ongoing effort to develop Dynamical systems theory in the language of Category theory. A new idea will be presented to describe a general dynamical systems as an enriched functor, and change of variables as enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a semigroup action on the domain; a parameterized family of endomorphisms; and a transformation of time-space into the collection of endomorphisms. A collection of categorical axioms are presented that provides a complete categorical language to develop dynamical systems theory. True to the philosophy of dynamical systems, none of these assumptions are rooted in specific contexts such as topology and measure spaces. The equivalence of the three descriptions is further used to construct other related notions,such as transfer operators, orbits and sub-shifts. All of these objects are defined by their structural role and universal properties, instead of their usual pointwise definitions. Source : https://arxiv.org/pdf/2509.05900

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1. 2024
3. STDC2024-DS

Dynamics of a General Non-autonomous Discrete Dynamical System — Puneet Sharma <puneet@iitj.ac.in>

In this talk, we discuss the dynamics of a general non-autonomous dynamical system. In particular, we discuss notions like equicontinuity, minimality and various notions of mixing and sensitivities for a general discrete non-autonomous system. We also discuss the case when the dynamics is generated by a uniformly convergent sequence of maps. We prove that if the system is generated by a commutative family converging at a "sufficiently fast rate" then many dynamical notions for non-autonomous system can be characterized by the limiting (autonomous) system.

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1. 2026
3. Continua

Dynamics of homeomorphisms of the Lelek and Cantor fans — Christopher Mouron <mouronc@rhodes.edu>

This is a continuation of Van Nall's talk {\it Specification on the Lelek Fan}. I will be discussing examples and non-examples of homeomorphisms of the Lelek and Cantor fans with the following properties: transitivity, mixing, shadowing, the specification property and maybe a few more.

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1. 2024
3. STDC2024-DS

Dynamics of rotated odometers — Henk Bruin <henk.bruin@univie.ac.at>

We study a family of infinite interval exchange transformations on the unit interval emerging from compositions of the Von Neumann-Kakutani map (dyadic odometer) with rational rotations (or more generally permutations of equal-length intervals. Hence the name ``rotated odometers''. By means of renormalization (similar to Rauzy-Veech induction) we cam translate the problem into one on symbolic substitutions, and determine the dynamic and ergodic structure of these rotated odometers. This is joint work with Olga Lukina

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1. 2024
3. STDC2024-DS

Dynamics of the shift action on linear sequence spaces over groups beyond $\mathbb{Z}$ — Sergei Miles <smiles15@charlotte.edu>

In linear dynamics, bounded linear operators over infinite-dimensional Banach spaces have been shown to be able to exhibit interesting characteristics including topological transitivity, topological mixing, and even chaos in the sense of Devaney. This talk will examine weighted $\ell^p$ sequence spaces together with the shift action as the operator. In the case the shift action is over the semi-group $\mathbb{N}$, the above topological properties have been characterized by conditions on the weight sequence associated with a given $\ell^p$ space. In this talk I will present recent results for new characterizations of these properties when we instead consider the group action over a countable group. I will also highlight other open questions. This is a joint work with Kevin McGoff and William Brian.

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1. 2026
3. Continua

Dynamics on Fences — Jernej Cinc <jernej.cinc@um.si>

We call a fence any compact metric space whose connected components are either points or arcs. In this talk I will present a very general method for raising maps of the Cantor space to various fences with dense set of endpoints, such as the Lelek Fence (in Complex Dynamics known also as the Hairy Cantor set) and Fraïssé Fence, while preserving the dynamics of the base homeomorphism of the Cantor space. As simple corollaries we obtain that Lelek Fan admits homeomorphisms with various dynamical properties.

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1. 2025
3. Continua

Dynamics on Hereditarily Decomposable Tree-like Continuum — Christopher Mouron <mouronc@rhodes.edu>

In this talk give an example of a hereditarily decomposable tree-like continuum that admits homeomorphisms that have the following dynamic properties: mixing, the specification property, and continuum-wise turbulence. I will also give results about topological properties (or lack of properties) that prevent hereditarily decomposable tree-like continuum from admitting homeomorphisms with some of the previous properties.

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1. 2026
3. Applied & Data

Early Functional Brain Network Alterations and Longitudinal Progression of Asymptomatic Alzheimer’s Disease — Altansuren Tumurbaatar <altaamgl@gmail.com>

As Alzheimer’s disease pathology begins decades before clinical symptoms, early functional brain changes in asymptomatic Alzheimer’s disease (AsymAD) remain poorly characterized, particularly from a longitudinal perspective. Although AsymAD individuals are biomarker-positive for Alzheimer’s pathology, they remain cognitively unimpaired, representing a preclinical stage that is clinically silent yet biologically active. At this stage, conventional MRI markers and cross-sectional analysis often lack sensitivity to detect the subtle functional alterations that precede symptom onset. Consequently, compared to symptomatic Alzheimer’s disease, AsymAD is substantially more difficult to identify using imaging markers alone, necessitating more sensitive, network-level, and longitudinal approaches. Resting-state functional MRI provides a noninvasive framework for probing intrinsic functional brain networks and detecting early network-level disruptions. Since brain networks exhibit a small-world topology, defined by high local clustering (segregation) and short average path lengths (integration), graph-theoretical metrics sensitive to subtle perturbations related to these properties may provide early network-level signatures of AsymAD. In this study, we examine longitudinal changes in functional connectivity in AsymAD compared with cognitively normal controls using complementary connectivity approaches, including region-to-region connectivity (RRC), graph-theoretical metrics, and seed-based connectivity (SBC). General linear models are used to assess between-subject and repeated-measure effects, with primary emphasis on group-by-session interactions.

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1. 2025
3. Applied

Efficient evader detection in mobile sensor networks — William Ott <william.ott.math@gmail.com>

Suppose one wants to monitor a domain with sensors, each sensing a small ball-shaped region, but the domain is hazardous enough that one cannot control the placement of the sensors. A prohibitively large number of randomly placed sensors could be required to obtain static coverage. Instead, one can use fewer sensors by providing mobile coverage, a generalization of the static setup wherein every possible evader is detected by the moving sensors in a bounded amount of time. Here, we use topology in order to implement algorithms certifying mobile coverage that use only local data to solve the global problem. Our algorithms do not require knowledge of the sensors' locations, only their connectivity information. We experimentally study the statistics of mobile coverage in two dynamical scenarios. We allow the sensors to move independently (billiard dynamics and Brownian motion), or to locally coordinate their dynamics (collective animal motion models). Our detailed simulations show, for example, that collective motion can enhance performance: The expected time until the mobile sensor network achieves mobile coverage is lower for the D'Orsogna collective motion model than for the billiard motion model. Further, we show that even when the probability of static coverage is low, all possible evaders can nevertheless be detected relatively quickly by the mobile sensor network.

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1. 2026
3. GeoGT
5. Plenaries

End-periodic homeomorphisms and volumes of mapping tori — Elizabeth Field <ecfield@uw.edu>

In this talk, we will introduce the notion of an end-periodic homeomorphism of an infinite-type surface. We will explore how the geometry of the associated mapping torus is related to certain topological and dynamical features of the end-periodic gluing map. In particular, we will see how the hyperbolic volume of the 3-manifold can be bounded both above and below in terms of a certain dynamical feature of the homeomorphism. This talk represents joint work with Autumn Kent, Heejoung Kim, Christopher Leininger, and Marissa Loving (in various configurations)

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1. 2024
3. STDC2024-CT

End-point-generated smooth fans — Rene Gril Rogina <rene.gril@student.um.si>

We define end-point-generated smooth fans and give known examples. We also define combs and use them to answer previously open problems about specific Mahavier products and endpoint-generated smooth fans as well as construct an uncountable family of such fans. This is joint work with Will Brian of UNC Charlotte.

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1. 2024
3. STDC2024-DS

Endpoints and Branchpoints in Inverse Limits of Dendrites — Jonathan Meddaugh <jonathan_meddaugh@baylor.edu>

In this talk we will use symbolic systems developed by Baldwin to analyze the structure of inverse limits of certain unimodal maps on dendrites. In particular, we will characterize the endpoints and branchpoints of such an inverse limit in terms of the kneading sequence associated with the map.

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1. 2025
3. GeoTop

Equivariant Smoothings and the Whitehead Group — Oliver Wang <wang.oliver96@gmail.com>

A closed manifold $M$ of dimension at least $5$ has only finitely many smooth structures. Moreover, the product structure theorem states that the smooth structures on such an $M$ are in bijection with smooth structures on the product $M\times\mathbb{R}$. In this talk, I will describe a construction that gives rise to infinitely many equivariant smooth structures of a closed $G$-manifold $M$ which become isotopic after taking a product with $\mathbb{R}$.

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1. 2025
3. Dynamics

Ergodic Averages along Sequences of Slow Growth — Kaitlyn Loyd <loydka@umd.edu>

Given Birkhoff's pointwise ergodic theorem, it is natural to consider whether convergence still holds along subsequences of the integers. In this talk, we investigate convergence of ergodic averages along the number theoretic sequence $\Omega(n)$, where $\Omega(n)$ denotes the number of prime factors of $n$ counted with multiplicities. In particular, we demonstrate that, although a pointwise ergodic theorem does not hold along $\Omega(n)$, there are multiple instances in which we can recover convergence. We also present a more general criterion for identifying slow-growing sequences possessing a certain divergence property exhibited by $\Omega(n)$. This talk is based on joint work with Sovanlal Mondal (Ohio State).

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1. 2025
3. Dynamics

Ergodic optimization with linear constraints — Kevin McGoff <kmcgoff1@charlotte.edu>

Let $T : X \to X$ be a continuous map on a compact metrizable space, let $f : X \to \mathbb{R}$ be continuous, and let $W \subset C(X)$ be a closed subspace of continuous functions from $X$ to $\mathbb{R}$. We consider the set $M_W(X,T)$ of all $T$-invariant Borel probability measures $\mu$ such that $\int g \, d\mu = 0$ for all $g$ in $W$. Then we consider optimization problems of the form $$ \max \int f \, d\mu + \tau h(\mu),$$ where $\mu$ ranges over $M_W(X,T)$, $h(\mu)$ denotes the entropy of $\mu$ with respect to $T$, and $\tau$ is either $0$ or $1$. Our main results concern the basic properties of such optimization problems, including feasibility, geometry of the solution set, uniqueness of solutions, and realizability. This talk is based on ongoing joint work with Shengwen Guo (UNC Charlotte).

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1. 2026
3. GeoTop
5. Plenaries

Exotic aspherical 4-manifolds — Kyle Hayden <kyle.hayden@rutgers.edu>

The Borel conjecture predicts that closed, aspherical manifolds (i.e., those with contractible universal cover) are topologically rigid: they are determined up to homeomorphism by their fundamental group. I will discuss the smooth version of this conjecture (concerning manifolds up to diffeomorphism), which is true in dimensions ≤ 3 but long known to be false in all dimensions ≥ 5. I will explain joint work with Davis, Huang, Ruberman, and Sunukjian that resolves the remaining 4-dimensional case by detecting exotic smooth structures on certain closed aspherical 4-manifolds.

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1. 2025
3. GeoTop

Exotic traces and the shake genus — Kai Nakamura <kainaka@stanford.edu>

The shake genus is the main tool used to detect exotic traces. This is a powerful tool to construct exotic traces, however it has some limitations. We will discuss several desirable properties of exotic traces that are inaccessible using the shake genus. By moving past needing to use the shake genus, we will be able to construct novel examples of exotic traces.

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1. 2025
3. Continua

Fan homogeneity — Rene Gril Rogina <rene.gril1@student.um.si>

We present recent results regarding different types of homogeneity for fans and discuss ongoing research into the topic. We define a larger class of fans with a specific property and use it to prove our results. This is joint work will Will Brian of UNC Charlotte.

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1. 2026
3. Applied & Data
5. Plenaries

Fiber bundles of toric arrangements — Christin Bibby <bibby@math.lsu.edu>

We present a combinatorial analysis of fiber bundles of generalized configuration spaces on connected abelian Lie groups and discuss topological consequences. These bundles are akin to those of Fadell-Neuwirth for configuration spaces, and their existence is detected by a combinatorial property of an associated finite partially ordered set. Of particular focus is the case of a toric arrangement: a finite collection of codimension-one subtori in a complex torus. If the intersection pattern of the subtori satisfies the combinatorial condition of supersolvability, the complement of the toric arrangement sits atop a tower of fiber bundles. This structure provides insight into topological invariants of these toric arrangement complements, including the homotopy groups, cohomology, and topological complexity. Based on joint work with Daniel C. Cohen and Emanuele Delucchi.

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1. 2026
3. GeoGT

Filling Links and Essential Systole — Yandi Wu <yw220@rice.edu>

The systole of a hyperbolic 3-manifold is the length of the shortest closed geodesic. Given a closed 3-manifold M and link L such that M\L is hyperbolic, the essential systole of M\L is the length of the shortest closed geodesic which is not nullhomotopic in M. In this talk, we will discuss and motivate the study of essential systoles of hyperbolic link complements, including their application towards answering a question of Freedman and Krushkal about the existence of "filling links" in closed 3-manifolds.

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1. 2026
3. Dynamics
5. Plenaries

Finite time evolution and finite time predictions for dynamical and random systems. — Leonid Bunimovich <leonid.bunimovich@math.gatech.edu>

TBA

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1. 2024
3. STDC2024-DS

Fixed point portraits for laminations of the unit disc. — Md Abdul Aziz <azizm@uab.edu>

Laminations are a combinatorial and topological model for studying the Julia sets of complex polynomials. Every complex polynomial of degree d has d fixed points, counted with multiplicity. From the point of view of laminations, at most d-1, of these fixed points are peripheral (approachable from outside the Julia set of the polynomial). Hence, at least one of the d fixed points is “hidden” from the laminational point of view. The purpose of this study is to identify, classify and count the possible fixed point portraits for any lamination of degree d. We will identify the “simplest” lamination for a given fixed point portrait and will show that there are polynomials that have these simplest laminations. An application of fixed point portraits is to establish a correspondence between locally unicritical laminations and locally maximally critical laminations with rotational polygons. This application is a joint work with Brittany E. Burdette.

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1. 2025
3. Dynamics

Flow equivalence and PSL_2(Q)-equivalence — Scott Schmieding <sks7247@psu.edu>

A real number gives rise to a Sturmian system encoding a rotation of the circle, and there are several beautiful connections between these systems and arithmetic properties of the associated parameters. One is a result of Fokkink, which shows that two Sturmian subshifts with parameters \alpha and \beta are flow equivalent if and only if \alpha and \beta lie in the same orbit of the action of PSL_2(Z) on the set of reals via Mobius transformations, a condition which is itself characterized by the tails of their continued fraction expansions. I'll describe some recent work, joint Christopher-Lloyd Simon, describing the action of PSL_2(Q) in terms of a certain relation on systems called isogeny.

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1. 2024
3. STDC2024-DS

Forcing among mixing patterns of triods — Sourav Bhattacharya <sourav210392@gmail.com>

We use rotation theory to deduce an order among periods of mixing patterns of some maps of triods.

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1. 2025
3. GeoGT

Frattini subgroups of hyperbolic-like groups — Ekaterina Rybak <ekaterina.rybak@vanderbilt.edu>

The Frattini subgroup $\Phi(G)$ of a group $G$ is the intersection of all maximal subgroups of $G$; if $G$ has no maximal subgroups, $\Phi(G)=G$ by definition. Frattini subgroups of groups with ``hyperbolic-like" geometry are often small in a suitable sense. Generalizing several known results, we prove that for any countable group $G$ admitting a general type action on a hyperbolic space $S$, the induced action of the Frattini subgroup $\Phi(G)$ on $S$ has bounded orbits, in particular, $\Phi(G)$ has infinite index in $G$. In contrast, we show that the Frattini subgroup of an infinite lacunary hyperbolic group can have finite index. The talk is based on a joint work with Gil Goffer and Denis Osin.

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1. 2026
3. Continua

Fraïssé fence "with" pseudo-arcs? — Bryant Rosado Silva <bryantrs99@hotmail.com>

Using as inspiration known and new results about the Fraïssé fence and the flow of its homeomorphism group on the space of chains of compacta, we suggest a new space by using pseudo-arcs instead of arcs and briefly discuss some of our questions and motivations. This is an ongoing project with Benjamin Vejnar (Charles University).

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1. 2024
3. STDC2024-GGT

Free product quotients acting on CAT(0) cube complexes — Thomas Ng <thomasng@brandeis.edu>

Quotients of free products are natural combinations of groups that have been exploited to study embedding problems. These groups have seen a resurgence of attention from a more geometric point of view following celebrated work of Haglund--Wise and Agol. I will discuss a geometric model for studying quotients of free products. We will use this model to adapt ideas from Gromov's density model to this new class of quotients, their actions on CAT(0) cube complexes, and combination theorems for residual finiteness. Results discussed will be based on ongoing work with Einstein, Krishna MS, Montee, and Steenbock.

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1. 2026
3. Applied & Data
5. Plenaries

From Descriptors to Interfaces: Visual Analytics for Topological Data Analysis — Federico Luricich <fiurici@clemson.edu>

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1. 2025
3. Dynamics

Full Groups of Cantor Dynamical Systems: Characters and Invariant Measures — Constantine Medynets <medynets@usna.edu>

Given a Cantor minimal dynamical system $(X, T)$, the topological full group $[[T]]$ consists of all homeomorphisms of $X$ that locally act as powers of $T$. These groups can be viewed as generalized symmetric groups on the continuous orbit equivalence relation of $(X,T)$. A series of works by Giordano–Putnam–Skau, Matui, Medynets, Nekrashevych, and others have demonstrated that the algebraic structure of topological full groups completely determines the orbit structure of the underlying systems. This naturally leads to the question of whether the structure of invariant measures, an invariant of orbit equivalence, is similarly reflected in the full group's algebraic properties. In this talk, we present joint work with Artem Dudko (IMPAN) on the classification of characters of topological full groups of Cantor minimal systems. We establish that every extreme character of the commutator subgroup of $[[T]]$ is of the form $\mu(Fix(g))$, where $\mu$ is an ergodic product measure on $X^n$, thereby confirming Vershik’s conjecture for the class of full groups. As a consequence, we show that prime indecomposable characters are in one-to-one correspondence with ergodic measures.

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1. 2026
3. Continua

Gehman Dendrite G3 as a Generalized Inverse Limit Space — Faruq Mena <faruq.mena@soran.edu.iq>

We show that the family of functions in the paper by Sherzad and Mena that give $G_3$ as the inverse limit space, can be expanded to include upper semi-continuous functions whose graphs have a finite number (or even one) of ``short'' line segments of the form $[x_1,\alpha]\times \{a_i\}$ and $[\alpha,x_2] \times \{b_i\}$ where $0 < x_1 < \alpha < x_2 <1$. This is joint work with Sarezh R. Rasul.

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1. 2024
3. STDC2024-CT

Gehman Dendrite G_4 as Generalize Inverse Limit Spaces of Upper Semi Continuous Bonding Functions on [0,1] — Faruq Mena <faruq.mena@soran.edu.iq>

In this talk we prove that the Gehman dendrite G_4 can be obtained as a generalized inverse limit space with a single upper semi-continuous bonding function on [0,1]. This answers a question of Farhan and Mena. Moreover, we find an uncountable family of inverse sequences on [0,1] whose inverse limit spaces are homeomorphic to the Gehman dendrite G_4.

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1. 2026
3. Continua
5. Plenaries

General Topology in Dynamical Systems — Hisao Kato <kato.hisao.fw@u.tsukuba.ac.jp>

Research in general topology is important for the study of dynamical systems. The complexity of dynamical systems suggests the existence of complex topological structures in their base spaces. This lecture will discuss the following two topics: (Part 1) Extended Takens-type reconstruction theorems for one-sided dynamical systems, and (Part 2) The existence of indecomposable continua in chaotic dynamical systems.

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1. 2026
3. General & ST

General and Set-Theoretic Topology Problem Session — Will Brian <wbrian.math@gmail.com>

Session participants are invited to join an interactive problem session discussing open questions in our discpline.

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1. 2025
3. Continua

Generalization of the specification property to CR-dynamical systems — Ivan Jelić <ivajel@pmfst.hr>

We will recall the definition and basic properties of the notion of the specification property in the case of a standard topological dynamical system (X,f). We will then define a CR-dynamical system (X,F) and introduce different generalizations of the specification property for this type of dynamical system. More precisely, we will introduce and investigate the notions of (strong/weak) specification property and compare them together with their "initial" versions.

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1. 2025
3. Continua

Generalizations of the notion of a hereditarily equivalent continuum — Bryant Rosado Silva <bryantrs99@hotmail.com>

We say that a continuum $X$ is a hereditarily equivalent continuum (HEC) if every non-degenerate subcontinuum of it is homeomorphic to $X$. We can weaken this condition in three different levels: If considered in the hyperspace of continua of $X$, denoted by $\operatorname{Cont}(X)$, being hereditarily equivalent means that $\operatorname{Cont}(X)\setminus \{\{x\} \ | \ x \in X\} = \{ K \in \operatorname{Cont}(X) \ | \ K \simeq X\}.$ This is an open and dense set, hence comeager, thus the first way to weaken it is to ask for the set of homeomorphic copies of $X$ to be a comeager subset of $\operatorname{Cont}(X)$. A continuum with this property we call a generically hereditarily equivalent continuum (GHEC). However, we can go further and consider the hyperspace of maximal order arcs $\operatorname{MOA}(X)$. In the case of an HEC, any maximal order arc is made of an initial unitary set called the root and homeomorphic copies of $X$, hence we can say that - GCHEC holds for a space $X$ if comeager many elements of $\operatorname{MOA}(X)$ have this property of being a chain made of copies of $X$ apart from the root. - GCGHEC holds for $X$ if comeager many elements of $\operatorname{MOA}(X)$ contain comeager many copies of $X$. In this talk, we partially address two natural questions that arise from these definitions: "What kind of spaces satisfy these properties?" and "How are these properties related?"

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1. 2026
3. Continua

Generalized Inverse Limits and a Property of Kelley — Mardan A. Pirdawood <mardan.ameen@koyauniversity.org>

Ingram, \cite[Problem 6.56, p.81]{ingram2012introduction}, asked what can be said about the Property of Kelley in the generalized inverse limit space $\varprojlim\{X_i,f_i\}$ where $\{f_i\}$ is a sequence of upper semi-continuous bonding functions. In this work, we give conditions on the projection maps from the graph of the functions $f_i$ to the domain and co-domain such that if the first factor space, in the case of Theorem 2.2, or all factor spaces, in the case of Theorem 2.4, have the Property of Kelley then the generalized inverse limit space $\varprojlim\{X_i,f_i\}$ has the Property of Kelley. Furthermore, we present examples demonstrating that if any condition is dropped then the inverse limit space may not have the Property of Kelley. These results also answers several questions by Charatonik, Mena and Roe \cite{Charatonik2020}. This is joint work with Faruq Mena and Robert Roe.

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1. 2026
3. Continua

Generalized Inverse Limits on Circles — Scott Varagona <svaragona@montevallo.edu>

It has now been twenty years since the publication of W. T. Ingram and W. S. Mahavier’s landmark paper, “Inverse limits of upper semi-continuous set valued functions” (Houston Journal of Mathematics, 2006, vol. 32, no. 1, p. 119-130). For all these years, generalized inverse limits whose factor spaces are arcs have been studied intensively by researchers around the world. However, generalized inverse limits whose factor spaces are circles have been far less thoroughly studied, and could offer researchers a whole new frontier to explore. We state some questions about these spaces and provide various examples, including an example of a generalized inverse limit on circles (with a single, continuum-valued bonding function) that gives rise to an indecomposable continuum.

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1. 2025
3. Continua

Generalized inverse limits with Markov set-valued functions on finite graphs — Hayato Imamura <hayato-imamura@asagi.waseda.jp>

In this talk, we introduce definitions of Markov set-valued functions on finite graphs and the same pattern between two Markov set-valued functions. These functions are defined using the framework of cell complexes. They allow for infinite Markov partitions and have graphs that may contain $2$-cells. We also show that two generalized inverse limits with bonding functions that are Markov set-valued functions following the same pattern are homeomorphic. This is joint work with E. Matsuhashi and Y. Oshima.

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1. 2026
3. Dynamics

Generic continuous Lebesgue measure preserving interval maps are nowhere monotone but invertible a.e. — Jozef Bobok <jozef.bobok@cvut.cz>

We consider all continuous maps of the interval preserving the Lebesgue measure $\lambda$ equipped with the uniform topology. Except for the identity map or $1 - id$ all such maps have topological entropy at least $\log2/2$ and generically they have infinite topological entropy. In this talk we discuss two generic properties: (i) invertibility $\lambda$-a.e. implied by the zero measure-theoretic entropy with respect to $\lambda$, and (ii) complicated structure of level sets. We also recall that there are Besicovitch maps (having no finite or infinite unilateral derivative at any point) preserving $\lambda$ and show that each such map has positive measure-theoretic entropy with respect to $\lambda$.

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1. 2026
3. Continua

Genericity of Shadowing — Jonathan Meddaugh <jonathan_meddaugh@baylor.edu>

A dynamical system is said to have the shadowing property provided that approximate orbits are well-approximated by true orbits. It has previously been established that for a continuum belonging to certain classes of continua, shadowing is a common, i.e. generic, property in its space of continuous self-maps. In particular, this is known for manifolds and for locally connected one-dimensional continua. We demonstrate that shadowing is a generic property in the space of continuous self-maps for any continuum which admits retractions onto graphs.

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1. 2024
3. STDC2024-GTop

Geometric Embeddings of Spaces of Persistence Diagrams with Explicit Distortions — Atish Mitra <atish.mitra@gmail.com>

Let $n$ be a positive integer. We provide an explicit geometrically motivated 1-Lipschitz map from the space of persistence diagrams on n points (equipped with the Bottleneck distance) into Hilbert space. Such maps are a crucial step in topological data analysis, allowing the use of statistics (and thus data analysis) on collections of persistence diagrams. The main advantage of our maps as compared to most of the other such transformations is that they are coarse and uniform embeddings with explicit distortion functions. Furthermore, we provide an explicit 1-Lipschitz map from the space of persistence diagrams on $n$ points on a bounded domain into a Euclidean space with an explicit distortion function. Our ideas come from geometric topology and dimension theory, and our methods are best described as quantitative dimension theory. This is joint work with Ziga Virk.

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1. 2025
3. Plenary

Geometry of Rips complexes and applications — Florian Frick <frick@cmu.edu>

In geometric group theory, Rips complexes provide a natural construction to give higher structure to a Cayley graph. In topological data analysis, Rips complexes are used to reconstruct a sufficiently nice space from a sample. I will show different but related applications of Rips complexes and similar constructions to Borsuk-Ulam results, understanding Gromov-Hausdorff distances, and roots of zero-mean real-valued maps.

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1. 2024
3. STDC2024-GGT

Girth Dichotomy Arising from the Ping-Pong Dynamics in HNN Extensions — Pratyush Mishra <mishrap@wfu.edu>

The notion of a girth was first introduced by S. Schleimer in 2003. Later, a substantial amount of work on the girth of finitely generated groups was done by A. Akhmedov, where he introduced the so-called Girth Alternative and proved it for certain classes of groups, e.g. hyperbolic, linear, one-relator, $PL_+(I)$ etc. Girth Alternative is similar to the well-known Tits Alternative in spirit, therefore it is natural to study it for classes of groups for which Titis Alternative has been investigated. In this talk, we will explore the girth of HNN extensions of finitely generated groups in its broadest sense by considering cases where the underlying subgroups are either full or proper subgroups. We will present a sub-class for which Girth Alternative holds. We will also produce counterexamples to show that beyond our class, the alternative fails in general. Recently, we extended one of the main results proving the Girth Alternative for HNN extensions of word hyperbolic groups (instead of HNN extensions of free groups). The talk will be based on joint work with Azer Akhmedov.

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1. 2026
3. Applied & Data

Graph polynomial encoding for RNA structure data analytics — Pengyu Liu <pengyu.liu@uri.edu>

Advancements in sequencing technologies have produced a wealth of genomic data. In parallel, the development of artificial intelligence has enabled novel folding models that predict molecular structures from sequences. These advancements have resulted in a myriad of biomolecular structure data. Analytics of structure data offers more accurate approaches to genotype-to-phenotype analyses, as biomolecular structures are more evolutionarily conserved than sequences and more directly linked to biological functions. A major challenge of structure data analytics is the lack of efficient and accurate structure encodings. In this talk, we introduce encodings of RNA secondary structures using polynomial invariants of graphs. We show that the graph polynomial encodings enable efficient, accurate and interpretable RNA secondary structure analyses using modern data analytics tools. 

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1. 2025
3. GeoGT

Green metrics on hyperbolic groups and reparameterizations of the geodesic flow — Eduardo Reyes <eduardo.c.reyes@yale.edu>

Teichmüller space is a classical construction that, for a given closed hyperbolic surface, parameterizes the geometric actions of its fundamental group on the hyperbolic plane. I will talk about a generalization of this space, where for an arbitrary hyperbolic group we consider a space parameterizing its geometric actions on Gromov hyperbolic spaces, simultaneously encoding negatively curved Riemannian metrics, Anosov representations, random walks, geometric cubulations, etc. In particular, I will discuss how Green metrics (those encoding admissible random walks on the group) are dense in this space. As an application, for fundamental groups of negatively curved manifolds we produce a dictionary between this space of geometric actions and the space of reparameterizations of the geodesic flow. This is joint work with Stephen Cantrell and Dídac Martínez-Granado.

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1. 2025
3. Applied

Gromov-Hausdorff distance between metric graphs and their subspaces — Nicolò Zava <nicolo.zava@ist.ac.at>

The Gromov-Hausdorff distance, a dissimilarity measure between metric spaces, is used in computational topology and geometry to compare datasets that can be represented as metric spaces. Despite the computational obstructions to its practical use, it still provides a theoretical framework to quantify invariants' stability and information loss. In this talk, we focus on a particular problem regarding the Gromov-Hausdorff distance: Given an object and a sample of it, under what conditions do their Hausdorff and Gromov-Hausdorff distances coincide? As the Gromov-Hausdorff distance describes how far they are from being isometric, and the Hausdorff distance measures the density of the sample, we can less formally restate the question as follows: When is a sample dense enough to describe the original object’s geometry faithfully? In particular, we discuss the case of metric graphs providing both negative and positive results.

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1. 2026
3. Applied & Data
5. Plenaries

Gromov-Wasserstein distances and distributional invariants — Tom Needham <tneedham@fsu.edu>

Gromov-Wasserstein (GW) distances provide a method for comparing probability measures defined on different metric spaces, thereby giving an optimal transport-inspired variant of the well-known Gromov-Hausdorff distance. As GW distances admit computationally tractable approximations, they have become popular in machine learning applications where one wishes to learn trends in a dataset consisting of incomparable spaces, such as ensembles of graphs. In this talk, I will overview recent advances in the theory of GW distances. In particular, I will discuss a certain approximation technique which relies on comparing the distributions of pairwise distances between metric measure spaces. This approach naturally gives rise to fascinating questions about the geometrical and topological features that are encoded in this distributional information, and I will explain some partial answers to these questions.

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1. 2026
3. GeoTop

Gromov’s Conjecture for Graph Product of Groups — Satyanath Howladar <showladar@ufl.edu>

Gromov defined macroscopic dimension of metric spaces to study manifolds admitting a Positive Scaler Curvature (PSC) metric, via their largeness properties. He conjectured universal cover of PSC n-manifolds should have macroscopic dimension at most n-2. This conjecture depends heavily on the fundamental group of the n-manifold. Under the assumption of the Strong Novikov Conjecture, we prove that closed spin manifolds having fundamental group a Graph Product of geometrically finite groups satisfies the conjecture, provided the vertex groups have classifying space which becomes wedge sum of Moore Spaces, after finitely many suspension. This generalizes our previous result when the fundamental group is a RAAG. We developed a crucial property called 1-Step Stabilization Property (1-SSP) for groups to prove the above. We also found an examples of groups not satisfying 1-SSP, inspiring more investigation towards possible counter example related to Gromov’s conjecture.

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1. 2025
3. Applied

Group Actions on Metric Spaces — Liam Barham <blb0081@auburn.edu>

Given a metric space $X$, the Vietoris-Rips complex VR$(X)$ is a classical simplicial complex obtained from $X$, and a group $G$ acting properly by isometries yields another metric space $X/G$ of the orbits of $X$ under $G$. There is a canonical way in which $G$ can act on VR$(X)$, so instead using the Vietoris-Rips metric thickening VR$^m(X)$ allows a meaningful comparison between VR$^m(X)/G$ and VR$^m(X/G)$ as metric spaces. This talk will survey a variety of properties which a group action on a metric space can have with some examples, and culminate with a discussion of the strong $r$-diameter action, which guarantees that under certain scale parameters VR$^m(X)/G\simeq$ VR$^m(X/G)$. I also discuss a strictly weaker condition and present some open questions concerning the connection between the two. Finally, I will briefly mention some analogous results for the Cech metric thickening.

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1. 2026
3. Applied & Data

Group actions on Vietoris-Rips complexes of hypercube graphs — Federico Galetto <f.galetto@csuohio.edu>

The hyperoctahedral group is the group of symmetries of the hypercube graph. It acts on the Vietoris-Rips complexes of the hypercube graph with the Hamming distance and, therefore, on their homology groups. I will present a method to understand this action and show how it can be used as an alternative approach to compute homology. This is joint work with Jonathan Montaño and Zoe Wellner.

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1. 2025
3. Continua

Hereditarily Decomposable Continua have Non-Block Points — Daron Anderson <daronanderson@live.ie>

We expand upon our earlier results, to show that every nondegenerate hereditarily decomposable Hausdorff continuum has two or more non-block points, i.e points whose complements contain a continuum-connected dense subset. The celebrated non-cut point existence theorem states that all nondegenerate Hausdorff continua have two or more non-cut points, and the corresponding result for non-block points is known to hold for metrizable continua. It is also known that there are consistent examples of Hausdorff continua with no non-block points, but that non-block point existence holds for Hausdorff continua that are either aposyndetic, irreducible, or separable.

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1. 2024
3. STDC2024-STT

High dimensional sequential compactness — Cesar Corral <cicorral@yorku.ca>

We will introduce high dimensional versions of sequential compactness for every ordinal $\alpha<\omega_1$. This will generalize a previous notion introduced by W. Kubis and P. Szeptycki for $\alpha\in\omega$. We then extend some known results in the finite case to the infinite case, exhibit some conditions that imply sequential compactness for higher dimensions and analyze the impact of some cardinal invariants in these classes of spaces. We will close with some remarks and applications.

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1. 2026
3. General & ST

Higher Lindelöf trees — Pedro Marun <marun@math.cas.cz>

Given an infinite cardinal $\kappa$ and a $\kappa$-splitting $\kappa^+$-tree $T$, we topologize $T$ as follows: if $x\in T$, then sets of the form $\uparrow x \setminus \uparrow F$, for $F$ a set of immediate successors of $x$ with $|F|<\kappa$, form a basis of neighbourhoods of $x$. We then ask whether $T$ is $\kappa^+$-compact with respect to this topology and characterize this property in purely order-theoretic terms. Such trees are necessarily $\kappa^+$-Aronszajn, so they may (consistently) not exist when $\kappa\ge\aleph_1$. In this talk, discuss how to construct such trees using Proxy Principles, introduced by Brodsky and Rinot. We will also mention a further consitency result on the non-existence of such trees together with the failure of the tree property at $\aleph_2$. This is joint work with Ari Meir Brodksy.

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1. 2024
3. STDC2024-GTop

Holomorphic maps to blowups of projective space — Philip Tosteson <philip.tosteson@gmail.com>

Let $C$ be a compact Riemann surface, and $X$ be smooth projective variety. We will consider the space of holomorphic maps $C \to X$. When $X = \mathbb P^n$, Segal demonstrated a remarkable stabilization phenomenon: as $d$ increases, the homology of the component of **degree $d$ holomorphic maps** converges to homology of the component of **degree $d$ continuous maps** $C \to X$. Ellenberg-Venkatesh and others have observed that this phenomenon is related to arithmetic conjectures about rational points on Fano varieties due to Batyrev and Manin. This suggests that this stabilization phenomenon may hold more generally. I will talk about joint work with Ronno Das using the Vassiliev method to study the case of blowups of projective space at finitely many points (in particular del Pezzo surfaces).

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1. 2024
3. STDC2024-GGT

Homological Representations of Low Genus Mapping Class Groups — Trent Lucas <trent_lucas@brown.edu>

The mapping class group Mod(S) of a surface S acts on the homology H_1(S), yielding the well-studied symplectic representation Mod(S) → Sp(2g,Z). In this talk, we discuss an equivariant refinement of the symplectic representation. Namely, given a finite group G acting on S, the symplectic representation restricts to a map from the centralizer of G in Mod(S) to the centralizer of G in Sp(2g,Z). The image of this restriction has been studied by many authors and is generally difficult to understand. We discuss our result that the image of this restriction is arithmetic when S has genus at most 3.

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1. 2025
3. Dynamics

Homomorphisms from aperiodic subshifts to subshifts with the finite extension property — Robert Bland <rbland5@charlotte.edu>

We are inspired by recent efforts to generalize the classical embedding theorem of Krieger for $\mathbb{Z}$ subshifts, which states that if $X$ is an SFT and $Y$ is a mixing SFT, then $X$ embeds into $Y$ if certain necessary conditions on the periodic points and entropy are satisfied. Moving to subshifts over groups $G$ beyond $\mathbb{Z}$, an extra essential hypothesis emerges: that there is a homomorphism (a continuous and shift-commuting map, not necessarily injective) from $X$ to $Y$ at all. This is trivially satisfied if, e.g., $Y$ contains a fixed point, but necessary and sufficient conditions for the existence of a homomorphism are not known in general. In this talk, we present joint work with K. McGoff that constructs a homomorphism $\phi : X \to Y$ in the case that $X$ is aperiodic, $Y$ has the finite extension property, and the underlying group $G$ has the property that every finitely generated subgroup of $G$ has polynomial growth (i.e., $G$ is locally virtually nilpotent by Gromov's theorem). The finite extension property (FEP) can be seen as a very strong mixing-like condition which has been considered before for subshifts over $\mathbb{Z}^d$ [Briceño, McGoff, Pavlov 2016].

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1. 2026
3. Continua
5. Plenaries

How complex is the arc-connection relation? — Benjamin Vejnar <benvej@gmail.com>

For a continuum, we consider the equivalence relation in which two points are equivalent if they can be joined by an arc. This equivalence relation is analytic in general (i.e. a continuous image of a Polish space). Recently, Debs and Saint Raymond proved that, for planar continua, this equivalence relation is always Borel measurable. We show that for every planar continuum, the arc-connection relation is in fact Borel reducible to the Vitali equivalence relation, where two real numbers are equivalent if their difference is rational. Moreover, the Knaster continuum is an example where this complexity is attained. This is joint work with Michal Hevessy and Yusuf Uyar. We also investigate several related questions concerning continuum-wise connectivity.

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1. 2025
3. Plenary

Hyperbolic actions of Thompson's group $F$ — Sahana H Balasubramanya <hassanba@lafayette.edu>

In this talk, I will present recent results about the poset of hyperbolic structures on Thompson's group $F$. While the global structure of this poset is as simple as one would expect, the local structure turns out to be incredibly rich, in stark contrast with the situation for the $T$ and $V$ counterparts. I will focus on the subposet of quasi-parabolic hyperbolic structures, which contains uncountably many \emph{lamplike} structures, called so as they can be described combinatorially in terms of certain hyperbolic structures on related lamplighter groups. On the other hand, there are also many non-lamplike structures, showing the vastness and complexity of this poset. Lastly, I will talk about how these actions can be extended to more general Thompson's groups $F_n$ for $n \geq 2$. This is joint work with Francesco Fournier-Facio and Matthew C.B.Zaremsky.

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1. 2026
3. GeoTop
5. Plenaries

Hyperbolic manifolds: Past, present, future — Matthew Stover <mstover@temple.edu>

The most basic Riemannian manifolds are those admitting a complete metric of constant curvature. The classification of closed manifolds with metrics of positive and zero curvature is has been relatively well-understood for quite a long time. Constant curvature -1 manifolds, hyperbolic manifolds, remain quite a bit more mysterious, particularly in high dimensions. I will give a (biased) narrative regarding what we know, including a number of exciting recent results with connections to dynamics and geometric group theory, and look forward to some problems I hope to see solved in the coming years.

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1. 2024
3. STDC2024-GGT

Hyperbolicity and relative hyperbolicity of free extensions of free groups — Funda Gültepe <funda.gultepe@utoledo.edu>

The interest in the geometry of group extensions started with the geometrization theorem of Thurston for compact irreducible atoroidal 3-manifolds. We will talk about the geometry of group extensions and the motivations behind such studies in the cases of closed surface groups and free groups. More specifically, we will talk about the most general case so far and, we will give necessary and sufficient conditions for a free extension of a (non-Abelian) free group given by a subgroup of the outer automorphism group of the free group (Out(F_n)) to be hyperbolic and relatively hyperbolic. Joint work with Pritam Ghosh.

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1. 2024
3. STDC2024-GGT

Hyperfiniteness of boundary actions of acylindrically hyperbolic groups — Koichi Oyakawa <koichi.oyakawa@vanderbilt.edu>

A Borel equivalence relation on a Polish space is called hyperfinite if it can be approximated by Borel equivalence relations with finite classes. This notion has long been studied in descriptive set theory to measure complexity of Borel equivalence relations. Although group actions on hyperbolic spaces don't always induce hyperfinite orbit equivalence relations on the Gromov boundary, some natural boundary actions were recently found to be hyperfinite. Examples of such actions include actions of hyperbolic groups and relatively hyperbolic groups on their Gromov boundary, actions of mapping class groups on arc graphs and curve graphs, and acylindrical group actions on trees. In this talk, I will show that any acylindrically hyperbolic group admits a non-elementary acylindrical action on a hyperbolic space with hyperfinite boundary action.

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1. 2024
3. STDC2024-CT

Hyperspaces of exactly n points — Alejandro Illanes <illanes@matem.unam.mx>

Given a topological space and a positive integer n, we consider the hyperspace [X]n of subsets of X with exactly n points. In this talk we discuss results we have obtained about the topological properties of [X]n, such as: connectedness, arcwise connectedness, contractibility, existence of selections, spaces [[0,1]]n, etc.

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1. 2026
3. GeoTop

Immersed incompressible surfaces in hyperbolic manifolds — Zhenghao Rao <zhenghao.rao@rutgers.edu>

The study of surface subgroups in 3-manifolds has drawn sustained attention for decades, motivated both by their intrinsic geometric richness and by their broad consequences in geometric topology, geometric group theory, and dynamics. A landmark result is the Surface Subgroup Theorem of Kahn–Markovic, which states that every cocompact Kleinian group contains a ubiquitous collection of closed surface subgroups. In this talk, we will introduce some key developments in the subject and highlight our recent progress, including joint work with Jeremy Kahn, and with Xiaolong Han and Jia Wan.

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1. 2024
3. STDC2024-GGT

Incoherence for right-angled Coxeter groups on surfaces — Lorenzo Ruffoni <lorenzo.ruffoni2@gmail.com>

A group is "coherent" if every finitely generated subgroup is finitely presented. In a certain sense, coherence is a low-dimensional phenomenon. For instance, 3-manifold groups and one-relator groups are coherent. In this talk we consider Coxeter groups defined by a graph that is a flag triangulation of a surface of genus g. For each g>0, we construct a Coxeter group that is right-angled, hyperbolic, and incoherent. In these examples the witness to incoherence is always the fiber in a virtual algebraic fibration. This provides positive evidence towards a variation on Singer's Conjecture for right-angled Coxeter groups proposed by Davis-Okun. This is joint work with G. Walsh.

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1. 2025
3. Applied

Independence Complexes of Kneser Graphs — Ziqin Feng <zzf0006@auburn.edu>

We will discuss the topological properties of the independence complex of Kneser graphs, Ind(KG$(n, k))$, with $n\geq 3$ and $k\geq 1$. By identifying one kind of maximal simplices through projective planes, we obtain homology generators for the $6$-dimensional homology of the complex Ind(KG$(3, k))$. Using cross-polytopal generators, we provide lower bounds for the rank of $p$-dimensional homology of the complex Ind(KG$(n, k))$ where $p=1/2\cdot {2n+k\choose 2n}$.

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1. 2025
3. GeoGT

Independence of Dehn, conjugator length, and annular Dehn functions of finitely presented groups — Conan Gillis <cg527@cornell.edu>

Brick and Corson introduced annular Dehn functions in 1998 to quantify the conjugacy problem for finitely generated groups and gave the fundamental relationships between it, the Dehn function, and the conjugator length function. I will discuss the key ideas behind these invariants, as well as joint work with T. Riley where we prove that these three invariants are independent—in general, no two of the three functions determine the other.

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1. 2026
3. Continua

Induced Dynamics on Hyperspaces: Periodic Points and Li–Yorke Chaos — Leonel Rito Rodríguez <leonel_rito@ciencias.unam.mx>

In this talk, we study the dynamical behavior of hyperspace maps induced by continuous functions on dendrites. Our main goal is to show that if $X$ is a dendrite and $f : X \to X$ is a continuous map for which every point of $X$ is periodic, then the induced map \[ 2^f : 2^X \to 2^X \] does not admit Li--Yorke pairs. To establish this result, we analyze two fundamental cases that capture the combinatorial structure of dendrites: closed intervals and trees.

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1. 2024
3. STDC2024-Semi

Infinite dimensional Ramsey theory on homogeneous structures — Natasha Dobrinen <ndobrine@nd.edu>

The Galvin-Prikry theorem states that Borel subsets of the Baire space are Ramsey. Silver extended this to analytic sets, and Ellentuck gave a topological characterization of Ramsey sets in terms of the property of Baire in the Vietoris topology. We present work extending these theorems to several classes of countable homogeneous structures. An obstruction to exact analogues of Galvin-Prikry or Ellentuck is the presence of big Ramsey degrees. We will discuss how different properties of the structures affect which analogues have been proved. Presented is work of the speaker for structures with SDAP$^+$ and joint work with Zucker for binary finitely constrained FAP classes. A feature of the work with Zucker is showing that we can weaken one of Todorcevic’s four axioms guaranteeing a Ramsey space, and still achieve the same conclusion.

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1. 2026
3. GeoTop

Infinitely many Lefschetz pencils on ruled surfaces — Seraphina Eun Bi Lee <slee@math.harvard.edu>

Works of Donaldson and Gompf show that a closed, oriented 4-manifold admits a symplectic structure if and only if it admits the structure of a Lefschetz pencil. However, the question of how many Lefschetz pencils (or fibrations) a given symplectic 4-manifold admits remains open. Works of Park--Yun and Baykur construct 4-manifolds admitting arbitrarily large (but finite) numbers of Lefschetz pencils or fibrations of the same genus. In this talk, we will construct infinitely many inequivalent Lefschetz pencils of the same genus on ruled surfaces of negative Euler characteristic. In fact, our construction gives the first example of infinitely many inequivalent but diffeomorphic Lefschetz pencils and fibrations of the same genus. This is joint work with Carlos A. Serván.

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1. 2026
3. GeoGT

Injective metrics and affine hyperplane arrangements — Katherine Goldman <kat.goldman@mcgill.ca>

A complex affine hyperplane arrangement is a locally finite collection of affine hyperplanes (complex codimension-1 subspaces) in a finite dimensional complex affine space. Since these subspaces have complex codimension 1, the complement of their union is a connected manifold. It is a broad, longstanding problem with many connections to different areas of mathematics to determine the arrangements for which this manifold is aspherical (has contractible universal cover). A subset of this problem dating back to the 1970s, commonly attributed to Arnol’d, Brieskorn, Thom, and Pham, concerns arrangements arising from reflection groups in real affine space. One approach that has seen success is to construct a cell complex which is homotopy equivalent to this complement and endow it with some kind of ("singular") non-positive curvature. Along these lines, by showing that a specific cell complex (based on a construction of Falk) carries an injective metric, we show that a broad class of affine arrangements (including the infinite families of affine reflection arrangements, modulo a conjecture about $D_n$-type) have aspherical complement. In particular, this provides some of the first examples of infinite affine arrangements which have aspherical complement, but do not arise from reflection groups. This is joint work with Jingyin Huang.

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1. 2026
3. Dynamics

Interval maps mimicking circle rotations — Fryderyk Falniowski <falniowf@uek.krakow.pl>

We investigate the dynamics of maps of the real line whose behavior on an invariant interval is close to a rational rotation on the circle. We focus on a specific two-parameter family, describing the dynamics arising from models in game theory, mathematical biology and machine learning. If one parameter is a rational number, k/n, with k, n coprime, and the second one is large enough, we prove that there is a periodic orbit of period n. It behaves like an orbit of the circle rotation by an angle 2 π k/n and attracts trajectories of Lebesgue almost all starting points. We also discover numerically other interesting phenomena.

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1. 2024
3. STDC2024-CT

Inverse Limits of Finite Path Graphs — Haley Pavlis <hjp0013@auburn.edu>

The author defines the graph topology for finite graphs. We discuss the properties of a continuous map between graphs and properties of a traditional inverse limit of graphs. Most importantly, that a traditional inverse limit of finite path graphs is non-Hausdorff. We introduce a generalized inverse limit, where the first space is a metric arc and all other spaces are finite path graphs. Using the Bucket Handle continuum as an example, a technique is shown for constructing a generalized inverse limit, where the first space is a metric arc and the others are finite path graphs, that is homeomorphic to a traditional inverse limit of Hausdorff arcs. Using crooked chains, we construct and analyze a non-Hausdorff hereditarily indecomposable continuum. This continuum has some interesting properties, which will be discussed. Ongoing research is discussed and open problems stated.

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1. 2024
3. STDC2024-CT

Inverse limits with Markov set-valued functions — Teja Kac <teja.kac1@um.si>

We introduce a new concept of Markov-type set-valued functions on trees allowing the graphs to be $2$-dimensional. Additionally, we present Markov set-valued functions on compact metric spaces. We establish the conditions under which two inverse limits of inverse sequences of trees or compact metric spaces are homeomorphic. This is joint work with Iztok Banič and Matevž Črepnjak, both University of Maribor.

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1. 2026
3. GeoTop

Isotopy versus Equivariant Isotopy — Trent Lucas <trentl1@uci.edu>

Given a finite group action on a manifold, we discuss the following question: if two equivariant diffeomorphisms are isotopic, must they be equivariantly isotopic? In the case of closed hyperbolic surfaces, a remarkable theorem of Birman and Hilden says that the answer is “yes”: isotopy implies equivariant isotopy. By contrast, we show that in dimensions three and higher, there are many diffeomorphisms which are isotopic but not equivariantly isotopic. We will explain the new obstructions that arise in higher dimensions, as well as some applications and further questions that don’t arise in the world of surfaces.

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1. 2025
3. Continua

Knaster continua in the plane — Ana Anusic <ana.anusic@fer.unizg.hr>

We show that for every Knaster continuum X, and every countable set C of composants of X, there exists a planar embedding of X in which the whole set C is accessible. I will also show that some of these embeddings can be done in dynamically significant way by using a generalization of Barge-Martin construction. This is a joint work with Logan Hoehn.

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1. 2024
3. STDC2024-DS

Laminations to Julia Sets — Brittany Burdette <bburdette@lander.edu>

This talk with discuss a method of finding Julia sets from particular laminations. We use Mathematica and Matlab to model and solve a system of equations that represent the lamination in order to find the unique corresponding Julia set. Issues surrounding this method will also be discussed.

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1. 2026
3. GeoGT
5. Plenaries

Large-scale geometry of right-angled Coxeter groups — Pallavi Dani <pdani@math.lsu.edu>

Right-angled Coxeter groups form an extremely accessible, yet remarkably rich class of objects in geometric group theory. They are defined by simple presentations: they are generated by involutions, with the only additional relations requiring certain pairs of generators to commute. Despite this elementary definition, they display an extraordinary range of geometric behaviors. Consequently, they have played a crucial role in the field, as a source of illuminating examples and counterexamples and as a testing ground for conjectures. In this talk, I will survey recent progress in understanding their large-scale geometry, focusing in particular on questions of quasi-isometry and commensurability. Along the way, I will illustrate some of the main tools and techniques used for establishing such results, many of which are applicable in more general settings.

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1. 2025
3. GeoGT

Latent symmetry of graphs and stretch factors in Out(Fn) — Paige Hillen <paigehillen@ucsb.edu>

Given an irreducible element of Out($F_n$), there is a graph and an irreducible "train track map" on this graph, which induces the outer automorphism on the fundamental group. The stretch factor of an outer automorphism measures the asymptotic growth rate of words in $F_n$ under applications of the automorphism, and appears as the leading eigenvalue of the transition matrix of such a train track representative. I'll present work showing a lower bound for the stretch factor in terms of the number of edges in the graph and the number of folds in the fold decomposition of the train track map. Moreover, in certain cases, a notion of the latent symmetry of a graph G gives a lower bound on the number of folds required for any irreducible train track map on G. I'll use this to classify all single fold train track maps.

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1. 2025
3. GeoTop

Lefschetz fibrations with infinitely many sections — Seraphina Eun Bi Lee <seraphinalee@uchicago.edu>

A Lefschetz fibration $M^4 \to S^2$ is a generalization of a surface bundle which also allows finitely many nodal singular fibers. The Arakelov--Parshin rigidity theorem implies that holomorphic Lefschetz fibrations of genus $g \geq 2$ admit only finitely many holomorphic sections. In this talk, we will show that no such finiteness result holds for smooth or symplectic sections by giving examples of genus-$g$ ($g \geq 2$) Lefschetz fibrations with infinitely many homologically distinct sections. This is joint work with Carlos A. Serván.

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1. 2025
3. GeoGT

Left-invariant Riemannian distances on higher-rank Sol-type groups. — Daniel Levitin <dlevitin@wisc.edu>

Describing the coarse geometry of solvable groups is one of the major projects of geometric group theory. One solvable group whose geometry is well-understood is Sol, a rank-1 group foliated by two families of hyperbolic planes. More generally, Le Donne, Pallier, and Xie recently described the geodesics in Sol-type groups, which are the rank-1 solvable groups foliated by a pair of negatively-curved spaces. Leveraging this description, they show that all left-invariant Riemannian distances on a Sol-type group are roughly similar. In this talk, I will describe the coarse geometry of the broader class of higher-rank Sol-type groups, and discuss my generalization of Le Donne-Pallier-Xie's result to certain distances on these groups.

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1. 2024
3. STDC2024-Semi

Leighton’s Property of X_{m,n} — Maya Verma <maya.verma-1@ou.edu>

In 1982, Leighton proved that any two finite graphs with a common cover admits a finite sheeted common cover. In this talk, I will introduce the combinatorial model X_{m,n} for Baumslag-Solitar group BS(m,n), and classify for which pairs of integers (m,n) the Leighton's theorem can be extended to the orbit space of covering actions on X_{m,n}.

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1. 2024
3. STDC2024-GGT

Leighton’s property for $X_{m,n}$ — Maya Verma <maya.verma-1@ou.edu>

In 1982, Leighton proved that any two finite graphs with a common cover admit a finite sheeted common cover. In this talk, I will introduce the combinatorial model $X_{m,n}$ for the Baumslag-Solitar group BS(m,n), and classify for which pairs of integers (m,n) Leighton's theorem can be extended to the orbit space of covering actions on $X_{m,n}$.

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1. 2025
3. Applied

Letter Insertion Homology and the Complexity of Word Sets: A Topological Approach to DNA Mutation and Repair — Francisco Martinez Figueroa <fmartinezfigueroa@usf.edu>

When studying mechanisms of DNA repair, short mutations often arise at the repair site, frequently manifesting as the insertion of short nucleotide sequences from the alphabet {A, C, G, T}. Each of these insertions occurs across millions of DNA molecules, generating a set of short words with varying frequencies. Our goal is to identify a suitable mathematical object to analyze these word sets and distinguish patterns across different experimental conditions. In this talk, we introduce the Insertion Chain Complex, a higher-dimensional generalization of insertion graphs, where homology serves as a measure of the complexity of a set of words. We present its construction, fundamental properties, and applications to biological data. In our case study, we analyze data from human cells in which DNA breaks were induced and the repaired sequences were sequenced. Our findings demonstrate that counting the highest-dimensional cells in these insertion complexes effectively distinguishes between different break locations.

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1. 2026
3. Continua

Local Variations of Shadowing — Ellie Stephens <ellie_stephens2@baylor.edu>

It is known that under the assumption of chain transitivity, shadowing is equivalent to other, weaker variations of shadowing. For example, a sequence of points in a continuum may act as a pseudo-orbit only on a thick set. We know that such a sequence can be shadowed on a different thick set under the assumption of chain transitivity and shadowing, but we lose information about where the pseudo-orbit begins. To address this, we study a form of shadowing in which the pseudo-orbit is shadowed on a thick set $T \subseteq \mathbb N$ such that $1 \in T$. We discuss the relationship of this form of shadowing with the standard shadowing property in the context of dynamical systems on continua.

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1. 2026
3. Applied & Data

Lower-bounding the Gromov-Hausdorff Distance Between Balls — Kushagri Sharma <kushagrisharma@ufl.edu>

We lower bound the Gromov-Hausdorff distance between Euclidean unit balls of different dimensions, $d_{GH}(B^m,B^n)$ for $m>n$. This is significant because the standard persistent homology lower bound is zero, since all balls possess trivial persistent homology. Our most powerful approach to lower bound the Gromov--Hausdorff distance between Euclidean unit balls of different dimensions leverages the Borsuk-Ulam theorem. We exploit the fact that any continuous map between a sphere and a ball of appropriate dimensions must identify antipodal points. This yields a positive metric distortion and a computable lower bound.

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1. 2025
3. Plenary

Mahavier products and Mahavier dynamical systems — Iztok Banic <iztok.banic@um.si>

During the pandemic, Judy Kennedy and I, later joined by Goran Erceg, began investigating the dynamics of closed relations in dynamical systems, which we termed CR-dynamical systems. With travel restrictions in place, we established regular online meetings to collaborate on this research. Our initial focus was on fixed-point problems from the perspective of closed relations, which led us to explore broader dynamical properties and ultimately to introduce Mahavier dynamical systems. Despite being spread across different time zones--Judy in the US, Goran in Croatia, and I in Slovenia--we managed to coordinate meetings in the early evening for Goran and me, and at 1:30 PM for Judy. Since then, we have published numerous papers on Mahavier dynamical systems, with several more in progress. Once travel resumed, Goran and I visited Judy in the US twice, while Judy visited Slovenia and Croatia on many more ocations, allowing us to collaborate in person. While online meetings and screen-sharing have been invaluable, we recognize that nothing fully replaces in-person discussions. Our research has continued to gain momentum, and we are committed to furthering this long-term project. We believe our work is both fundamental and significant, and we remain excited about its potential. Along the way, we named our group the Topology Nerds, and later, Van Nall, Sina Greenwood, Rene Gril Rogina, Chris Mouron and Ivan Jeli\' c joined our efforts. In this talk, I will present an overview of the most important results achieved by the Topology Nerds group.

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1. 2026
3. GeoGT

Manifold models for hyperbolic graph braid groups — Saumya Jain <sjain15@lsu.edu>

Given a finite graph $\Gamma$, the associated *graph braid group* $B_n(\Gamma)$ is the fundamental group of the unordered $n$-point configuration space of $\Gamma$. Genevois classified which graph braid groups are Gromov hyperbolic and asked the question: When do these groups arise as $3$-manifold groups? In this talk, we give a partial answer for $B_3(\Theta_m)$ where $\Theta_m$ is the *generalized $\Theta$-graph*.

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1. 2025
3. Applied

Mapp(er)ing brain states using EEG data — Brittany Story <brittany.m.story.civ@army.mil>

There is a lot to be gained by using topological data analysis (TDA) in conjunction with domain knowledge. As an example, consider the task where one wants to cluster brain states based on the underlying neural activity. Electroencephalograms (EEGs) are a common tool used to investigate neural activity by detecting electrical signals through sensors affixed to the scalp. EEG is relatively easy to use and provides high temporal resolution. However, it has low spatial resolution and prone to contamination with artifacts of movement or signals from external sources. Thus, for tasks like clustering brain states, it is difficult to capture the underlying structure and connectivity of individual states from EEG data. TDA, specifically the Mapper algorithm, has been used successfully in these types of problem spaces to pull important and relevant information from datasets. But, when applied directly to EEG data, Mapper does not reveal any structure or information. Luckily, there is a plethora of research and tools that have been developed to process and examine EEG data. Specifically, researchers have found that looking at the signal in the frequency domain can often provide insight into the neural activity. As such, we use the power spectral density paired with Mapper to create MapperEEG (MEEG). MEEG is neuroscience-infused topological tool that can cluster brain states without any pre-labeling or prior knowledge. In this talk, we will illustrate the importance of using prior domain knowledge within the EEG context, introduce the MEEG algorithm as an example of combining domain knowledge and TDA, and demonstrate its use on clustering brain state during a teaming task.

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1. 2024
3. STDC2024-GGT

Mapping Class Groups of Surfaces with Noncompact Boundary — Ryan Dickmann <rdickmann3@gatech.edu>

We will talk about the widely unknown classification of general surfaces due to Brown and Messer. Then we will discuss how the classification was used to get general results about the mapping class groups of orientable surfaces. In particular, we classified the automatically continuous pure mapping class groups over all orientable surfaces.

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1. 2024
3. STDC2024-GTop

Mapping class group actions on 3-manifolds — Bena Tshishiku <bena_tshishiku@brown.edu>

For a surface S, Thurston asked if the natural surjection Homeo(S) → π_0 Homeo(S) splits, i.e. if there a natural action of the mapping class group Mod(S):= π_0 Homeo(S) on S. Markovic showed that no such action exists. On the other hand, there is a natural action of Mod(S) on the unit tangent bundle of S. More generally, for a 3-manifold M that fibers as a circle bundle over S, there is natural surjection Homeo(M) → Mod(S). We study when this surjection splits. This is joint work with Lei Chen and Alina al Beaini.

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1. 2024
3. STDC2024-Semi

Mapping class group of low complexity subshifts — Kitty Yang <kyang2@unca.edu>

Given a subshift $(X,\sigma)$, the mapping class group $\mathcal{M}(\sigma)$ is the group of self-flow equivalences of $(X,\sigma)$, up to isotopy. For a minimal shift, there is an embedding $\textrm{Aut}(X)/\langle \sigma \rangle \xhookrightarrow{} \mathcal{M}(\sigma)$, where $\textrm{Aut}(X)$ is the group of automorphisms. If $(X,\sigma)$ is conjugate to a primitive substitutive shift, then $\mathcal{M}(\sigma)$ is a finite extension of $\mathbb{Z}$, and under mild conditions, this finite group is precisely $\textrm{Aut}(X)/\langle \sigma \rangle$. We discuss more the general case when $(X,\sigma)$ is a minimal subshift of linear complexity, subject to a technical condition, and give some examples. This is joint work with Scott Schmieding.

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1. 2026
3. GeoTop

Mapping class groups and Freudenthal compactifications of infinite type surfaces — Jeremy Brazas <jbrazas@wcupa.edu>

Let $\textbf{MCG}(X)$ denote the group of isotopy classes of self-homeomorphisms of a space $X$. When $S$ is an orientable infinite type surface $S$ with no planar ends and without boundary, the extended mapping class group $\textbf{MCG}(S)$ is isomorphic to $\textbf{MCG}\left(\overline{S}\right)$ where $\overline{S}$ is the Freudenthal compactification of $S$. Using this identification, it follows that $\textbf{MCG}(S)$ canonically embeds into $\text{Out}\left(\pi_1\left(\overline{S}\right)\right)$. It remains open if $\textbf{MCG}(S)$ is isomorphic to $\text{Out}\left(\pi_1\left(\overline{S}\right)\right)$ in the spirit of the Dehn-Neilsen-Baer Theorem. A clear difficulty is the fact that $\overline{S}$ is not locally simply connected and $\pi_1\left(\overline{S}\right)$ is uncountable and not free. In this talk, we will show that $\overline{S}$ is the quotient of $\mathbb{D}^2$ by a countable edge-pairing on $\mathbb{S}^1$. This structural decomposition implies that $\overline{S}$ may constructed by attaching a single 2-cell to a one-dimensional Peano continuum. Using established technology for dealing with fundamental groups of one-dimensional Peano continua, we show that $\pi_1\left(\overline{S}\right)$ is the free product with amalgamation of two locally free groups along an infinite cyclic group. We also show that every automorphism $\phi:\pi_1\left(\overline{S}\right)\to\pi_1\left(\overline{S}\right)$ is induced by a continuous map $f:\overline{S}\to \overline{S}$ that restricts to a homeomorphism on the end set $\overline{S}\backslash S$.

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1. 2025
3. Dynamics

Maximal Pattern Complexity for General Alphabets — Casey Schlortt <casey.schlortt@du.edu>

Maximal pattern complexity was introduced by Teturo Kamae and Luca Zamboni in 2002 as a way to link word complexity and sequence entropy. In this same paper, they introduced the idea of a pattern Sturmian over two letters, an aperiodic sequence with the lowest possible maximal pattern complexity on a two letter alphabet. In this talk, we will introduce some established results about sequences with low maximal pattern complexity and some new results extending the understanding of sequences of low maximal pattern complexity on larger alphabets.

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1. 2024
3. STDC2024-STT

Maximal quotients of extremally disconnected flows via discrete group actions with respect to coarser group topology — Dana Bartosova <dbartosova@ufl.edu>

We describe how to obtain a maximal quotient flow of a flow of a discrete group on an extremally disconnected space when we equip the group with a non-discrete topology. This generalized such description previously done for special types of flows, namely the greatest ambit and the Samuel compactification.

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1. 2025
3. Dynamics

Measures of maximal entropy on coded shift spaces — Christian Wolf <cwolf@ccny.cuny.edu>

In this talk, we present results about the uniqueness of measures of maximal entropy on coded shift spaces. A coded shift space is defined as the closure of all bi-infinite concatenations of words from a fixed countable generating set. We derive sufficient conditions for the uniqueness of measures of maximal entropy and equilibrium states of Hoelder continuous potentials based on the partition of the coded shift into its concatenation set (sequences that are concatenations of generating words) and its residual set (sequences added under the closure). We also discuss flexibility results for the entropy on the concatenation and residual sets. Finally, we present a local structure theorem for intrinsically ergodic coded shift spaces. This shows that our results apply to a larger class of coded shift spaces compared to previous works by Climenhaga, Climenhaga and Thompson, and Pavlov. The results presented in this talk are joint work with Tamara Kucherenko and Martin Schmoll.

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1. 2024
3. STDC2024-Semi

Metric big Ramsey degrees — Noe de Rancourt <nderancour@univ-lille.fr>

Distortion problems, from Banach space geometry, ask about the possibility of distorting the norm of a Banach space in a significant way on all of its subspaces. Big Ramsey degree problems, from combinatorics, are about proving weak analogues of the infinite Ramsey theorem in sets carrying structure. Both topics come back to the seventies and are still not well understood. While their motivations are quite disjoint, both problems share a surprisingly similar flavour. In a ongoing work with Tristan Bice, Jan Hubička and Matěj Konečný, as a step forward towards the unification of those two topics, we developped an analogue of big Ramsey degrees adapted to the study of metric structures (metric spaces, Banach spaces...). Those metric big Ramsey degrees are compacts metric spaces which are invariants associated to certain monoid actions by isometry, quantifying their default of Ramseyness. We were able to prove the existence of big Ramsey degrees for certain classical metric structures and in some cases, to give an explicit description of them ; it also seems that some classical invariants from topological dynamics can be represented as big Ramsey degrees. In this talk, I will present this theory, illustrate it on concrete examples (the Urysohn sphere and the Banach space $\ell_\infty$) and give an overview of its motivations and potential applications (to Banach space theory, Ramsey theory and dynamics).

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1. 2025
3. Applied

Metric thickenings of Vietoris-Rips complexes — Alexandre Karassev <alexandk@nipissingu.ca>

Vietoris-Rips complexes play an important role in geometric topology, geometric group theory, and topological data analysis. For a given scale parameter $r>0$ and a metric space $X$, a Vietoris-Rips complex, $\mathrm{VR(}X,r)$, is defined as a simplicial complex with the vertex set $X$, and so that the simplices are finite collections of points from $X$ of diameter $< r$. One of the main difficulties in working with Vietoris-Rips complexes is that $\mathrm{VR}(X,r)$ is not metrizable unless $X$ is discrete. Moreover, the space $X$, in general, cannot be viewed as naturally embedded in $\mathrm{VR} (X,r)$. To remedy these problems, one can consider so-called metric thickening $\mathrm{VR}^m(X,r)$ of $\mathrm{VR}(X,r).$ To this end, we can view $\mathrm{VR}(X,r)$ as a set of all finitely supported measures with diameter of support $ < r$, and endow it with the Wasserstein metric. The main focus of this talk will be on the relation between the homotopy types of $\mathrm{VR} (X,r)$ and $\mathrm{VR}^m(X,r).$ A recent result by Gillespie implies that $\mathrm{VR}(x,r)$ and $\mathrm{VR}^m(X,r)$ are weekly homotopy equivalent. Therefore, to conclude that they are homotopy equivalent it is sufficient to show that $\mathrm{VR}^m(X,r)$ is an ANR. It has been previously demonstrated by Adams, Frick, and Virk that $\mathrm{VR}^m(X,r)$ is locally contractible. Using different method, we prove that $\mathrm{VR}^m(X,r)$ is strongly locally contractible for a compact metric space $X.$ We also show that if such X is finite-dimensional then $\mathrm{VR}^m(X,r)$ is an ANR. (Note: this is a joint work with Henry Adams and Ziga Virk).

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1. 2024
3. STDC2024-DS

Metrical limit theorems for maximal digits in complex continued fraction expansions — Maxim Kirsebom <maximkirsebom@gmail.com>

Continued fractions have long been an object of interest to both number theorists and dynamicists. In the 1970's and 80's great progress was made on understanding metrical properties of continued fractions, i.e. measure-theoretic properties. A particular focus was on the the maximal digits of continued fractions and their properties. In this talk I will discuss some of these results including an extreme value law proved by Galambos and a Poisson Law by Iosifescu. I will also discuss some recent developments in the field, primarily generalisations of these results to complex continued fractions.

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1. 2026
3. GeoGT

Metrizability of Furstenberg boundaries — Sumun Iyer <sumuni@andrew.cmu.edu>

Let G be a Polish group. A G-flow is a continuous action of G on a compact Hausdorff space. G is amenable if every G-flow has an invariant probability measure. G has metrizable universal minimal flow if every G-flow contains a metrizable G-flow. We consider the property of G having a metrizable Furstenberg boundary. This is a common weakening of amenability and having metrizable universal minimal flow. We prove a characterization of G having metrizable Furstenberg boundary in the spirit of Kechris-Pestov-Todorcevic, Bartosova, Moore, and Zucker. We show mapping class groups of infinite type surfaces never have a metrizable Furstenberg boundary. This strengthens a theorem of Long that such groups are not amenable. This is joint work with George Domat and Forte Shinko.

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1. 2024
3. STDC2024-GGT

Minimal surface entropy for asymptotically cusped metrics in 3-manifolds — Franco Vargas Pallete <franco.vargaspallete@yale.edu>

In this talk we will discuss how the minimal area of almost Fuchsian subgroups (more precisely, their asymptotic growth) of a Kleinian group detects the hyperbolic metric under pinched curvature conditions. This is based on upcoming joint work with Ruojing Jiang.

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1. 2024
3. STDC2024-DS

Minimal zero entropy subshifts are unrestricted along a sparse set — Ronnie Pavlov <rpavlov@du.edu>

A recent polynomial version of the celebrated Sarnak's conjecture asked whether, given a nonlinear polynomial $p \in \mathbb{Z}[x]$, zero entropy minimal topological dynamical system $(X,T)$, $f \in C(X)$, and $x_0 \in X$, the sequence $f(T^{p(x)} x_0)$ is uncorrelated with the Mobius function $\mu$. This conjecture is false, and has been refuted in two recent works with interesting and somewhat difficult constructions. However, we can use a simple symbolic construction to prove the following: when $(k_n)$ has zero Banach density, then not only may the sequence $f(T^{k_n} x_0)$ be correlated with $\mu$, there are actually no restrictions on the sequence whatsoever.

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1. 2026
3. GeoTop

Monodromy of curves in a simply connected surface (joint with Nick Salter) — Ishan Banerjee <banerjee.238@osu.edu>

We compute the image of the monodromy representation (as a subgroup of the mapping class group) associated to a complete linear system of curves in a simply connected smooth projective surface X under some ampleness hypotheses. It turns out to always be of finite index.

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1. 2024
3. STDC2024-STT

More Trivial and non-Trivial autohomeomorphisms of $\mathbb{N}^*$ — Alan Dow <adow@charlotte.edu>

We investigate the situation regarding autohomeomorphisms of $\mathbb{N}^*$, primarily in the Mathias model.

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1. 2025
3. Continua

More on the hyperspace of non-cut subcontinua of a continuum — Jorge E. Vega <vegacevedofcfm@fcfm.buap.mx>

We give conditions under which the Vietoris hyperspace of non-cut subcontinua is the same as the hyperspace of all subcontinua. Also, we give in the class of finite graph conditions under which the hyperspace of non-cut subscontinua is connected. This is joint work with A. Illanes and V. Martínez-de-la-Vega.

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1. 2026
3. GeoTop

Morse theory on moduli of curves — Changjie Chen <changjie.chen@umontreal.ca>

In 1997, Sarnak conjectured that the determinant of the Laplacian is a Morse function on the space of unit area Riemannian metrics on a given real surface, and hence induces a Morse function on its moduli space. Meanwhile, the systole function, defined as the length of a shortest essential closed geodesic with respect to the base Riemannian metric, is topologically Morse on the Teichmüller space of n-dimensional flat tori (due to Ash) and of Riemann surfaces of genus g with n marked points (due to Akrout), though it does not yield a classical Morse theory. In this talk, I will introduce a family of Morse functions, denoted sys_T, defined as weighted exponential averages of all geodesic-length functions, on the Deligne--Mumford compactification (M_{g,n} bar). These functions are compatible with the Deligne--Mumford stratification and the Weil--Petersson metric, and their critical points can be characterized by a combinatorial property named eutaxy. I will talk about the index gap theorem for sys_T and its homological consequences, in the form of a stability theorem for the homology of moduli spaces of stable curves. I will also briefly explain how sys_T connects to Sarnak’s conjecture.

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1. 2026
3. Applied & Data

Multi-parameter Čech complexes — Carl Ye <jye1@ufl.edu>

In "A Multicover Nerve for Geometric Inference" paper, Sheehy shows that filtering the barycentric decomposition of a Čech complex by the cardinality of the vertices recovers exactly the topology of k-covered regions among a collection of balls. We describe this construction and present ideas related to this.

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1. 2026
3. Applied & Data

MultiPersistence Topological Fusion with Vision Transformers for Skin Cancer Detection — Sayoni Chakraborty <sayoni.chakraborty@utdallas.edu>

Skin cancer is a common and potentially fatal disease where early detection is crucial, especially for melanoma. Current deep learning systems classify skin lesions well, but they primarily rely on appearance cues and may miss deeper structural patterns in lesions. We present TopoCon-MP, a method that extracts multiparameter topological signatures from dermoscopic images to capture multiscale lesion structure, and fuses these signatures with Vision Transformers using a supervised contrastive objective. Across three public datasets, TopoCon-MP improves in-distribution performance over strong pretrained CNN and ViT baselines, and in cross-dataset transfer, it maintains competitive performance. Ablations show that both multiparameter topology and contrastive fusion contribute to these gains. The resulting topological channels also provide an interpretable view of lesion organization that aligns with clinically meaningful structures. Overall, TopoCon-MP demonstrates that multipersistence-based topology can serve as a complementary modality for more robust skin cancer detection.

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1. 2025
3. Applied

Multiparameter landscapes for latent representations — Evgeniya Lagoda <evgeniya.lagoda@gmail.com>

Recent work by Wayland, Coupette, and Rieck (2024) proposes a method to characterize and compare the latent embedding spaces arising from machine learning models. Their method is based on persistent homology and allows variability and sensitivity analysis of various hyperparameter choices for these models. Inspired by this idea but focusing on the case of classification problems, we would like to develop tools for a similar analysis. In this talk, we define a variant of multiparameter persistence landscapes, which can be seen as a generalization of the definition in the recent work by Vipond (2020). For practical applications, we are interested in the landscapes that are defined over a poset that is a product of $\mathbb R$ and a subposet of an inclusion poset. We discuss the properties of this definition, the theoretical challenges, and future directions.

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1. 2025
3. GeoTop

Multiplane diagrams of surfaces in 4-space — Roman Aranda <jarandacuevas2@unl.edu>

Surfaces in 4-space can be described using tuples of b-string tangles called multiplane diagrams. In this talk, we will discuss local modifications for multiplane diagrams that affect the embedded surface in a controlled way. This talk will explore such operations in the context of bridge multisections. We show a uniqueness result for multiplane diagrams representing isotopic surfaces. If time permits, we will show that any n-valent graph with an n-edge coloring is the spine of a bridge multisection of an unknotted surface.

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1. 2026
3. GeoTop

Negatively Curved Einstein Metrics — Barry Minemyer <bminemyer@commonwealthu.edu>

Gromov and Thurston famously used hyperbolic branched cover manifolds to construct the first examples of manifolds which admit a pinched negatively curved metric, but do not admit any locally symmetric metric. Much more recently, Fine and Premoselli (n=4) and Hamenstadt and Jackel (n>4) proved that many of these hyperbolic branched covers admit negatively curved Einstein metrics. In this talk I will give an overview of these results and show how, in joint work with Lafont, we extended the construction of Fine and Premoselli to complex hyperbolic branched covers. This gives an explicit description of the first known negatively curved Kahler-Einstein metric on a manifold which does not admit a locally symmetric metric, whose existence was first proved by Guenancia and Hamenstadt.

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1. 2025
3. Dynamics

Neighborhood N-Shadowing — Ellie Stephens <ellie_stephens2@baylor.edu>

We define neighborhood $N$-shadowing property and discuss the relationship of this property to mixing sofic shifts. Specifically, we show all mixing sofic shifts over a finite alphabet have neighborhood 2-shadowing.

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1. 2024
3. STDC2024-CT

New embeddings of Knaster continuum in the plane — Ana Anusic <anaa@nipissingu.ca>

Given $n\in\mathbb{N}$, we show that there exists a planar embedding of Knaster continuum with $n$ (fully) accessible composants. This answers a question of Debski and Tymchatin from 1993. This is a joint work with Logan Hoehn.

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1. 2026
3. GeoTop
5. Plenaries

Nielsen realization problems in the Zimmer program — Bena Tshishiku <bena_tshishiku@brown.edu>

The Zimmer program seeks to classify smooth actions of arithmetic groups, like SL(n,Z), on compact manifolds. Separately, the Nielsen realization problem asks when a subgroup of a mapping class group Mod(M) can be realized by a group of diffeomorphisms of M. In many natural situations, the mapping class group is closely related to an arithmetic group, and the realization problem is tied to the Zimmer program. I will discuss examples of this connection and describe some recent results and open questions.

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1. 2026
3. Continua

Non-existence of a Common Model for a Class of Indecomposable Continua — Eiichi Matsuhashi <matsuhashi@riko.shimane-u.ac.jp>

In 1971, Bellamy proved that every continuum can be embedded in an indecomposable continuum as a retract. In 2017, together with Fukaishi, we showed that any continuum 𝑍 can be embedded as an open retract with Cantor set fibers in an indecomposable continuum, which is obtained as the closure of a countable union of topological copies of 𝑍. Building on this construction, together with Ortega, we investigate, for a fixed continuum 𝑍, the class of all indecomposable continua arising in this manner. We present the result that this class admits no common model, in the sense that there exists no single continuum admitting continuous surjections onto all members of the class. If time permits, we will also discuss other classes of continua that admit no common models.

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1. 2024
3. STDC2024-GGT

Non-hyperbolicity of single-isotopy-class fine curve graphs — Roberta Shapiro <shapirorh@gmail.com>

The fine curve graph of a surface is a graph whose vertices are essential simple closed curves in the surface and whose edges connect disjoint curves. Following a rich history of hyperbolicity in various graphs based on surfaces, the fine curve was shown to be hyperbolic by Bowden–Hensel–Webb. Given how well-studied the curve graph and the case of “up to isotopy” is, we ask: what about the part of the fine curve graph not captured by isotopy classes? In this talk, we introduce the result that the subgraph of the fine curve graph spanned by curves in a single isotopy class is not hyperbolic; indeed, it contains a flat of EVERY dimension. Joint work with Ryan Dickmann.

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1. 2024
3. STDC2024-CT

Non-metric Hereditarily Indecomposable Continua — Michel Smith <smith01@auburn.edu>

The author has shown techniques for producing non-metric hereditarily indecomposable continua. Examples are presented. However, attempts to generalize metric construction techniques yield situations in which hereditary indecomposability implies metrizability. We review the author's recent results regarding such situations. Open problems in the area are stated.

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1. 2026
3. Dynamics

Observable attractors and typical dynamics on the interval — Piotr Oprocha <oprocha@icloud.com>

In this talk we will compare three versions of attractors with large (in the sense of Lebesgue measure) basins of attraction: Milnor, statistical, and physical (in the sense of Ilyashenko). The emphasis will be put on typical continuous (i.e. in topology of uniform convergence) dynamical systems on the unit interval. We will go beyond what is known so far about characteristics of these attractors. We will also explain why in the typical family the attractors depends continuously on the map with respect to the Hausdorff metric. The talk is based on joint work with Magdalena Forys-Krawiec, Jana Hantakowa and Michal Kowalewski

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1. 2024
3. STDC2024-STT

On Arhangel'skii's inequality — Ivan Gotchev <gotchevi@ccsu.edu>

In 1969, Arhangel'skiĭ proved that if $X$ is a Hausdorff space, then $|X|\le 2^{\chi(X)L(X)}$, where $\chi(X)$ is the character and $L(X)$ is the Lindelöf degree of $X$. Since then it has been an open question if his inequality is true for every $T_1$-space $X$. In 2013, we proved that if $X$ is a $T_1$-space, then $|X|\le nh(X)^{\chi(X)L(X)}$, where $nh(X)$ is the non-Hausdorff number of $X$. In that way we were able to positively answer this question for every $T_1$-space for which $nh(X)\le 2^{\chi(X)L(X)}$, and, in particular, when $nh(X)$ is not grater than the cardinality of the continuum. A simple example shows that our inequality is not always true for $T_0$-spaces. Arhangel'skiĭ and Šapirovskiĭ strengthened Arhangel'skiĭ's inequality in 1974 by showing that if $X$ is a Hausdorff space, then $|X|\le 2^{t(X)\psi(X)L(X)}$, where $t(X)$ is the tightness and $\psi(X)$ is the pseudocharacter of $X$. In this talk we will show how Arhangel'skiĭ--Šapirovskiĭ's inequality, and therefore, Arhangel'skiĭ's inequality, could be extended to be valid for all topological spaces.

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1. 2024
3. STDC2024-STT

On Uniformly Continuous Surjections Between Function Spaces — Ali Emre Eysen <aemreeysen@hotmail.com>

Joint work with V. Valov We consider uniformly continuous surjections between $C_p(X)$ and $C_p(Y)$ (resp, $C_p^*(X)$ and $C_p^*(Y$)) and show that if $X$ has some dimensional-like properties, then so does $Y$. In particular, we prove that if $T:C_p^*(X)\to C_p^*(Y)$ is a continuous linear surjection, then $\dim Y=0$ provided $\dim X=0$. This provides a partial answer to a question raised by Kawamura-Leiderman.

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1. 2025
3. Plenary

On a generalization of the Ingram conjecture — Matevž Črepnjak <matevz.crepnjak@um.si>

After Ingram's conjecture was proven, new questions arose concerning tent functions. One of them is to identify all skew tent maps with their top vertices in the unit square whose (generalized) inverse limits are homeomorphic. In particular, it is interesting to identify the regions of top vertices in the unit square for which inverse limits are homeomorphic. In this talk, we revisit the skew tent maps problem and give some partial results.

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1. 2024
3. STDC2024-DS

On block gluing property in Hom shifts — Piotr Oprocha <piotr.oprocha@osu.cz>

Hom shifts form a class of multidimensional shifts of finite type (SFT) where adjacent symbols must be neighbors in a fixed finite undirected simple graph $G$. This talk is about gluing distance in Hom shifts: given two $n x n$ admissible partial blocks, how far do they need to be so that we can glue them together (i.e embed) in a larger admissible block. The gluing gap measures how far any two square patterns of size $n$ can be glued, which has a clear analogy with gap fo specification property in one-dimensional subshifts. We prove that the gluing gap either depends linearly on $n$ or is dominated by $log(n)$. It is clear that there are Hom shift, where gluing gap is bounded by constant, thus independent of $n$. To support our results, we find a Hom shift with gap ${\Theta}(log(n))$, infirming a conjecture formulated by R. Pavlov and M. Schraudner. This talk is based on a joint work with Silvere Gangloff and Benjamin Hellouin de Menibus

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1. 2025
3. Set-Theoretic

On cardinal inequalities for topological spaces — Ivan Gotchev <gotchevi@ccsu.edu>

In this talk some recent results about cardinal inequalities for topological spaces will be presented and some open questions will be discussed.

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1. 2025
3. Set-Theoretic

On discrete and disjoint shrinking properties — Vladimir Tkachuk <vvtmdf@gmail.com>

A space $X$ has the disjoint (discrete) shrinking property if for any family $\{U_n: n\in\omega\}$ of non-empty open subsets of $X$ there exists a disjoint (discrete) family $\{V_n: n\in\omega\}$ of non-empty open sets such that $V_n \subset U_n$ for every $n\in\omega$. We present a topological equivalent of the disjoint shrinking property in general spaces and apply it to characterize the disjoint shrinking property in topological groups and locally convex spaces.

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1. 2025
3. Set-Theoretic

On expansive homeomorphisms on a quasi-uniform space — Olivier Olela-Otafudu <olivier.olela-otafudu@ul.ac.za>

In this talk, we present the concepts of expansive homeomorphisms in the context of quasi-uniform spaces. We continue with our analysis on expansive homeomorphisms by extending the results from quasi-metric spaces to quasi-uniform spaces. It turns out that an expansive homeomorphism on a quasi-uniform space is also an expansive homeomorphism on its induced quasi-uniformity but the converse does not hold in general. We show that if a homeomorphism on a quasi-uniform space is expansive then the quasi-uniform space is always a Kolmogorov space. Moreover, we generalize the concept of expansive measures in the sense of Morales and Sirvent to quasi-uniform spaces point of views.

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1. 2024
3. STDC2024-DS

On extending Cantor subsystems on dendrites — Jakub Tomaszewski <tomaszew@agh.edu.pl>

During the talk we will focus on surjective Cantor systems. Each such system can be easily embedded in the Gehman dendrite, as its set of endpoints is a Cantor set. We will show that for each such embedding there exists a mixing map of the dendrite such that the endpoints' subsystem is conjugate to the Cantor system of choice. The main tool to obtain this result follows from Shimomura's method of approximating the dynamics on zero dimensional systems by analysing the dynamics of coverings of the underlying space. We will discuss the dynamical properties of the constructed map. The talk is based on joint work with Dominik Kwietniak and Piotr Oprocha.

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1. 2024
3. STDC2024-GGT

On horofunction boundaries of homogeneous groups — Nate Fisher <nfisher6@wisc.edu>

In this talk, I will define and motivate the use of horofunction boundaries to study groups. I will discuss some examples which demonstrate interesting properties of the horofunction boundary and share new results about the horofunction boundaries of homogeneous groups.

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1. 2026
3. General & ST

On hyperconvexity in partial metric spaces — Dariusz Bugajewski <ddbb@amu.edu.pl>

The notion of hyperconvexity of metric spaces was introduced by Aronszajn and Panitchpakdi in 1956 in their study of extensions of uniformly continuous mappings between metric spaces. From the topological point of view, a hyperconvex space is an absolute retract via a nonexpansive retraction. By the theorem of Nachbin and Kelley, hyperconvex real Banach spaces can be treated as Stonian spaces C(K) of all real-valued continuous functions on extremally disconnected compact Hausdorff spaces K. On the other hand, the notion of a partial metric space was introduced by Matthews in 1994. He showed, roughly speaking, how metric-like tools can be extended to non-Hausdorff topologies, and he also indicated some applications of this class of spaces in the study of the denotational semantics of programming languages. Further applications of partial metrics can also be found in the geometry of Banach spaces. In this talk, we present several different approaches to defining hyperconvexity in partial metric spaces. In particular, we show that the analogue of the Aronszajn–Panitchpakdi notion of hyperconvexity fails to possess certain key properties present in the classical metric setting. Finally, we outline some perspectives for further research.

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1. 2025
3. Continua

On increasing and persistent Whitney properties — Hugo Villanueva <hugo.villanueva@udlap.mx>

In 2009, increasing Whitney properties were defined by F. Orozco and give results and examples of topological increasing Whitney properties. In this talk we define Whitney persistent and locally Whitney persistent properties. We present results and examples of continua and topological properties to establish relations between these concepts and those of Whitney and increasing Whitney properties. This is a joint work with José Gerardo Ahuatzi-Reyes and Norberto Ordoñez-Ramírez.

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1. 2024
3. STDC2024-CT

On open and monotone mappings — Lex Oversteegen <overstee@uab.edu>

In 1972 A.R. Stralka asked if every open and monotone retraction from a dendroid to an arc is the identity map. In this talk we will review some old results, including a solution to this problem, and connect these results to more recent developments.

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1. 2025
3. Set-Theoretic

On some Selection Principles and Games involving Countable Networks — Davide Giacopello <dagiacopello@unime.it>

We introduce new selection principles involving networks, namely, M-nw-selective, R-nw-selective, and H-nw-selective. These spaces represent a strengthening of both M-separability, R-separability, and H-separability, as well as the Menger, Rothberger, and Hurewicz properties. We also define and investigate two new games: the R-nw-selective game and the M-nw-selective game, which arise naturally from their corresponding selection principles. We give consistent results, and we define trivial R-, H-, and M-nw-selective spaces the ones with countable netweight and cardinality and weight strictly less than $\text{cov}(\mathcal{M})$, $\mathfrak{b}$, and $\mathfrak{d}$, respectively. We establish that spaces with cardinalities greater than $\text{cov}(\mathcal{M})$, $\mathfrak{b}$, and $\mathfrak{d}$ fail to possess the R-, H-, and M-nw-selective properties, respectively. Non-trivial examples, therefore, should eventually have weight greater than or equal to these small cardinals. Using forcing methods, we construct consistent countable non-trivial examples of R-nw-selective and H-nw-selective spaces. Finally, we study relations between nw-selective properties and a strong version of the HFD property.

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1. 2026
3. General & ST
5. Plenaries

On some new star selection principles among covering properties and separability — Davide Giacopello <davide.giacopello@unime.it>

We present some properties recently introduced by Bal and Bhowmik: the $R$-, $H$-, and $M$-star Lindelöfness. These properties are defined via selection principles involving the star operator and lie between covering properties (in particular, star-covering properties) and certain selective strengthenings of separability. This dual perspective leads to several implications and connections among known properties, some of which we present. Additionally, we provide some examples. In particular, we prove that there exists a Tychonoff M-star Lindelöf space of cardinality $\frak{c}$ which is not $R$-star Lindelöf answering a question posed by Bal and Bhowmik.

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1. 2025
3. Dynamics

On the Equivalence of Equilibrium and Freezing States — Evans Hedges <evans.hedges@du.edu>

This talk is concerned with freezing phase transitions in general dynamical systems. A freezing phase transition is one in which, for a given potential $\phi$, there exists some inverse temperature $\beta_0 > 0$ such that for all $\alpha, \beta > \beta_0$, the collection of equilibrium states for $\alpha \phi$ and $\beta \phi$ coincide. In this sense, below the temperature $1 / \beta_0$, the system "freezes" on a fixed collection of equilibrium states. We will provide an overview of this direction of study, and conclude with some novel results related to the obtainability of a given measure as a freezing state, as well as the fact that the collection of potentials that freeze is dense in $C(X)$ under certain conditions on the dynamical system.

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1. 2026
3. Dynamics

On the Holomorphic and Random Dynamics for some examples of higher rank Free Groups generated by Hénon type maps — Andres Quintero-Santander <aequinte@iu.edu>

We study the Holomorphic and Random Dynamics of some rank 2 free groups generated by two Hénon type maps. For these simply constructed examples we prove that the Fatou set is non-empty and that the stationary measures are supported on a compact set. With some further care this allows us to construct examples having no stationary measures. These examples illustrate the types of phenomena that may arise when studying holomorphic group actions on non-compact manifolds.

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1. 2026
3. Dynamics
5. Plenaries

On the Mandelbrot set and the MLC Conjecture — Dzmitry Dudko <dzmitry.dudko@stonybrook.edu>

The Mandelbrot set encodes the dynamical dependence of quadratic polynomials on a parameter. The MLC Conjecture (asserting that the Mandelbrot set is locally connected) is a rigidity property that yields a satisfactory topological description of the Mandelbrot set. In this talk, we describe the historical motivation for the conjecture, explain how it became a central topic in Renormalization Theory (analyzing first-return maps to small neighborhoods of special points), and outline some of the ideas behind the most recent advances toward MLC and related questions.

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1. 2025
3. Dynamics

On the existence of freezing phase transitions for lattice systems — Tamara Kucherenko <tkucherenko@ccny.cuny.edu>

We establish the existence of freezing phase transitions in the settings of multi-dimensional shift spaces. Precisely, given an arbitrary proper subshift $X$ of a d-dimensional shift space we explicitly construct a continuous potential $\phi$ such that for all $\beta$ above some critical value $\beta_c$ the equilibrium states of $\beta\phi$ are the measures of maximal entropy of $X$, whereas for $\beta$ below $\beta_c$ no equilibrium state of $\beta\phi$ is supported on $X$. This phenomenon is referred to as a freezing phase transition for potential $\phi$ with the motivation stemming from quasicrystal models in statistical physics. To contrast this result we establish sufficient conditions on the potential which guaranty that the system never freezes. This is a joint work with J.-R. Chazottes and A. Quas.

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1. 2026
3. GeoGT

Order-Preserving Braids via the Burau Representation — Jonathan Johnson <jcj055@shsu.edu>

I will discuss a new sufficient condition for when a braided link, a braid closure together with its braid axis, is bi-orderable meaning the fundamental group of its exterior admits an order invariant under both left and right multiplication. In 2006, Perron and Rolfsen provided a condition which ensures that an automorphism of a free group preserves a bi-order of the free group and shows that many fibered 3-manifolds are bi-orderable, including many exteriors of braided links. Recent work of Khanh Le and I provide another new criterion, via the Burau representation, for a free group automorphism to be order-preserving. Using the new criterion, we produce new examples of bi-orderable braided link groups including some examples produced from braids whose underlying permutation is a full cycle which answers in affirmative a question of Kin and Rolfsen. This work is partially supported by the NSF grant DMS-2213213.

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1. 2025
3. Plenary

Order-reversing maps on $\mathbb N^\ast$ and $\mathbb H^\ast$ — Will Brian <wbrian.math@gmail.com>

I will discuss two related questions concerning the two spaces in the title: the Čech-Stone remainder of the natural numbers $\mathbb N$, and the Čech-Stone remainder of the half-line $\mathbb H = [0,\infty)$. Both $\mathbb N$ and $\mathbb H$ are naturally ordered from left to right. These orders on $\mathbb N$ and $\mathbb H$ are reflected in their Čech-Stone remainders, in certain dynamical systems on $\mathbb N^\ast$ and in certain subcontinua of $\mathbb H^\ast$. Are these left-to-right aspects of $\mathbb N^\ast$ and $\mathbb H^\ast$ truly topological, or can either of the spaces be "reversed" via some self-homeomorphism?

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1. 2024
3. STDC2024-Workshops

Panel: The future of topology and dynamics meetings and publications — Steven Clontz <sclontz@southalabama.edu>

A panel of community members serving on the steering committees and editorial boards of the Spring Topology and Dynamics Conference series, the Summer Conference on Topology and its Applications series, and Topology Proceedings will discuss the state of their organizations and potential futures for our shared research infrastructure and community.

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1. 2026
3. Dynamics

Parabolic Implosion via Blaschke Product — Ricky Simanjuntak <rsimanju@iu.edu>

Classic theory of Parabolic Implosion deals with perturbation around parabolic point using Lavaurs theory. Here I will present a new approach using perturbation and rescaling limit of Blaschke product. As a consequence I will show a necessary and sufficient condition for continuity of Julia set around $z^2 + z$, allowing only movement within main hyperbolic component.

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1. 2024
3. STDC2024-Semi

Parameter space of symmetric cubic polynomials — FirstName LastName <selinger@uab.edu>

Since the space of all cubic polynomials is (complex) two-dimensional and thus too difficult to comprehend, we study a one-dimensional slice of it: the space of all cubic symmetric polynomials of the form $f(z)=z^3+\lambda^2 z$. Thurston has built a topological model for the space of quadratic polynomials $f(z)=z^2+c$ by introducing the notion of quadratic invariant laminations. In the spirit of Thurston’s work, we parametrize the space of cubic symmetric laminations and create a model for the space of cubic symmetric polynomials. This is a joint work with Alexander Blokh, Lex Oversteegen, Vladlen Timorin, and Sandeep Vejandla.

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1. 2025
3. GeoTop

Parametrized Legendrian Surgery — Eduardo Fernández <eduardofernandez@uga.edu>

Given a parametrized Legendrian $\Lambda$ in a contact manifold $(M, \xi)$, there is a well-defined operation called Legendrian surgery, which produces a new contact manifold $(M(\Lambda), \xi(\Lambda))$. The contactomorphism type of the surgered manifold depends only on the Legendrian isotopy class of the initial Legendrian. Given a loop of Legendrians $\Lambda_t$, it is also possible to realize a 1-parameter family of Legendrian surgeries. From this, we naturally obtain a bundle over the circle with fiber $(M(\Lambda), \xi(\Lambda))$. The non-triviality of the bundle depends on the contact isotopy class of a gluing contactomorphism, which we call the “Legendrian surgery contactomorphism.” Its contact isotopy class depends only on the homotopy class of the given loop of Legendrians within the space of parametrized Legendrians. The obvious realization problem is: which contactomorphisms of a given contact manifold are Legendrian surgery contactomorphisms? In this talk, I will address this question by showing that every formally trivial contactomorphism arises as a Legendrian surgery contactomorphism associated with a certain loop of Legendrians in some overtwisted contact manifold with controlled topology. As a consequence, in 3-dimensional contact topology, we will deduce the existence of formally contractible but non-contractible loops of loose Legendrians in every overtwisted contact 3-manifold. This is a joint work in progress with Fabio Gironella.

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1. 2025
3. GeoGT

Pattern preserving quasi-isometries in lamplighter groups — Beibei Liu <bbliumath@gmail.com>

In this talk, I will explore the interplay between aspects of the geometry and algebra of three families of groups of the form $B\rtimes Z$, namely Lamplighter groups, solvable Baumslag-Solitar groups and lattices in $SOL$. In particular we examine what kind of maps are induced on $B$ by quasi-isometries that coarsely permute cosets of the $Z$ subgroup. By the results of Schwartz(1996) and Taback(2000) in the lattice in $SOL$ and solvable Baumslag-Solitar cases respectively such quasi-isometries induce parallelogram preserving maps of $B$. We show that this is no longer true in the lamplighter case but the induced maps do share some features with parallelogram preserving maps. This is joint work with Dymarz, Macura and Morris-Wright.

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1. 2025
3. Dynamics

Percolation Theory and the Diversity of Cellular Automata on Groups — Felipe García-Ramos <felipegra@yahoo.com>

We will explain a connection between the diversity of cellular automata observable on a given countable group and the percolation threshold associated with the Cayley graphs of such groups. As a consequence, we show that Gilman's dichotomy holds for the endomorphism semigroup of a countable group if and only if the group is locally virtually cyclic.

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1. 2026
3. Continua

Period Bounds and Induced Systems in the Hyperspace of Continua in One Dimension — Domagoj Jelic <djelic@pmfst.hr>

Given a self-map $f$ of a compact metric space $X$, one can associate to it the induced mappings $\overline{f}$ and $\tilde{f}$ on the hyperspace $2^X$ of compact subsets of $X$ and on the hyperspace $C(X)$ of continua in $X$, respectively, both defined in a natural way. Within this framework, it is natural to investigate the relationship between individual and collective dynamics. In this talk, we address the following question. Let $f$ be a self-map of a topological tree $T$, and let $x$ be a periodic point of $f$ with period $p$. What are the possible periods of periodic points of $\left(C(T), \tilde{f}\right)$, that is, of periodic subtrees containing $x$? We then discuss the significance of this result for the study of further properties of the system $\left(C(T), \tilde{f}\right)$. In particular, using this result, we show that the induced system is always almost equicontinuous and we characterize its Birkhoff center. \emph{The talk is based on a joint work with Piotr Oprocha.}

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1. 2026
3. Continua

Persistent Recurrence and Inverse Limits of Unimodal Maps — Lori Alvin <lori.alvin@furman.edu>

Given a unimodal map, the recurrent critical point $c$ is reluctantly recurrent if there exists a $\delta > 0$ such that for every $\ell\in \mathbb{N}$ there is a backward orbit $\overline{x} = (x_{-\ell},\ldots, x_{-2},x_{-1},x)$ in $\omega(c)$ such that $B(x,\delta)$ has a monotonic pull-back along $\overline{x}$; otherwise we say that $c$ persistently recurrent. Given a unimodal map $f$ with an infinite kneading sequence, it is known that the collection of endpoints for the inverse limit space $\varprojlim \{[c_2,c_1],f \}$ is precisely the collection of folding points if and only if $c$ is persistently recurrent. We revisit this known result and also show that when $c$ is infinitely recurrent and longbranched, then it is not possible for $c$ to be persistently recurrent.

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1. 2025
3. Applied

Persistent cohomology operations and Gromov-Hausdorff estimates — Ling Zhou <zhouling0903@gmail.com>

We establish the foundations of the theory of persistent cohomology operations, derive decomposition formulas for wedge sums and products, and prove their Gromov–Hausdorff stability. We use these results to construct pairs of Riemannian pseudomanifolds for which the Gromov-Hausdorff estimates derived from persistent cohomology operations are strictly sharper than those obtained using persistent homology. This work is joint with Anibal M. Medina-Mardones.

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1. 2025
3. Dynamics

Phase transitions in the Potts model on Cayley tree. — Diyath Pannipitiya <dinepann@iu.edu>

The Ising model is one of the most important theoretical models in statistical physics, which was originally developed to describe ferromagnetism. A system of magnetic particles, for example, can be modeled as a linear chain in one dimension or a lattice in two dimensions, with one particle at each lattice point. Then each particle is assigned a spin $\sigma_i\in \{\pm 1\}$. The $q$-state Potts model is a generalization of the Ising model where each spin $\sigma_i$ may take on $q\geq 3$ number of states $\{0,\cdots, q-1\}$. Both models have temperature $T$ and an externally applied magnetic field $h$ as parameters. Many statistical and physical properties of the $q$-state Potts model can be derived by studying its partition function. This includes phase transitions as $T$ and/or $h$ are varied. The celebrated Lee-Yang Theorem characterizes such phase transitions of the $2$-state Potts model (the Ising model). This theorem does not hold for $q>2$. Thus, phase transitions for the Potts model as $h$ is varied are more complicated and mysterious. We give some results that characterize the phase transitions of the $3$-state Potts model as $h$ is varied for constant $T$ on the binary rooted Cayley tree. Similarly to the Ising model, we show that for fixed $T>0$ the $3$-state Potts model for the ferromagnetic case exhibits a phase transition at one critical value of $h$ or not at all, depending on $T$. However, an interesting new phenomenon occurs for the $3$-state Potts model because the critical value of $h$ can be non-zero for some range of temperatures. The $3$-state Potts model for the antiferromagnetic case exhibits phase transition at up to two critical values of $h$. The recursive constructions of the $(n+1)^{st}$ level Cayley tree from two copies of the $n^{th}$ level Cayley tree allow one to write a relatively simple rational function relating the Lee-Yang zeros at one level to the next. This allows us to use techniques from dynamical systems.

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1. 2025
3. Continua

Planarity of compactifications of R with arc-like remainder — Andrea Ammerlaan <ajammerlaan879@my.nipissingu.ca>

In 1972, Nadler and Quinn asked if for any arc-like continuum $X$, and point $x \in X$, there exists a plane embedding of $X$ in which $x$ is accessible. A continuum $X$ is arc-like if it can be expressed as an inverse limit on arcs and, if $X$ is in the plane $\mathbb{R}^2$, a point $x \in X$ is called accessible if there exists an arc $A \subset \mathbb{R}^2$ such that $A \cap X =$ {$x$}. The question was recently answered in the positive (AA, Anušić, Hoehn 2024). This talk will discuss some consequences of the result: if $X$ is an arc-like continuum, then any continuum which is the disjoint union of $X$ and a ray $R$, with cl$(R) \setminus R \subseteq X$, is embeddedable in the plane, as is any compactification of a line having remainder $X$. Joint work with Logan Hoehn.

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1. 2026
3. Continua

Plane continua, canals and dead ends — Rene Gril Rogina <rene.gril@um.si>

Given a continuum $X$ in the Euclidean plane, a canal of $X$ is a way of "approaching" the continuum from outside of $X$ or the bounded components of its complement. Often we search for simple dense canals, which are canals and also rays with $X$ as their remainder. While some things are known about planar continua with embeddings that admit such canals, there are still open questions on this topic. In this talk, we first define canals and then "dead ends", which are used in a construction to obtain new planar continua and new embeddings of these continua, all of which have canals with the desired properties. This is joint work with my PhD advisor Jernej Činč. This work was co-financed by the Slovenian Research and Innovation Agency (ARIS) under Contract No. SN-ZRD/22-27/0552.

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1. 2026
3. Dynamics

Prime periods on the interval — Gabriel Fuhrmann <gabrielfuhrmann@gmail.com>

Given two continuous self-maps f and g on the interval which have all periodic orbits in common (that is, O(x)={x,f(x),...,f^(p-1)(x)} is a p-periodic orbit of f if and only if it is a p-periodic orbit of g but a priori, f may permute the elements of O(x) in a different fashion than g does), it is natural to ask whether f=g on the closure of the periodic points (which is known to coincide with the closure of the recurrent points!). We show this is the case wherever orbits with prime periods are dense. Specifically, we show that mixing interval maps are uniquely determined by (the location of) their periodic orbits.

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1. 2024
3. STDC2024-CT

Projective Fraïssé limits of trees with confluent epimorphisms — Robert Roe <rroe@mst.edu>

An earlier version of this article had a error in the proof that monotone epimorphisms of finite trees amalgamated. In this talk we will show an example of finite trees that do not amalgamate with monotone epimorphisms. Further, we show how we can use a subfamilies of the family of monotone epimorphisms, that we call simple-monotone and simple*-monotone, to obtain results similar to those in the original paper. We also show the new result that the topological realization of the projective Fraïssé limit of the family of finite trees with simple*-confluent epimorphisms is the Mohler-Nikiel dendroid. This is joint work with W.J. Charatonik, A. Kwiatkowska, and S. Yang.

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1. 2025
3. GeoTop

Prym Representations and Twisted Cohomology of the Mapping Class Group with Level Structures — Xiyan Zhong <xzhong4@nd.edu>

The Prym representations of the mapping class group are an important family of representations that come from abelian covers of a surface. They are defined on the level-$\ell$ mapping class group, which is a fundamental finite-index subgroup of the mapping class group. One consequence of our work is that the Prym representations are infinitesimally rigid, i.e. they can not be deformed. We prove this infinitesimal rigidity by calculating the twisted cohomology of the level-$\ell$ mapping class group with coefficients in the Prym representation, and more generally in the $r$-tensor powers of the Prym representation. Our results also show that when $r\ge 2$, this twisted cohomology does not satisfy cohomological stability, i.e. it depends on the genus $g$.

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1. 2024
3. STDC2024-Plenary

Pseudo-Anosov Homeomorphisms — Yvon Verberne <yverber@uwo.ca>

The mapping class group is the group of orientation preserving homeomorphisms of a surface up to isotopy. In particular, the mapping class group encodes information about the symmetries of a surface. The Nielsen-Thurston classification states that elements of the mapping class group are of one of three types: periodic, reducible, and pseudo-Anosov. In this talk, we will focus our attention on the pseudo-Anosov elements, which are the elements of the mapping class group which mix the underlying surface in a complicated way. In this talk, we will discuss both classical and new results related to pseudo-Anosov mapping classes, as well as the connections to other areas of mathematics.

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1. 2026
3. GeoGT

Pseudo-Anosov subgroups of surface bundles over tori — Junmo Ryang <jr95@rice.edu>

In 2002, Farb and Mosher introduced the notion of convex cocompactness in the mapping class group to capture coarse geometric information of the associated surface group extensions. Convex cocompact subgroups are necessarily finitely generated and purely pseudo-Anosov, but it is an open question whether the converse is true. Several partial results are known in certain settings, however. For example, work of Dowdall, Kent, Leininger, Russell, and Schleimer give a positive answer for subgroups of fibered 3-manifold groups (aka surface-by-cyclic extensions) naturally embedded in punctured mapping class groups via the Birman exact sequence. We present a generalization of this in the setting of surface-by-abelian extensions.

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1. 2026
3. GeoTop

Pseudo-isotopy versus isotopy for homeomorphisms of 4-manifolds — Daniel Galvin <daniel.galvin@austin.utexas.edu>

Pseudo-isotopy is an equivalence relation on homeomorphisms that lies between isotopy and homotopy. Classifying homeomorphisms of 4-manifolds up to pseudo-isotopy is a potentially tractable problem, whereas isotopy classifications currently elude us outside of the simply-connected case. I will explain a program to understand some of this difference using the smooth invariants of Hatcher-Wagoner and Igusa. A result is the construction of many examples of homeomorphisms that are pseudo-isotopic to the identity but not isotopic to the identity on a range of 4-manifolds, including the 4-torus. This is joint work with Isacco Nonino.

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1. 2026
3. GeoGT

Quasi-isometric embeddings of Ramanujan complexes — Hyein Choi <hc71@rice.edu>

Euclidean buildings (a.k.a. affine buildings and Bruhat-Tits buildings) are considered as a p-adic analogue of symmetric spaces. We show that there is no quasi-isometric embedding between the symmetric space of SL(n,R) and the Euclidean building of SL(n,Q_p). Generalizing this, we distinguish Ramanujan complexes constructed by Lubotzky-Samuels-Vishne as finite quotients of Euclidean buildings of PGL(n,F_p((y))) up to quasi-isometric embeddings. These complexes serve as high dimensional expanders with fruitful applications in mathematics and computer science.

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1. 2024
3. STDC2024-GGT

Quasi-isometric rigidity of commensurated subgroups — Alex Margolis <margolis.93@osu.edu>

A finitely generated group can be thought of as a metric space when equipped with the word metric with respect to a finite generating set. This metric space is well-defined up to quasi-isometry. A major program in geometric group theory, initiated by Gromov, is determining to what extent the coarse geometry of a group determines its algebra. In this talk, we investigate when normal and commensurated subgroups, and their associated quotient groups and spaces, are preserved by quasi-isometries.

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1. 2024
3. STDC2024-DS

Quasi-uniform entropy vs topological entropy — OLIVIER OLELA OTAFUDU <olmaolela@gmail.com>

In 2023 Haihambo and Olela Otafudu introduced and studied the notion of quasi-uniform entropy $h_{QU}(\psi)$ for a uniformly continuous self-map $\psi$ of a quasi-metric or a quasi-uniform space $X$. In this talk, we discuss the connection between the topological entropy functions $h, h_f$ and the quasi-uniform entropy function $h_{QU}$ on a quasi-uniform space $X$, where $h$ and $h_f$ are the topological entropy functions defined using compact sets and finite open covers, respectively. In particular, we have shown that for a uniformly continuous self-map $\psi$ of a $T_0$-quasi-uniform space $(X,\mathcal{U})$ we have $h(\psi)\leq h_{QU}(\psi)$ when $X$ is compact and $h_{QU}(\psi)\leq h_f(\psi)$ with equality if $X$ is a compact $T_2$ space.

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1. 2026
3. GeoGT

Quasiconvex Subgroups of Acylindrically Hyperbolic Groups — Ping Wan <pwan5@uic.edu>

As a generalization of hyperbolic groups, the class of acylindrically hyperbolic groups includes many interesting examples and has has received considerable attention. In the world of hyperbolic groups, quasiconvex subgroups are important subjects. What would be a proper analog of quasiconvex subgroups in the context of acylindrically hyperbolic groups? In this talk, I will share my answer to this question and some more questions.

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1. 2024
3. STDC2024-GGT

Random Bowditch Boundaries for Free Groups — Aaron Messerla <amesse4@uic.edu>

The topology of the Bowditch boundary of a relatively hyperbolic group pair gives information about relative splittings of the group. It is therefore interesting to ask if there is generic behavior of this boundary. In this talk I plan to describe previously known results about the Bowditch boundary of a free group with cyclic peripheral structure, and discuss why there is no generic case when the peripheral structure is produced randomly.

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1. 2025
3. GeoGT

Random branched covers of 2-complexes — Jean-Francois Lafont <lafont.1@osu.edu>

I'll introduce a random model for branched covers of 2-complexes. I'll explain why asymptotically almost surely, a random branched cover has Gromov hyperbolic fundamental group. This is joint work with Hyeran Cho (OSU) and Rachel Skipper (Univ. Utah).

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1. 2025
3. Applied

Random complexes with free involution — Andrew Newman <anewman@andrew.cmu.edu>

In this talk I will discuss a new model for random simplicial complexes. Unlike other models, which are generically simply-connected when sufficiently dense, the complexes in this model generically have fundamental group $\mathbb{Z}/2\mathbb{Z}$. I'll describe results on the asymptotic behavior of the homology and homotopy groups in these complexes as well as how these results imply a "random Borsuk--Ulam theorem". This talk is based on joint work with Florian Frick.

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1. 2024
3. STDC2024-GGT

Random walks on groups and superlinear divergent geodesics — Vivian He <vivian.he@mail.utoronto.ca>

The central limit theorem of random walks answers the question "how quickly does the random walk drift away from the origin". Historically, it has been proven (under some assumptions) for free groups, hyperbolic groups, and various generalizations of hyperbolic groups. We proved this for one generalization of hyperbolic groups: groups containing superlinear divergent quasi-geodesics. The advantage of this setting compared to previous versions of CLT is that it is invariant under quasi-isometry. In this talk, I will delve into the superlinear divergence property, as well as its geometric consequences that led to the theory of random walks on groups containing superlinear divergent quasi-geodesics. This talk is based on joint work with Kunal Chawla, Inhyeok Choi, and Kasra Rafi.

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1. 2025
3. GeoTop

Rational points on quartic del Pezzo surfaces via homological stability — Philip Tosteson <philip.tosteson@gmail.com>

A quartic del Pezzo surface $X$ is an intersection of two degree $2$ hypersurfaces in $$\mathbb P^4$$. So rational points on $X$ correspond to solutions of a pair of homogeneous quadratic equations in $5$ variables. I will discuss joint work with R. Das, B. Lehmann, and S. Tanimoto, using topological methods to determine statistics of rational points on $X$ (over the function field $\mathbb F_q(t)$)

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1. 2024
3. STDC2024-DS

Realisation of Choquet simplices on manifolds — Sejal Babel <babelsejalm@gmail.com>

It is well known that the set of invariant measures of a topological dynamical system is a non-empty metrisable Choquet simplex. In 1991, Downarowicz proved that all such simplices arise as the sets of invariant measures of a class of minimal subshifts. Hence, one can ask the following question: which non-empty Choquet simplices can be realised as the sets of invariant measures for minimal homeomorphisms on manifolds? In the case of one-dimensional manifolds, we observe that the geometry of manifolds restricts the available dynamics. In my talk, I will discuss which measurable dynamical system can be realised as a minimal homeomorphism on a manifold. This will answer the question of realisation of Choquet simplex on manifolds of higher dimension. I will also talk about necessary and sufficient conditions for an ergodic measure in Choquet simplex to have a discrete spectrum. The criterion is imposed on generic points of such a measure. The talk is based on the results obtained in joint works with Melih Emin Can, Jernej Činč, Till Hauser, Dominik Kwietniak, and Piotr Oprocha.

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1. 2024
3. STDC2024-STT

Recent results about proximal and semi-proximal spaces — Khulod Almontashery <khulod@yorku.ca>

We consider the class of proximal and semi-proximal spaces defined by Jocelyn Bell and introduce a strengthening of this class by examining the proximal game defined on totally bounded uniformities. We also discuss recent results about proximal and semi-proximal spaces. Joint work with Paul Szeptycki.

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1. 2024
3. STDC2024-GTop

Rectangles inscribed in plane sets as a consequence of the non-embeddability of certain cones in $\mathbb{R}^3$ — Ulises Morales-Fuentes <ulises.morales@uaem.mx>

A plane set admits an inscribed rectangle if every homeomorphic copy of it in $\mathbb{R}^2$ contains the 4 vertices of at least one Euclidean rectangle. Vaughan proved that $S^1$ admits an inscribed rectangle by reducing the problem to the non-embeddability of the projective plane in $\mathbb{R}^3$ (it is not known if $S^1$ admits an inscribed rectangle of aspect ratio 1:1 i.e. a square). In this talk, using the non-embeddability of the Cone($K_5$) and the Cone($K_{3,3}$) in $\mathbb{R}^3$ we classify plane compact connected locally-connected sets that admit inscribed rectangles. Using similar topological techniques, we also present a one-dimensional non-connected set such that every copy of it in $\mathbb{R}^2$ admits an inscribed rectangle with at least one vertex in each component.

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1. 2024
3. STDC2024-STT

Refining and dominating families at the uncountable — Vera Fischer <vera.fischer@univie.ac.at>

We will discuss some recent results, including ZFC inequalities, concerning the higher Baire spaces analogues of some of the classical combinatorial cardinal characteristics of the continuum. Of special interest for the talk will be the generalized bounding, splitting, refining and dominating numbers.

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1. 2026
3. GeoGT

Relative Quasi-Convexity in the Sageev Construction — Jagerynn Verano <jveran2@uic.edu>

Given a group *G* and a collection of codimension--one subgroups *H* of *G*, one can construct a CAT(0) cube complex on which *G* acts isometrically with no global fixed point. This is known as Sageev's construction. In this construction, codimension--one subgroups of *H* are commensurable with hyperplane stabilizers. By imposing certain conditions on *G* and *H*, one can promote the group action to a proper or cocompact one. A proper action is harder to obtain than a cocompact one. In this talk, we introduce a relative version of Groves--Manning's result on quasi-convexity in the Sageev construction. Let *(G,P)* be a finitely generated relatively hyperbolic group acting cocompactly and *P*-elliptically on a CAT(0) cube complex. In this setting, we show that vertex stabilizers are full relatively quasi-convex if and only if hyperplane stabilizers are full relatively quasi-convex.

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1. 2026
3. Dynamics

Renormalization, equipotential annuli, and the Hausdorff measure — Vladlen Timorin <vtimorin@hotmail.com>

For a complex single variable polynomial $f$ of degree $d$, let $K(f)$ be its filled Julia set, i.e., the union of all bounded orbits. Assume that $K(f)$ has an invariant component $K^{\*}$ on which $f$ acts as a degree $d^{\*}<d$ map. This is a simplest instance of _holomorphic polynomial-like renormalization_ (Douady-Hubbard): the dynamics of a higher degree (degree $d$) polynomial $f$ near $K^*$ can be understood in terms of a suitable lower degree (degree $d^{\*}$) polynomial to which the restriction $f{\|}_{K^{\*}}$ is conjugate. One can associate a certain Cantor-like subset $G’$ of the circle with $K^{\*}$; the latter is defined in a combinatorial way. We will describe a role the Hausdorff dimension of $G’$ and the respective Hausdorff measure play in geometry of $K^{\*}$.

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1. 2025
3. Applied

Restricted Distortions of Embedded Length Spaces — Atish Mitra <atish.mitra@gmail.com>

In geometric and topological reconstruction of compact length spaces embedded in some metric space, one needs an appropriate notion of distortion of the embedding. We consider variants of the classical notion of distortion, by controlling the coarseness of the distance scale of the ambient space and the discreteness of the coarse paths used to generate the length structure. In addition to discussing the stability and convergence of these notions of distortion, we compare them with existing notions of sampling parameters used in shape reconstruction and show some applications of our approach. This is based on joint work with Rafal Komendarczyk and Sushovan Majhi.

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1. 2024
3. STDC2024-STT

Riemann integral on a space with a fractal structure — José F. Gálvez-Rodríguez <jgr409@ual.es>

Joint work with Miguel A. Sánchez-Granero and Cristina Martín-Aguado. In this work we start developing a Riemann-type integration theory on spaces which are equipped with a fractal structure. These topological structures have a recursive nature, which allows us to guarantee a good approximation to the true value of a certain integral with respect to some measure defined on the Borel $\sigma$-algebra of the space. We give the notion of Darboux sums and lower and upper Riemann integrals of a bounded function when given a measure and a fractal structure. Furthermore, we give the notion of a Riemann-integrable function in this context and prove that each $\mu$-measurable function is Riemann-integrable with respect to $\mu$. Moreover, if $\mu$ is the Lebesgue measure, then the Lebesgue integral on a bounded set of $\mathbb{R}^n$ meets the Riemann integral with respect to the Lebesgue measure in the context of measures and fractal structures. Finally, we give some examples showing that we can calculate improper integrals and integrals on fractal sets.

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1. 2025
3. GeoTop

Rigidity Phenomena for Surface Amalgams — Yandi Wu <yandi.wu@rice.edu>

Geometric rigidity theory aims to determine a geometric object with the smallest amount of data possible. For instance, one could ask whether the volume or length set of a manifold determines its metric. In this talk, I will motivate and present some results related to length spectrum and volume rigidity for negatively curved surface amalgams, natural generalizations of negatively curved surfaces.

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1. 2024
3. STDC2024-DS

Rigidity for Toeplitz and Enumeration Systems — Silvia Radinger <radinger.silvia@gmail.com>

In this talk we will study measure-theoretical rigidity and partial rigidity for classes of Cantor dynamical systems including Toeplitz systems and enumeration systems. With the use of Bratteli-Vershik dynamical systems we can control invariant measures. Their structure in the Bratteli diagram leads us to find systems with the desired properties. Among other things, we will analyse different Toeplitz systems for their rigidity and show that there exist Toeplitz systems which have zero entropy and are not partially measure theoretically rigid with respect to any of its invariant measures. Further we show varying rigidity in the family of enumeration systems defined by a linear recursion. This talk is based on joint work with Henk Bruin, Olena Karpel and Piotr Oprocha.

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1. 2026
3. GeoTop

Root lattices and series valued invariants of plumbed 3-manifolds — Allison Moore <moorea14@vcu.edu>

Given a reduced plumbing tree and a spin-c structure, I will discuss how to construct a plumbed 3-manifold invariant in the form of a Laurent series twisted by a root lattice. Such a series is invariant under the Neumann moves on plumbing trees and the action of the Weyl group. These series-valued invariants generalize the Z-hat series of Gukov-Pei-Putrov-Vafa, Gukov-Manolescu, Park and Ri. They are motivated by the study of the WRT invariants, and the work of Akhmechet-Johnson-Krushkal which found connections with lattice cohomology. Time permitting, I will also discuss a multivariable generalization of the root lattice-twisted series for knot complements and gluing formulas. This is joint work with N. Tarasca.

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1. 2024
3. STDC2024-DS

Scaling properties of (generalised) Thue-Morse measures — Tanja Schindler <tanja.schindler@uj.edu.pl>

The Thue-Morse measure and its generalisations are diffraction measures of simple aperiodic systems. Besides that, they are paradigmatic examples of purely singular continuous probability measures on the unit interval given as an infinite Riesz product. To study their scaling behaviour a classical method, the thermodynamic formalism can be used - which however has to be adapted to an unbounded potential. We will in particular see how one has to meaningfully define the topological and variational pressure in this setting. Besides seeing this method, we will also see how quantitatively the Birkhoff and dimension spectrum changes depending on the point of the singularity. This is joint work with M. Baake, P. Gohlke, and M. Kesseböhmer.

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1. 2026
3. General & ST
5. Plenaries

Selection Games with Compact Sets — Christopher Caruvana <chcaru@iu.edu>

Selection principles and their corresponding games involving points and open covers have a long and well-developed history. In this talk, we will highlight how many results for points and open covers have analogues involving compact sets and k-covers. Such examples will include traditional Menger/Rothberger variants, as well as various connections with the space of real-valued continuous functions with the topology of uniform convergence on compacta. Most of the results to be discussed come from joint work with Steven Clontz and Jared Holshouser.

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1. 2025
3. Plenary

Semi-Kelley fans have contractible hyperspaces — David Maya <dmayae@outlook.com>

Semi-Kelley continua were introduced by J. J. Charatonik and W.J. Charatonik in 1998, who proved that every Kelley continuum is semi-Kelley. Since then, this class of continua has been studied by several authors. The most important problem in this area is determining whether the hyperspaces of a semi-Kelley continua are contractible. In this talk, we present a positive partial answer to this question in the case of fans.

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1. 2024
3. STDC2024-GGT

Separable homology of graphs and the Whitehead complex — Becky Eastham <becky.eastham23@gmail.com>

We introduce a 1-complex $\mathrm{Wh}(\Gamma)$ associated with a finite regular cover $\Gamma$ of the rose which is connected if and only if the fundamental group of the associated cover is generated by elements in a proper free factor of the free group. When the associated cover represents a characteristic subgroup of the free group, the complex admits an action of $\mathrm{Out}(F_n)$ by isometries. We then explore the coarse geometry of $\mathrm{Wh}(\Gamma)$. Every component of $\mathrm{Wh}(\Gamma)$ has infinite diameter, and the complex $\mathrm{Wh}(\mathbf{R}_n)$ associated with the rose is nonhyperbolic. As corollaries, we obtain that the Cayley graph of the free group with the infinite generating set consisting of all primitive elements has infinite diameter and is nonhyperbolic.

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1. 2025
3. Dynamics

Sets of pointwise recurrence and answers to some questions of Host, Kra, and Maass — Anh Le <anh.n.le@du.edu>

A subset of the positive integers is dynamically central syndetic if it contains the times of return of a point to a neighborhood of itself in a minimal dynamical system. This class of syndetic sets forms an important bridge between dynamics and combinatorics. We show that a set is dynamically central syndetic if and only if it is a member of a syndetic, idempotent filter. We elaborate on the consequences of this characterization for the dual family: sets of pointwise recurrence. For example, we provide several combinatorial characterizations of sets of pointwise recurrence, show that these sets do not have the Ramsey property, and they are sets of multiple recurrence. These results answer several questions asked by Host, Kra, and Maass. This talk is based on an joint work with Daniel Glasscock (University of Massachusetts Lowell).

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1. 2026
3. Applied & Data

Sheaf Laplacian Sparsification on Graphs — Minghua Wang <minghuaw@buffalo.edu>

Sheaf Laplacians generalize graph Laplacians to vector-valued node signals, enabling richer relational models but increasing computational cost. We present a spectral sparsification method for the $0$-dimensional sheaf Laplacian using leverage-style edge sampling from trace effective resistance with reweighting. The resulting sparse operator preserves the original quadratic form on $(\ker L_{\mathcal F})^\perp$ with high probability: for $\varepsilon\in(0,1)$ and $p_{\mathrm{fail}}\in(0,1)$, we obtain a $(1\pm\varepsilon)$ approximation with probability at least $1-p_{\mathrm{fail}}$. This gives a principled path to faster sheaf diffusion and scalable sheaf-based learning, and supports empirical study of the sparsity--accuracy tradeoff through tunable sampling.

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1. 2026
3. Dynamics

Simple Smale Flows on S^3 — Anthony Sloan <tonesval@outlook.com>

We discuss the linking structure of the attractor-repeller pairs in simple Smale flows on the 3-sphere in which the chaotic saddle set is modeled by four- band templates with twisted bands. We obtain new theorems which illustrate that the dynamics of simple Smale flows are sensitive to half-twists in the bands of the embedded template. Haynes and Sullivan showed that the attractor- repeller pair a∪r in a simple Smale flow with chaotic saddle set modeled by embedded template U^+ is either a Hopf link or a trefoil and meridian. By placing a single half-twist in a selected band of U^+, we obtain new templates that model chaotic saddle sets of Smale flows. For simple Smale flows on S^3 with chaotic saddle sets modeled by those templates, we find that such simple Smale flows are realizable and that a∪r must be a Hopf link, a figure-8 knot and meridian, or a trefoil and meridian. This is joint work with Michael Sullivan.

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1. 2024
3. STDC2024-STT

Some examples concerning $L\Sigma(\leq\omega)$ and metrizably fibered compacta — Mikolaj Krupski <mkrupski@mimuw.edu.pl>

The class of $L\Sigma(\leq\omega)$-spaces was introduced in 2006 by Kubiś, Okunev and Szeptycki as a natural refinement of the classical and important notion of Lindelof $\Sigma$-spaces. Compact $L\Sigma(\leq\omega)$-spaces were considered earlier, under different names, in the works of Tkachuk and Tkachenko in relation to metrizably fibered compacta. In this talk we will present counterexamples to several open questions about compact $L\Sigma(\leq\omega)$-spaces that are scattered in the literature. Among other things, we refute a conjecture of Kubiś, Okunev and Szeptycki by constructing a separable Rosenthal compactum which is not an $L\Sigma(\leq\omega)$-space. We also give insight to the structure of first-countable $(K)L\Sigma(\leq\omega)$-compacta. The talk is based on a joint work with Antonio Aviles.

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1. 2026
3. GeoTop

Some fibrations of some pseudomanifold groups — Genevieve Walsh <genevieve.walsh@gmail.com>

3-dimensional pseudomanifolds are CW-complexes with the property that the link of each point is a closed, orientable surface. We give some interesting examples of these, show that there are many examples of these groups virtually algebraically fibering, and give some applications to higher-dimensional Coxeter groups. This is joint work with Lorenzo Ruffoni.

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1. 2025
3. Set-Theoretic

Some recent results on $\Delta$-spaces — Paul Szeptycki <szeptyck@yorku.ca>

A $\Delta$-space is a Tychonoff space with the property that every partition of the space (into arbitrary sets) has a point finite open expansion. M. Reed defined a set of reals with this property to be a $\Delta$-set and was motivated by the characterization of a $\Delta$-set as those sets of reals $X$ for which the Moore plane over $X$ is countably paracompact. Recently, Leiderman and Kąkol characterized $\Delta$-spaces as those $X$ for which the locally convex space $C_p(X)$ is distinguished. I will survey some recent results concerning $\Delta$-spaces and mention a number of open problems.

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1. 2024
3. STDC2024-Semi

Some recent results on decomposable continua — Eiichi Matsuhashi <matsuhashi@riko.shimane-u.ac.jp>

This is a joint work with Benjamin Espinoza, Alejandro Illanes, Hayato Imamura and Yoshiyuki Oshima. In this presentation, we discuss some recent results on decomposable continua, in particular, Wilder continua, continuum-wise Wilder continua, closed set-wise Wilder continua, $D$-continua, $D^{*}$-continua and $D^{**}$. First, we introduce some basic definitions and terminology that are used in this talk. Then, we discuss results on the above continua related to Whitney properties and Whitney reversible properties. Also, we deal with product properties as for those continua. Finally, we show the existence of singular decomposable continua using those notion.

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1. 2025
3. Dynamics

Specification and $\omega$-chaos in non-compact systems — Jonathan Meddaugh <jonathan_meddaugh@baylor.edu>

We demonstrate conditions under which a dynamical system on a Lindelöf space exhibits $\omega$-chaos. In particular, we show that a system which satisfies a generalized version of the specification property and which contains at least three mutually separated orbit closures exhibits dense $\omega$-chaos.

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1. 2026
3. Continua

Specification on the Lelek Fan — Van Nall <vnall@richmond.edu>

Recent work of Piotr Oprocha and his collaborators has provided a number of delicate examples of dynamical systems separating specification, shadowing, and periodic-point density, primarily in symbolic or totally disconnected spaces. The goal of the present paper is to demonstrated that similar - and in some cases sharper - separations occur on the Lelek fan, a continuum that can be embedded in a Cantor fan. Our constructions rely on Mahavier products of closed relations. By carefully choosing relations on the unit interval, we obtain Mahavier products that are homeomorphic to the Lelek fan whose associated shift maps display diverse dynamical behavior. This approach yields a unified framework for producing and analyzing examples on a familiar continuum.

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1. 2026
3. Continua

Spirals — Alejandro Illanes <illanes@matem.unam.mx>

A spiral is a compactification of the ray [0,1) with remainder a simple closed curve. In this talk we will discuss how spirals have appeared in important results of Continuum Theory, including some new results.

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1. 2025
3. Plenary

Steps on the Way to and from Persistent Homology — Herbert Edelsbrunner <edels@ist.ac.at>

The formation of topological data analysis (TDA) as a research area with dedicated meetings and funding happened during the years around the beginning of this millenium. A crucial step in this development was the introduction of persistent homology. The root system of this idea goes back to the dependent and independent work of a number of mathematicians, including Marston Morse. This talk recalls a few of the steps on my personal journey leading to this concept, and steps that expand the basic notion toward other branches of mathematics and applications outside of mathematics.

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1. 2024
3. STDC2024-GGT

Surface Houghton Groups — George Domat <gd23@rice.edu>

Surface Houghton groups are a generalization of Houghton groups to the surface setting. They are defined as groups of asymptotically rigid mapping classes of an infinite-type surface. We will give commensurability and isomorphism classication results for this class of groups. Some time will be spent motivating these groups as "medium" mapping class groups that live somewhere between the world of mapping class groups of finite-type surfaces and those of infinite-type surfaces. This is joint work with Javier Aramayona and Christopher Leininger.

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1. 2026
3. GeoTop

Surgeries on knots and tight contact structures — Shunyu Wan <swan48@gatech.edu>

The existence and nonexistence of tight contact structures on the 3-manifold are interesting and important topics studied over the past thirty years. Etnyre-Honda found the first example of a 3-manifold that does not admit tight contact structure, and later Lisca-Stipsicz extended their result and showed that a Seifert fiber space admits a tight contact structure if and only if it is not the smooth (2n − 1)-surgery along the T(2,2n+1) torus knot for any positive integer n. Surprisingly, since then no other example of a 3-manifold without tight contact structure has been found. Hence, it is interesting to study if all such manifolds, except those mentioned above, admit a tight contact structure. Towards this goal, I will discuss the joint work with Zhenkun Li and Hugo Zhou about showing any negative surgeries on any knot in S^3 admit a tight contact structure.

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1. 2025
3. Plenary

Suspending the pigeonhole principle: amenability, dynamics, and C*-algebras — David Kerr <kerrd@uni-muenster.de>

The Rokhlin lemma is a finite approximation property that underpins a great many constructions in classical ergodic theory, including most spectacularly those at the basis of the Ornstein isomorphism theory for Bernoulli shifts. In the 1970s Ornstein and Weiss showed amenability to be the natural setting for finite approximation in dynamics by establishing a general form of the Rokhlin lemma in this setting, and this led, among other things, to a much broader recasting of the Ornstein isomorphism theory. Over the last couple of decades a growing interest in the interplay between dynamics and the geometric and analytic structure of groups has set the stage for a resurgence of applications of the Ornstein-Weiss Rokhlin lemma, not only in its original measure-theoretic incarnation but also as a versatile tiling principle that has turned out be intimately connected, on the topological side, to the remarkable recent successes in the Elliott classification program for separable nuclear C*-algebras. I will sketch a picture of these various developments at the interface of measure, topology, dynamics, geometric group theory, and operator algebras.

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1. 2025
3. GeoTop

Symmetry and arithmetic structures — Yanlong Hao <ylhao@umich.edu>

Arithmetic manifolds admit many 'Hidden' symmetries. In this talk, we want to discuss the inverse problem: if a object admit many symmetries, is it arithmetic? We will invest the question from variety of aspects: algebra, differential geometry and coarse geometry and answer the question for non-compact negatively curved manifolds.

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1. 2024
3. STDC2024-STT

THE CLASS $C(\omega_1)$ AND COUNTABLE NET WEIGHT — Istvan Juhasz <juhasz@renyi.hu>

Hart and Kunen and, independently, Ríos-Herrejón defined and studied the class $C({\omega}_1)$ of topological spaces $X$ having the property that for every neighborhood assignment $\{U(y) : y \in Y\}$ with $Y \in [X]^{\omega_1}$ there is $Z \in [Y]^{\omega_1}$ such that $Z \subset \bigcap \{U(z) : z \in Z\}.$ It is obvious that spaces of countable net weight, i.e. having a countable network, belong to this class. We present several independence results concerning the relationships of these two and several other natural classes that are sandwiched between them. In particular, we prove that the continuum hypothesis, in fact a weaker combinatorial principle called super stick, implies that every regular space in $C({\omega}_1)$ has countable net weight, answering a question that was raised by Hart and Kunen. These results are joint with L. Soukup and Z. Szentmiklossy.

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1. 2024
3. STDC2024-GTop

The Alexander Polynomial and Gordian Distance — Ana Wright <anwright1@davidson.edu>

We call a knot K a complete Alexander neighbor if every possible Alexander polynomial is realized by a knot one crossing change away from K. It is unknown whether there exists a complete Alexander neighbor with nontrivial Alexander polynomial. I will discuss how to eliminate infinite families of knots with nontrivial Alexander polynomial from having this property and possible strategies for unresolved cases. I will also discuss how a related condition on determinants of knots one crossing change away from unknotting number one knots gives an obstruction to unknotting number one. This obstruction appears similar to an obstruction introduced by Lickorish, but Lickorish’s obstruction does not subsume the obstruction coming from the condition on determinants.

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1. 2025
3. Plenary

The Borel Conjecture for compact aspherical 4-manifolds with boundary — James Davis <jfdavis@iu.edu>

The Borel Conjecture for closed manifolds implies that two closed aspherical manifolds with isomorphic fundamental group are homeomorphic. The Borel conjecture for compact aspherical manifolds with boundary states that a homotopy equivalence which is homeomorphism on the boundary is homotopic to a homeomorphism. Jonathan Hillman and I classify and prove the Borel Conjecture for all compact aspherical four manifolds with boundary with good (= elementary amenable) fundamental group. We classify all possible fundamental groups and all possible 3-manifold boundaries.

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1. 2026
3. General & ST

The Cofinality Of Generating Familes — Thomas Gilton <tdgilton@gmail.com>

The Cofinality of Generating Familes (joint with Paul Gartside) Cofinal sets, which study what happens "eventually" in a given order, are ubiquitous in mathematics. In Topology, they play a particularly noticeable role. Consider, for example, a subspace $M$ of the reals. The topology can be captured by convergent sequences, and hence we can ask the question: how many sequences are needed to characterize the topology on $M$? As another example, consider questions (essentially about cofinalities) such as: how many compact sets cover $M$ (the "compact covering number" of $M$)? or how many compact subsets generate the topology on $M$ (the $k$-ness number of $M$)? In this talk, we will discuss recent work of Paul Gartside and the speaker on these questions. We will show how these questions about how many sequences (or compact sets) generate the topology of $M$ can be viewed through the lens of the Tukey order on relations and how, as such, we can apply set-theoretic techniques. We show how certain cardinal invariants are used to answer these topological questions. Finally, we discuss how (in light of recent work of James Cummings and the speaker on extender-based forcing and mod-finite scales) we can, among spaces with a fixed value of the compact covering number, the $k$-ness number can be quite varied.

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1. 2024
3. STDC2024-DS

The Critical Strip Lemma for $\sigma_d$-Symmetric Laminations of the Unit Disc - a Generalization of Thurston's Central Strip Lemma for $\sigma_2$ Laminations. — Thomas Sirna <tsirna@uab.edu>

Every complex polynomial with a locally connected Julia set generates a lamination of the unit disc --- a closed set of non-crossing chords inside $\mathbb{D}$ whose endpoints on $\mathbb{S}$ are allowed to touch. This was a tool developed and explored by Thurston in order to study degree 2 complex polynomials, their Julia sets, and the parameter space of LC polynomials, the Mandelbrot set. The dimension of the corresponding `multi-brot' sets increases in higher dimension so one usually restricts themselves to studying slices of the parameter space. The restriction we make in this talk is to focus on symmetric polynomials, which we define as a degree $d$ complex polynomial whose locally connected Julia set --- and therefore, whose lamination --- has $\frac{2\pi}{d-1}$ rotational symmetry. It turns out that this leads to behavior very similar to the degree 2 case. Thurston utilized the Central Strip Lemma to help prove two main results in the degree 2 case --- the No Wandering Triangles theorem (NWT) and the No Identity Return Triangles theorem (NIRT). The symmetric degree $d$ case has an analogous result, which we call the Critical Strip Lemma. In this talk we prove the Critical Strip Lemma, which puts restrictions on the placement of leaves in $\sigma_d$-symmetric laminations. We will then outline how it's used to prove that in the $\sigma_d$-symmetric case, the NWT and NIRT theorems still hold.

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1. 2026
3. Applied & Data

The Geometric Latschev's Theorem: Euclidean Shape Reconstruction via Vietoris–Rips Shadow — Sushovan Majhi <s.majhi@gwu.edu>

The shadow of an abstract simplicial complex $\mathcal{K}$, whose vertices are in $\mathbb{R}^{N}$, is defined as the union of the convex hulls of its simplices. For a metric space $(S,d)$ at scale $\beta$, the Vietoris–Rips complex $\mathcal{R}_{\beta}(S)$ is the abstract simplicial complex where each $k$-simplex corresponds to $(k+1)$ points in $S$ with a diameter at most $\beta$. Latschev's theorem provides a qualitative guarantee for manifold reconstruction: for any closed Riemannian manifold $X$, there exists a scale $\epsilon_{0}>0$ such that for any $0<\beta \leq \epsilon_{0}$, there is a $\delta >0$ where any metric space $S$ within Gromov–Hausdorff distance $\delta$ of $X$ yields a Vietoris–Rips complex homotopy equivalent to $X$. Recently, Latschev's theorem has been quantified, allowing $X$ to be a more general geodesic space. When $X\subset \mathbb{R}^{N}$ is a Euclidean geodesic space (e.g., submanifold, graph), we address the theorem's geometric analog: under what conditions is the shadow of the Vietoris–Rips complex of a Hausdorff-close Euclidean sample $S\subset\mathbb{R}^N$ both homotopy equivalent and Hausdorff-close to $X$? Unlike the abstract complex, the shadow provides a geometric embedding within the host space, which is essential for the practical reconstruction of Euclidean shapes. In this talk, we discuss recent developments in answering this question and explore their implications for faithful reconstruction of low-dimensional submanifolds and Euclidean-embedded graphs.

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1. 2025
3. Plenary