1. STDC
3. 2025
5. 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. SumTopo
3. 2026
5. TDS
7. Plenary

Dissipative Dynamics on the Disc — Sylvain Crovisier <sylvain.crovisier@universite-paris-saclay.fr>

The dynamics of continuous interval maps admit a remarkably rich topological description, including the structure of attractors, criteria for positive entropy, and the density of periodic points in the recurrent set. In recent years, several extensions of these results have been obtained for dissipative diffeomorphisms of the disc, including Hénon maps. In this talk, I will survey some of these developments and present a new closing lemma, proved in collaboration with Enrique Pujals.

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1. STDC
3. 2024
5. 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. STDC
3. 2026
5. Continua
7. 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. SumTopo
3. 2026
5. GSTT

$\mathbb H^*$ — Will Brian <wbrian.math@gmail.com>

Let $\mathbb H$ denote the half-line $[0,\infty)$, and let $\mathbb H^* = \beta \mathbb H \setminus \mathbb H$ denote its \v{C}ech-Stone remainder. We aim to discuss a recent theorem showing that the Continuum Hypothesis ($\mathsf{CH}$) implies $\mathbb H^*$ is the ``generic'' continuum of weight $\aleph_1$. What precisely this means is the main topic of the talk, but roughly it means that, in the appropriate generalized sense, $\mathsf{CH}$ implies $\mathbb H^*$ is the inverse Fra\"{i}ss\'e limit of the class of metrizable continua. This leads directly to a topological characterization of $\mathbb H^*$ under $\mathsf{CH}$: i.e., a topological property of $\mathbb H^*$ such that $\mathsf{CH}$ implies $\mathbb H^*$ is, up to homeomorphism, the only weight-$\aleph_1$ continuum with this property.

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1. SumTopo
3. 2025
5. Dynamics/CT

$k$-type chaos of $\mathbb{Z}^d$-actions — Anshid Aboobacker <anshidaboobackerk@gmail.com>

In this talk, we define and study the notions of $k-$type proximal pairs, $k-$type asymptotic pairs and $k-$type Li Yorke sensitivity for dynamical systems given by $\mathbb{Z}^d$ actions on compact metric spaces. We prove the Auslander-Yorke dichotomy theorem for $k-$type notions. The preservation of some of these notions under conjugacy is also studied. We also study relations between these notions and their analogous notions in the usual dynamical systems.

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1. SumTopo
3. 2026
5. CT

1/2-Indecomposability and positive entropy for inverse limits of Markov set-valued functions — James Kelly <james.kelly@cnu.edu>

We discuss a class of upper semi-continuous set-valued functions called Markov set-valued functions. Such set-valued functions have a corresponding symbolic dynamical system. Through examples, partial results, and open questions we explore the relationship between the topology of the set-valued function's inverse limit and the topological entropy of the symbolic system. In particular, we establish some conditions where positive topological entropy is equivalent to the inverse limit containing a 1/2-indecomposable subcontinuum.

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1. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2026
5. GGT

A Combinatorial Characterization of Sol 3-Manifolds — Leslie Mavrakis <l.mavrakis@utah.edu>

A family F of compact n-manifolds is locally combinatorially defined (LCD) if there is a finite collection of triangulated n-balls (called models) such that the set F is exactly the set of compact n-manifolds that have a triangulation which locally looks like one of these models. In previous work with Daryl Cooper and Priyam Patel, we show that being LCD is equivalent to the existence of a compact branched n-manifold W, such that F is precisely those manifolds that immerse into W. In this way, W can be thought of as a universal branched manifold for F. In this talk, I will explain why the set of Sol 3-manifolds is LCD by constructing a universal branched manifold for the family. The construction is based on regular languages that detect Anosov monodromies of torus bundles and the gluing maps of Sol semi-bundles.

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1. STDC
3. 2025
5. 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. SumTopo
3. 2026
5. TDS

A Family of Wild Attractors for Unimodal Maps — Lori Alvin <lori.alvin@furman.edu>

It is well-known that a unimodal map $f$ has a unique metric attractor that is either an attracting periodic orbit, the union of $n$ open intervals that are cyclically permuted by $f$, or a Cantor set. A Cantor attractor that arises from a non-infinitely renormalizable map is called an _absorbing Cantor set_ or a _wild attractor_. We present a symbolic construction that can be used to generate the kneading sequences for a family of unimodal maps with embedded strange odometers and wild attractors. This is joint work with Jernej Činč.

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1. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2026
5. TDS

A Tits alternative for groups of surface homeomorphisms — Frédéric Le Roux <frederic.le-roux@imj-prg.fr>

I will present recent results using the natural action of Homeo(S), for a compact surface S, on the fine curve graph introduced by Bowden, Hansel and Webb, who also proved that this graph is Gromov hyperbolic.

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1. SumTopo
3. 2025
5. Graphs

A Transversal of Planar Graph Faces — Joseph Briggs <joseph.guy.briggs@gmail.com>

Suppose you have a subset $S$ of the vertices of a planar graph which contains at least one vertex from every face. Then $S$ must have at least half of the vertices, and for some planar graphs *every* such $S$ must have at least half of the vertices. We believe this extends to higher dimensions, but don’t really know why, and have found some situational evidence (but also some counter-evidence). This is based on joint work with Michael Dobbins and Seunghun Lee.

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1. STDC
3. 2024
5. 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. STDC
3. 2024
5. 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. STDC
3. 2024
5. 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. STDC
3. 2026
5. 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. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2026
5. TMAA

A dynamical hierarchy of Banach algebras — Matthias Neufang <mneufang@math.carleton.ca>

The concept of stability in the sense of Krivine--Maurey has proven very useful in Banach space geometry. We introduce and study a corresponding notion in the setting of Banach algebras, which we call multiplicative stability. As we shall see, the algebra of Schatten $p$-class operators on a separable Hilbert space is multiplicatively stable, where $p \in [1, \infty)$, while no infinite-dimensional $C^*$-algebra is. We also explore stronger and weaker versions of this concept, using the rich structure of spaces of functions defined on topological semigroups, including almost periodic, weakly almost periodic, and tame functions. This leads us to a novel classification of Banach algebras, providing a dynamical hierarchy. In this context, we also investigate further important classes of Banach algebras, such as group algebras and Fourier algebras, algebras of compact operators on Banach spaces, and algebras of differentiable functions. The talk is based on joint work with (my former PhD student) Narjes Alabkary, (my former postdoctoral fellow) Reza Esmailvandi, and Stefano Ferri.

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1. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2026
5. GGT

A language-theoretic characterization of f.g. subgroups of Thompson V — Davide Perego <dperego9@gmail.com>

The intersection of formal language theory and group theory provides a fascinating lens for studying algebraic structures, most notably through the word problem. This connection has allowed mathematicians to classify groups based on the Chomsky hierarchy. While the landmark Muller-Schupp theorem completely characterized groups with context-free word problems, progressing beyond this boundary has remained a major challenge. In this talk, we shift toward a more combinatorial and geometric approach. We will introduce a new framework that yields a characterization of the f.g. subgroups of Thompson V. Notably, this group is central to a well-known 2008 conjecture regarding groups with co-context-free word problems. Joint works with Corentin Bodart, Daniele D'Angeli, Francesco Matucci and Emanuele Rodaro.

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1. SumTopo
3. 2026
5. GGT

A linearity criterion for automorphism groups of hyperbolic groups — Mark Pengitore <mpengito@gmail.com>

This talk will introduce various growth functions associated to a finitely generated group which measure the difficulty of separating an element from the identity using epimorphisms to a fixed family of nonabelian finite simple groups with characteristic kernels as a function of the word length. As an application of these functions, we provide a characterization of when the automorphism group of a hyperbolic group is linear.

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1. SumTopo
3. 2025
5. General/ST

A measure of Isbell-convexity for a quasi-metric space — Collins Amburo Agyingi <agyinca@unisa.ac.za>

Let $(X,d)$ be a $T_0$-quasi-metric space. Then it has been shown that $X$ has a $q$-hyperconvex hull which is denoted by $Q_X$. It is known that every $q$-hyperconvex $T_0$-quasi-metric space is bicomplete. However, the converse is not true, that is, there exist bicomplete $T_0$-quasi-metric spaces that are not $q$-hyperconvex. In this talk, we shall present a parameter that measures how far a bicomplete $T_0$-quasi-metric space is from being hyperconvex. We will present some characteristics of this new parameter.

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1. SumTopo
3. 2025
5. Computing

A mechanized characterization of coherent $2$-groups — Perry Hart <hart1262@umn.edu>

In this talk, we will outline an Agda implementation of a higher-dimensional piece of the homotopy hypothesis, which provides a general correspondence between groupoids and homotopy types. The groupoids we look at are monoidal groupoids where every element has the structure of an adjoint equivalence, called coherent $2$-groups. The correspondence for such groupoids takes the form of a biequivalence between the $\left(2,1\right)$-category of coherent $2$-groups and the $\left(2,1\right)$-category of pointed connected (homotopy) $2$-types. We build this biequivalence in homotopy type theory (HoTT) and use Agda to verify the construction (see https://github.com/PHart3/2-groups-agda). Thanks to the univalence axiom, we also obtain a verified identity between the two $\left(2,1\right)$-categories in question. This biequivalence has been suggested at a few places in the literature. Inside HoTT, Buchholtz, van Doorn, and Rijke (2018) propose it as a $2$-dimensional generalization of the equivalence they construct between $\mathbf{Grp}$ and pointed connected $1$-types. It also was suggested in the classical setting by Baez and Lauda (2004). Indeed, the biequivalence we construct generalizes the $1$-dimensional equivalence. It consists of two broad steps. First, we construct the classifying space of a coherent $2$-group $G$ as a higher inductive type by generalizing the first Eilenberg-MacLane space of a group. This defines a function from the type of coherent $2$-groups to the type of pointed connected $2$-types. Second, we equip this function with the structure of a pseudofunctor and prove that it forms a biequivalence with the loop space pseudofunctor, which takes a pointed connected $2$-type to its fundamental $2$-group. Each step is purely algebraic, and all our proofs are constructive. Notably, combined with recent work by Owen Milner (unpublished), our biequivalence computes the Sinh invariant of a coherent $2$-group within a constructive system, whereas the traditional method relies on the axiom of choice. Our formalization, however, involves several huge computations, and we will discuss our experience managing its memory requirements and its arduous type-checking.

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1. SumTopo
3. 2025
5. Low-Dimensional

A minimality criterion for SL(4) skeins — Anup Poudel <poudel.33@osu.edu>

We provide a 4-valent ribbon model for SL(4) skein category by working with a category with object an oriented marking and morphisms generated by tagged and untagged 4-valent vertices. The category is defined combinatorially in terms of diagrammatic generators and relations. We use linear algebraic and skein theoretic methods to explore topological invariants coming from such a category. As a consequence, we show that a specialization of our parameters provides a 4-valent category that is equivalent to the SL(4) representation category. We further provide a topological evaluation algorithm of closed webs providing a (topological) criterion for reducible webs. We also show that certain HOMFLY relations exist in our category. Our evaluation algorithm works at a very abstract level and doesn’t use any algebraic constraints coming from the representation theory. This is a joint work with Giovanni Ferrer and Jiaqi Lu. 

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1. STDC
3. 2025
5. 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. SumTopo
3. 2026
5. GSTT

A quantitative measure of non-Isbell convexity in T_0-quasi-metric spaces — Collins Amburo Agyingi <agyingic@gmail.com>

Isbell-convex (q-hyperconvex) T₀-quasi-metric spaces are known to be bicomplete, although the converse does not hold in general. This talk introduces a quantitative invariant that measures the extent to which a bicomplete T₀-quasi-metric space fails to be Isbell-convex. The invariant is defined as a two-component parameter h_q(X)=((h_q)₁(X),(h_q)₂(X)) capturing the inherently asymmetric forward and backward deviations from convexity. Using the framework of minimal function pairs arising in the Isbell hull, we show that h_q(X)=(0,0) characterizes Isbell-convexity. We further establish key properties of this invariant, including non-negativity, invariance under isometries, and monotonicity with respect to subspaces and nonexpansive maps, as well as boundedness in the finite case. Concrete examples demonstrate how bicomplete spaces may fail to be Isbell-convex and illustrate how the invariant quantifies this deviation. This provides a new quantitative tool for studying the interplay between convexity and completeness in asymmetric topology.

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1. STDC
3. 2026
5. 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. SumTopo
3. 2026
5. GSTT

A soft version of Magill's theorem on n-point Hausdorff compactifications — Robert Gryczka <robert.jakub.gryczka@gmail.com>

Magill's theorem on necessary and sufficent conditions for topological space to have n point Hausdorff compactification is one of the classical tools in the theory of compactifications of topological spaces. In this talk, a soft version of this theorem will be presented in the context of soft topological spaces. Basic concepts of soft set theory and soft topology will be discussed, with particular emphasis on soft Hausdorff compactifications and their relationships with classical topological constructions. Subsequently, a generalization of Magill's theorem to the framework of soft topology will be presented, together with conditions characterizing the existence of soft n-point Hausdorff compactifications.

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1. SumTopo
3. 2025
5. Plenary

A survey of intrinsically linked and intrinsically knotted graphs, including an outline of an incomplete possible alternate proof of Sachs' linkless embedding conjecture — Joel Foisy <foisyjs@potsdam.edu>

A graph is *intrinsically linked* (resp. *intrinsically knotted*) if it contains, in every spatial embedding, a pair of cycles that form a nonsplit link (resp. a cycle that forms a nontrivial knot). In the early 1980s, Conway-Gordon and Sachs showed that the complete graph on 6 vertices is intrinsically linked, and Conway-Gordon showed that the complete graph on 7 vertices is intrinsically knotted. Sachs' linkless embedding conjecture is that the Petersen Family of graphs (those obtained from $K_6$ by triangle-Y and Y-triangle exchanges) form the complete set of minor-minimal (in some sense, simplest) intrinsically linked graphs. In the early 1990s, Robertson, Seymour and Thomas proved Sachs' linkless embedding conjecture; in a formidable work spanning three journal articles covering 99 pages. In the early 2000s, Flapan encouraged researchers to find another proof, leveraging more topology. Since that time, the speaker has been in and out of the rabbit hole of seeking a new proof. Minor-minimal intrinsically knotted graphs have not yet been fully characterized, and hundreds of such graphs have been found (Foisy, Goldberg-Mattman-Naimi, Kohara-Suzuki Schwartz, etc...). The problem of classifying all such graphs seems elusive at this time. In this talk, we present a survey of minor-minimal intrinsically knotted and intrinsically linked graphs, as well as discuss an outline of an incomplete alternate proof of Sachs' linkless embedding conjecture, in the hopes that someone within earshot of this talk will be inspired to complete Flapan's vision of a new proof.

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1. SumTopo
3. 2026
5. GSTT

A topological Ramsey space for pseudotrees — David Chodounsky <chodounsky@math.cas.cz>

Topological Ramsey spaces introduced by Todorcevic are spaces equipped with further structure (an ordering, a notion of approximation) which satisfy certain axioms. These spaces can be seen as abstract variations of the classical Ellentuck space and provide a unified framework for proving combinatorial partition theorems. We introduce a new type of A topological Ramsey space consisting of certain strong (sub)trees, which can be can be used for coding rational countable pseudotrees.

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1. SumTopo
3. 2026
5. GSTT

A tree-based perfectly normal space whose square is not countably metacompact — Assaf Rinot <rinotas@math.biu.ac.il>

The study of the interval topology of trees traces back to the 1960's with Jones' work on the normal Moore space problem. There are various limitations on the kind of spaces that can be obtained this way, for instance, Nyikos proved that for every tree $T$, if $X_T$ is normal, then it is also countably metacompact (CMC), i.e., there are no Dowker trees. Throughout the years, many consistency results were proven concerning the topological characteristics of spaces of the form $X_T$, but we couldn't find similar results dealing with the spaces' square. Here, we present a consistent construction of an Aronszajn tree $T$ such that $X_T$ is perfectly normal but $(X_T)^2$ it not even CMC. A key component of the construction is the use of `elevators' -- a device that enables to construct the tree level-by-level while optimally controlling features of its powers.

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1. STDC
3. 2025
5. 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. STDC
3. 2024
5. 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. SumTopo
3. 2026
5. GGT

Acyclicity of homeomorphism groups of stable Stone spaces — Michael Kopreski <michaelkopreski@gmail.com>

A stable second-countable Stone space is a closed subspace of the Cantor space with nice local structure. Examples arise as the end spaces of stable infinite-type surfaces and graphs. We classify the acyclicity of the homeomorphism groups of such spaces and describe progress toward computing their homology when not acyclic. These results are joint work with Mladen Bestvina and Rachel Skipper.

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1. STDC
3. 2025
5. 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. STDC
3. 2024
5. 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. STDC
3. 2025
5. 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. STDC
3. 2024
5. 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. SumTopo
3. 2026
5. QTBD

Adjoining germs of exponentials to R_an, exp while preserving o-minimality — Salma Kuhlmann <salma.kuhlmann@uni-konstanz.de>

Let κ be a regular uncountable cardinal. We construct non-archimedean exponential logarithmic models (R, an, exp) of cardinality κ, for T_an, exp (the elementary theory of the reals with restricted analytic functions and exponentiation), which admit a family F of 2^κ exponentials of pairwise distinct growth rates. These model exhibits the following remarkable features: 1. For each exponential exp' in F, (R, an, exp') is a model of T_an, exp and is thus o- minimal. 2. All exponentials in F agree exactly on the convex valuation ring of R. In particular, the germs of these exponentials are incompatible, in the sense that the structure (R, an, exp, exp') is no longer o-minimal.

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1. SumTopo
3. 2026
5. GGT

Algebraic fibrations, hyperbolic Coxeter groups and a hidden icosahedron. — Giovanni Italiano <giovanni.italiano.math@gmail.com>

A group is said to algebraically fibre if it admits an epimorphism onto $\mathbb{Z}$ whose kernel satisfies suitable finiteness properties, such as finite generation or finite presentability. The study of algebraic fibrations of hyperbolic groups has been a major theme in geometric group theory over the past two decades, motivated in part by the virtual fibering conjecture for odd-dimensional hyperbolic manifolds. Recently, Lafont, Minemyer, Sorcar, Stover, and Wells constructed, for every $d \geq 2$, a $d$-dimensional hyperbolic group admitting an algebraic fibration with finitely generated kernel. We strengthen this result by showing that, for every $d \geq 3$, there exists a $d$-dimensional hyperbolic group admitting an algebraic fibration whose kernel is _finitely presented_. Our construction combines right-angled Coxeter groups and Bestvina--Brady theory with a new collar-coning procedure inspired by a family of polytopes introduced by Löbell in the 1930s. This is joint work with M. Migliorini and A. Ng.

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1. STDC
3. 2025
5. 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. STDC
3. 2024
5. 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. STDC
3. 2026
5. 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. STDC
3. 2026
5. 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. STDC
3. 2025
5. 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. SumTopo
3. 2026
5. GGT

An alternative for subgroups of Thompson group V — Corentin Bodart <cobodart123@gmail.com>

In this talk, I will explain some applications of the characterization of finitely generated subgroups of Thompson group V given in Davide Perego's talk. I will recall some of the previously known obstructions, start building up by rephrasing them in our new framework, and then give some ideas towards the following stronger alternative: every finitely generated subgroup of V is either virtually abelian, or contains a free non-abelian semigroup.

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1. STDC
3. 2026
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2025
5. Graphs

An intrinsically linked simplicial $n$-complex — Ryo Nikkuni <nick@lab.twcu.ac.jp>

We say that a simplicial $n$-complex is intrinsically linked if every embedding of its polyhedron into $(2n+1)$-dimensional Euclidean space contains a pair of disjoint $n$-spheres with a nonzero linking number. Several examples of intrinsically linked $n$-complexes are known. In this talk, we present a new example of such an $n$-complex.

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1. SumTopo
3. 2025
5. General/ST

An iterable forcing property and universally meager sets — Valentin Haberl <valentin.haberl.math@gmail.com>

By a space we mean a metrizable separable zero-dimensional space. A space $X \subseteq 2^\omega$ is universally meager if for any Polish space $Y$ and any continuous nowhere constant map $f:Y \rightarrow 2^\omega$ the preimage $f^{-1}[X]$ is meager in $Y$. We call a space totally imperfect if it contains no copy of $2^\omega$. We present a forcing property $(\dagger)$, which is a strenthening of properness and implies that no dominating reals are added. It is known that many classical forcing posets like Cohen, Sacks and Miller satisfy this property. We showed that property $(\dagger)$ is preserved by countable support iterations. We then used this preservation result to prove that if we have such an iteration of length $\omega_2$ over a model of CH, where the single forcings have size at most $\omega_1$, all universally meager sets $X \subseteq 2^\omega$ have size at most $\omega_1$ in the forcing extension. \\ This has multiple set-theoretic applications: In the Miller model, we generalized our result of having no concentrated and $\gamma$-sets of size continuum to totally imperfect Hurewicz sets, which are universally meager by a result of Zakrzewski. Moreover, since Bartoszyński showed that all perfectly meager spaces are universally meager in the Miller model, we get that indeed even all perfectly meager spaces have size stricly less than continuum in the Miller model. Miller proved in 2005 that there exists a strong measure zero set of size $\omega_1$ iff there exists a Rothberger space of size $\omega_1$. Goldstern, Judah and Shelah constructed in 1993 a forcing iteration for which there is a strong measure zero set of size $\omega_2$ in the extension. However, this iteration satisfies property $(\dagger)$ and Rothberger spaces are universally meager in this model. Hence our result implies that it is consistent with ZFC to have a strong measure zero set of size $\omega_2$, but no Rothberger spaces of size $\omega_2$. This is joint work with Piotr Szewczak (Cardinal Stefan Wyszyński University in Warsaw) and Lyubomyr Zdomskyy (TU Vienna).

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1. SumTopo
3. 2026
5. QTBD

An unbounded number of canard limit cycles in linear regularizations of piecewise linear systems — Renato HUZAK <renato.huzak@uhasselt.be>

It is known that the number of limit cycles of piecewise linear (PWL) systems is bounded. We show, using Hopf and jump-breaking mechanisms, that the number of (canard) limit cycles in linear regularizations of PWL systems is unbounded.

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1. SumTopo
3. 2026
5. GSTT

Analogues of Hindman's Theorem for Topological Groups — Serhii Bardyla <sbardyla@gmail.com>

We shall discuss the partition regular properties of topological groups, and obtain an extension of Hindman’s theorem where the monochromatic sets of finite sums are required to satisfy additional topological constraints. In particular, our results imply that for every nowhere dense subset $C\subseteq \mathbb R^n$ there exists an open set $P\supseteq C$ such that for every finite coloring of $\mathbb Q^n\setminus P$ there exists a family $\mathcal A$ of sequences in $\mathbb Q^n\setminus P$ satisfying the following conditions: (i) the set of finite sums $\operatorname{FS}(A)$ is a closed discrete subset of $\mathbb R^n$ for all $A\in\mathcal A$; (ii) the set $\bigcup_{A\in\mathcal A}\operatorname{FS}(A)$ is monochromatic; and (iii) the set $\bigcup_{A\in\mathcal A}\operatorname{FS}(A)$ is dense in an open unbounded subset of $\mathbb R^n$. The aforementioned result was obtained using a new characterization of spaces whose Stone-Čech compactifications possess remote points.

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1. SumTopo
3. 2025
5. Plenary

Analyzing the Geometric Topology of Artificial (ReLU) Neural Networks — Marissa Masden <mmasden@pugetsound.edu>

This talk is intended as an introduction to and overview of the geometric topology of (some) artificial neural network functions, with aims towards advancing the understanding of deep learning models. First, I will introduce the type of neural network functions under consideration ("ReLU networks," or multilayer perceptrons with ReLU activation) and their relation to contemporary machine learning. I will then discuss some of the perspectives from which geometric and topological measures of ReLU networks may be exploited to understand and analyze the structure of individual such functions as well as the class of all such functions, both theoretically and computationally. I will pay special attention towards the "decision region/boundary" interpretation of classification models, which corresponds to (sub)level set approximation. A concern is that sublevel sets with too high of complexity (as measured via topological invariants) corresponds to "memorization/overfitting" of a machine learning model, but sublevel sets of insufficient complexity will fail to generalize over a large portion of the problem domain. Resultingly, we seek tools to assess the complexity of a given ReLU network. One result in this direction is that, under certain genericity and transversality assumptions on intermediate layers, the (mod-2) Betti numbers of level sets of ReLU networks can be computed exactly by exploiting hyperplane arrangement combinatorics. I will additionally discuss some of the unique challenges faced when extending piecewise linear and discrete Morse theory to this function class, including current progress. This talk is based on, in part, work done jointly with J. Elisenda Grigsby, Kathryn Lindsey, and Robyn Brooks.

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1. STDC
3. 2025
5. 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. SumTopo
3. 2025
5. Low-Dimensional

Another proof of functoriality for odd Khovanov homology — Dean Spyropoulos <spyropou@msu.edu>

In 2024, Migdail and Wehrli proved that odd Khovanov homology is functorial with respect to link cobordism (up to sign). Unlike Khovanov's proof that the original theory is functorial, Migdail-Wehrli's is interesting in that it does not depend on any of the recent extensions of odd Khovanov homology to tangles. In recent ongoing work, we adapt Khovanov's original argument to one of these tangle theories to get a proof that Naisse-Putyra's odd tangle invariant is functorial with respect to tangle cobordisms (up to unit). This approach motivates a few novel constructions, including a new generalization of Hochschild (co)homology.

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1. STDC
3. 2024
5. 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. SumTopo
3. 2026
5. TDS

Area-preserving surface homeomorphisms without zero entropy — Fabio Armando Tal <fabiotal@ime.usp.br>

The dynamics of area-preserving flows on closed orientable surfaces is a well-understood topic, and there exists a canonical invariant decomposition of the phase space into a region (a collection of topological annuli) where the dynamics is integrable, and a finite number of pieces of positive genus where the dynamics is quasi-minimal (closely resembling the dynamics of an irrational flow on a torus). In this work, we show that a very similar canonical decomposition remains valid when dealing with conservative homeomorphisms with zero topological entropy. We present this decomposition while also exhibiting examples of different phenomena that may arise, as well as several properties of the “quasi-minimal” regions. Part of the work involves proving a Thurston–Nielsen–type reduction result, showing that maps homotopic to Dehn twists and with zero entropy actually possess invariant “Dehn-like” annuli. Time permitting, we will also discuss some applications to Reeb flows on three-dimensional manifolds.

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1. STDC
3. 2025
5. 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. STDC
3. 2026
5. GeoGT
7. 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. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. STDC
3. 2025
5. 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. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. Community
3. Carolinas

Behavior of discrete reflexivity in presence of an algebraic structure — Vladimir Tkachuk <vvtmdf@gmail.com>

If $\mathcal P$ is a topological property, then a space $X$ is called discretely $\mathcal P$ if the closure of every discrete subset of $X$ has $\mathcal P$. The property $\mathcal P$ is discretely reflexive in a class $\mathcal A$ if a space $X$ from $\mathcal A$ has $\mathcal P$ if and only if it is discretely $\mathcal P$. I proved in 1988 that compactness is discretely reflexive in the class of all spaces and it is still an open question whether the Lindel\"of property is discretely reflexive. However, Arhangel'skii and Buzyakova proved in 1999 that the Lindel\"of property is discretely reflexive in spaces of countable tightness. In this talk I will show that pseudocharacter is discretely reflexive in Lindel\"of $\Sigma$-groups but countable tightness is not discretely reflexive in hereditarily Lindel\"of spaces. Besides, I will present some results on discrete reflexivity of topological properties in spaces $C_p(X)$.

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1. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. STDC
3. 2025
5. 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. Community
3. vALANtines 2026

Big generic models — Will Brian <wbrian.math@gmail.com>

Given a suitable class $\mathcal K$ of finite structures, a theorem of Fraïssé shows how to construct a special countable model, called the Fraïssé limit of $\mathcal K$: the unique dense $G_\delta$ (a.k.a., "generic") isomorphism type in the space of all countable structures built from $\mathcal K$. Assuming the Continuum Hypothesis (CH), the same is true one cardinality higher: if $\mathcal K$ satisfies the hypotheses of Fraïssé's Theorem, then there is a unique generic isomorphism type in the space of all size-$\mathfrak c$ structures built from $\mathcal K$, and furthermore, these special models of size $\mathfrak c$ have properties analogous to their corresponding Fraïssé limits. Some classes of finite structures do not satisfy the hypotheses of Fraïssé's theorem, and these classes do not have Fraïssé limits. Interestingly, however, a class $\mathcal K$ may have no Fraïssé limit, but still have a unique size-$\mathfrak c$ generic model under CH. In other words, under CH, big generic models exist for any even broader range of classes than Fraïssé limits do, giving rise to Fraïssé-like uncountable structures with no true countable analogues. We will describe some aspects of the construction of these higher Fraïssé limits, and give several examples of familiar structures that can be understood in this way.

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1. STDC
3. 2024
5. 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. SumTopo
3. 2026
5. TDS

Birkhoff-like attractors — Martin Sambarino <martinsambarino@gmail.com>

Birkhoff attractors arise from the study of dissipative annulus maps that twist the vertical direction. When their rotation set is nontrivial, these attractors exhibit a complicated topological structure, namely that of an indecomposable continuum. In this talk, we introduce a class of Birkhoff-like attractors for dissipative annulus maps and study the continuity properties of these attractors and their rotation sets under perturbations of the dynamics.

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1. SumTopo
3. 2026
5. GGT

Book decompositions and Morse complexity — Bena Tshishiku <bena_tshishiku@brown.edu>

A book decomposition of a manifold is a way of decomposing it as a union of codimension-1 submanifolds (the pages) that are glued along a codimension-2 submanifold (the binding). For example, each fibered knot gives a book decomposition of the 3-sphere; more generally, every odd dimensional manifold has a book decomposition by work of Alexander, Lawson, and Quinn. In this talk I’ll explain why even-dimensional hyperbolic manifolds do not have book decompositions. The main tool is Morse complexity, a norm on singular homology introduced by Gromov for which we give some new computations for locally symmetric manifolds. This is joint work with Fedor Manin and Shmuel Weinberger.

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1. STDC
3. 2025
5. 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. SumTopo
3. 2025
5. Plenary

Bounded cohomology of transformation groups of $\mathbb{R}^n$ — Francesco Fournier-Facio <ff373@cam.ac.uk>

Bounded cohomology is a functional analytic analogue of group cohomology, with many applications in rigidity theory, geometric group theory, and geometric topology. A major drawback is the lack of excision, and because of this some basic computations are currently out of reach; in particular the bounded cohomology of some “small” groups, such as the free group, is still mysterious. On the other hand, in the past few years full computations have been carried out for some “big” groups, most notably transformation groups of $\mathbb{R}^n$, where the ordinary cohomology is not yet completely understood. I will report on this recent progress, which will include joint work with Caterina Campagnolo, Yash Lodha and Marco Moraschini, and joint work with Nicolas Monod, Sam Nariman and Sander Kupers.

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1. STDC
3. 2026
5. 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. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. STDC
3. 2026
5. 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. STDC
3. 2025
5. 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. STDC
3. 2025
5. 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. SumTopo
3. 2025
5. Dynamics/CT

Building Continua with non-trivial self covers — Mathew Timm <mtimm@bradley.edu>

We will look at several methods for building continua with non-trivial self covers and discuss their relationships with some problems in topology and group theory.

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1. SumTopo
3. 2026
5. CT

Building Spaces with Non-trivial Self Covers — Mathew Timm <mtimm@bradley.edu>

We consider a dynamical systems approach for building spaces which have non-trivial self covers and a connection to self similar groups.

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1. SumTopo
3. 2026
5. TC

Building confidence regions for Reeb graphs using the interleaving distance — Matteo Pegoraro <matteopegoraro.91@gmail.com>

Reeb graphs and Mapper graphs are widely used in topological data analysis to summarize the evolution of connected components of level sets of a scalar function. However, using these summaries in practice requires principled methods for parameter selection and uncertainty quantification under sampling assumptions. In this talk, I will present a framework for building confidence regions for Reeb graphs using the interleaving distance. The key advantage of this metric viewpoint is that zero distance corresponds to isomorphism of the underlying Reeb-type objects, so confidence balls provide object-level guarantees rather than guarantees only on persistence signatures. Starting from a finite sample, we define intrinsic and extrinsic Mapper-type cosheaf estimators and prove stability bounds comparing them to the target Reeb cosheaf. These bounds lead to confidence regions once the sampling scale is controlled, either through standard sampling assumptions or via subsampling-based estimates. I will also explain how these interleaving bounds relate to classical persistence-based guarantees: in particular, we prove that the extended-persistence pseudometric is controlled by the interleaving distance, with sharp constant 1 for the $H_0$-related components and global constant 2. This provides a direct bridge with previous Mapper confidence frameworks, while giving stronger, metric-level control of the underlying Reeb graph.

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1. STDC
3. 2024
5. 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. STDC
3. 2026
5. 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. STDC
3. 2026
5. 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. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2025
5. General/ST

Cancelled: $Q$-sets, $\Delta$-sets and $L$-spaces — Pourya Memarpanahi <pourya.memarpanahi@utoronto.ca>

The concept of a ∆-set of reals was originally defined by G.M. Reed. An equivalent version was defined by Eric van Douwe and later on was generalized to an arbitrary topology space, (∆-space) . Historically, this notion arose in the study of the normal Moore space conjecture, where Q-sets were used to construct important counterexamples to the conjecture. We prove that Moore's L-space (a hereditarily Lindelöf but not separable space in ZFC) is not a Q-set space and if Aronszajn tree naturally associated with Moore’s L-space is special Moore's L-space will not be a ∆-space.

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1. SumTopo
3. 2025
5. General/ST

Cancelled: The $F_\sigma$-below relation and some new separation axioms in the category of locales — Mbekezeli Nxumalo <sibahlezwide@gmail.com>

We use $F_\sigma$ sublocales to define a relation on locales called the $F_\sigma$-below relation. This relation is weaker than the rather below relation. Two separation axioms, namely weakly D-completely regularity and $F_\sigma$-regularity, between perfectness and weakly subfitness are introduced using the $F_\sigma$-below relation. We discuss properties of these two locales and find their relationship with other locales such as regularity and subfitness.

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1. STDC
3. 2024
5. 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. STDC
3. 2025
5. 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. SumTopo
3. 2025
5. General/ST

Cardinal bounds in spaces with a $\pi$-base whose elements have an H-closed closure — Davide Giacopello <dagiacopello@unime.it>

We deal with the class of Hausdorff spaces having a $\pi$-base whose elements have an H-closed closure. Carlson proved that $|X|\leq 2^{wL(X)\psi_c(X)t(X)}$ for every quasiregular space $X$ with a $\pi$-base whose elements have an H-closed closure. We provide an example of a space $X$ having a $\pi$-base whose elements have an H-closed closure which is not quasiregular (neither Urysohn) such that $|X|> 2^{wL(X)\chi(X)}$ (hence, $|X|> 2^{wL(X)\psi_c(X)t(X)}$). Still in the class of spaces with a $\pi$-base whose elements have an H-closed closure, we establish the bound $|X|\leq2^{wL(X)k(X)}$ for Urysohn spaces and we give an example of an Urysohn space $Z$ such that $k(Z)<\chi(Z)$. Lastly, we present some equivalent conditions to the Martin's Axiom involving spaces with a $\pi$-base whose elements have an H-closed closure and, additionally, we prove that if a quasiregular space has a $\pi$-base whose elements have an H-closed closure then such a space is Baire.

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1. SumTopo
3. 2025
5. Plenary

Cardinal inequalities for non-Hausdorff topological spaces — Ivan Gotchev <gotchevi@ccsu.edu>

For a Hausdorff space $X$, Hajnal and Juhász showed in 1967, that $|X| \le2^{c(X)\chi(X)}$ and $|X| \le 2^{2^{s(X)}}$, where $c(X)$ is the cellularity, $\chi(X)$ is the character and $s(X)$ is the spread of $X$; Arhangel'skii, in 1969, proved that $|X|\le 2^{\chi(X)L(X)}$, where $\chi(X)$ is the character and $L(X)$ is the Lindelӧf degree of $X$; and, in 1974, Arhangel'skiĭ and Šapirovskiĭ strengthened Arhangel'skiĭ's inequality by showing that $|X|\le 2^{t(X)\psi(X)L(X)}$, where $t(X)$ is the tightness and $\psi(X)$ is the pseudocharacter of $X$. It has been an open question for a long time if Arhangel'skiĭ's inequality is true for every $T_1$-space $X$. In this talk we will mention what is known in relation to the above question and how by using other cardinal functions, some of the above inequalities could be extended to be valid for all $T_1$-spaces and, in some cases, even for all topological spaces.

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1. STDC
3. 2025
5. 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. SumTopo
3. 2025
5. Dynamics/CT

Chaos on Peano continua — Klára Karasová <karasova@karlin.mff.cuni.cz>

Among all notions of chaos, there are three widely accepted: Devaney chaos, Li-Yorke chaos and (positive) topological entropy. It is known that exact Devaney chaos, i.e. an exact map with dense set of periodic points, satisfies all these three notions. Various results establish the existence of maps with properties related to chaos (e.g., transitivity) for specific spaces such as the interval, the Cantor set or the Lelek fan, as well as for broader classes, including manifolds and dendrites. Furthermore, chaotic behavior often emerges as a generic phenomenon in the sense of Baire category. Together with Benjamin Vejnar, we prove that every Peano continuum (i.e. a locally connected continuum) admits exact Devaney chaos. Additionally, we generalize some prior results by showing that if a Peano continuum $X$ satisfies the condition that selfmaps locally constant on some dense open subset form a dense subset of all selfmaps, then: • exactly Devaney chaotic maps form a dense subset of chain transitive self- maps of X, • mixing is generic among chain transitive self-maps of X, • shadowing is generic among all self-maps of $X$.

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1. STDC
3. 2025
5. 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. STDC
3. 2025
5. 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. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2026
5. TC

Chromatic topological data analysis and the stability of the six-pack via constrained Gromov–Hausdorff distances — Nicolò Zava <nicolo.zava@ist.ac.at>

Topological Data Analysis (TDA) utilise topology-inspired invariants, most notably persistent homology, to extract structural features from complex datasets. A fundamental requirement for these invariants in computational applications is stability under spatial perturbations. Within the standard setting of TDA, the Gromov–Hausdorff distance serves as a rigorous metric framework for comparing underlying datasets and establishing stability guarantees, ensuring that small metric deformations result in bounded changes in the corresponding persistence diagrams. While classical TDA focuses primarily on the geometric arrangement of unlabelled point clouds, modern applications frequently require integrating qualitative features, usually represented by different colours, directly onto the points of a dataset. A prominent example is bioimages of tissues, where different cell types are represented in different colours. This necessity has driven the emergence of chromatic TDA. To capture the homological interactions between distinct coloured subsets, recent techniques utilise the "six-pack", a collection of six interlinked persistence diagrams. In this talk, we recall the standard framework of TDA and the role of the Gromov–Hausdorff distance. We then present some of the techniques utilised to study and compute features from these coloured datasets. Finally, we introduce the $C$-constrained Gromov–Hausdorff distance, a suitable variation of the classical metric adapted for chromatic frameworks, and demonstrate its application in evaluating invariants in chromatic TDA—specifically by establishing the stability of the six-pack.

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1. STDC
3. 2025
5. 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. STDC
3. 2025
5. 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. SumTopo
3. 2026
5. TDS

Classification of Henon maps with strange attractors via the topology of a stable manifold — Sonja Stimac <sonja@math.hr>

In an earlier work with Boronski, we classified (up to conjugacy) the Henon maps with strange attractors in terms of three invariants that we introduced for them: (a) kneading sequences, (b) pruned trees, and (c) folding patterns of the unstable manifold of the hyperbolic fixed point $X$ in the attractor. In my talk, I will introduce yet another way to determine conjugacy classes of these maps, this time purely from the topology of the stable manifold $W^s$ of $X$. We consider a region of dissipation $D$ for the Henon map and study the connected components of $D \cap W^s$. To each such component, we assign a separation type and prove that two Henon maps are conjugate if and only if their corresponding components share the same separation type. This is joint work with Jan Boronski.

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1. SumTopo
3. 2026
5. GSTT
7. Plenary

Classification of countably tight groups. — Alex Shibakov <ashibakov@tntech.edu>

We provide a classification of convergence structures in countably tight groups using the Invariant Ideal Axiom and the related Definable Ideal Axiom. We then show some applications to countable groups and the boolean groups with the bounded topology, answering a few published questions. A number of open problems will also be mentioned.

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1. STDC
3. 2025
5. 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. STDC
3. 2025
5. 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. STDC
3. 2024
5. 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. STDC
3. 2024
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2026
5. GGT
7. Plenary

Cohomology of arithmetic lattices and link complements — Jean Raimbault <jean.raimbault@univ-amu.fr>

I will present a proof of the following conjecture of Baker--Reid: given any rational homology 3-sphere N, there are at most finitely many congruence arithmetic quotients of hyperbolic space which are homeomorphic to the complement of a link in N. There are many ingredients to the proof but the final step is an asymptotic lower bound on the cuspidal homology of certain congruence subgroups of Bianchi groups. I will therefore use the conjecture as an excuse to talk about various ways to give such bounds, and finally present the somewhat new method we used to get to the result we needed. (Joint work with Steffen Kionke).

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1. STDC
3. 2024
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2025
5. 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 classical Baire space $\omega^\omega$ with the generalized Baire space $\kappa^\kappa$. This is joint work with Piotr Szewczak and Lyubomyr Zdomskyy.

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1. SumTopo
3. 2025
5. General/ST

Combinatorial structures of concentrated sets — Piotr Szewczak <p.szewczak@wp.pl>

Let $X$ be a set of reals and $\kappa$ be an uncountable cardinal number. The set $X$ is $\kappa$-concentrated, if $X$ has size at least $\kappa$ and contains a countable set $D$ such that each closed subset of $X$, disjoint with $D$, has size smaller than $\kappa$. Various forms of concentrated sets play an important role in the study of combinatorial covering properties such as Rothberger’s, Hurewicz’s, and Menger’s properties. We investigate the behavior of such sets in different models of set theory. This is a joint work with Michał Pawlikowski and Lyubomyr Zdomskyy. The research was funded by the Polish National Science Center and Austrian Science Fund; Grant: Weave-UNISONO, Project: Set-theoretic aspects of topological selections 2021/03/Y/ST1/00122.

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1. Community
3. vALANtines 2026

Comments on Alan's construction of a countable Fréchet space of uncountable pi-weight — Michael Hrusak <michael@matmor.unam.mx>

Joint work with R. Figueroa, O. Guzmán and A. Kwela. We shall comment on Alan's construction of a countable Fréchet space of uncountable pi-weight.

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1. STDC
3. 2026
5. 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. SumTopo
3. 2025
5. Computing

Comparison of Precinct and District Voting Data Using Persistent Homology to Identify Gerrymandering in North Carolina — Ananya Shah <ananya.neytri.shah@gmail.com>

We present an extension of Feng & Porter’s 2019 paper on the use of the level-set method for the construction of a filtered simplicial complex from geospatial election data, by applying their method to identify gerrymandering. Using the fact that precincts are regarded to be too small to be gerrymandered, we identify discrepancies between precinct and district level voting data to quantify gerrymandering. Comparing the persistent homologies of democratic voting areas on the precinct and district level shows when areas have been ‘cracked’ or ‘packed’ for partisan gain. This analysis was done for North Carolina House of Representatives elections (2012-2024). NC has been redistricted 4 times in the past 10 years, whereas most states redistrict decennially, allowing us to understand how and when redistricted maps deviate from precinct-level voting data, and when gerrymandering occurs. Comparing persistence barcodes at the precinct and district levels (using the bottleneck distance) shows that precinct-level voting patterns do not significantly fluctuate biannually, while district level patterns do, suggesting that shifts are likely a result of redistricting rather than voter behavior, providing strong evidence of gerrymandering. NC Election data was collected from the public domain. Composite shapefiles were created using QGIS and R, and rasterized using Python. The level-set method was employed to generate filtered similar complexes. Persistence barcodes were produced using GUDHI and PHAT libraries. Additionally, we compare our results with traditional measures such as Polsby-Popper and Reock scores (gerrymandering identification measures). This research presents a novel application of topological data analysis in analyzing gerrymandering.

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1. STDC
3. 2025
5. 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. STDC
3. 2024
5. 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. SumTopo
3. 2026
5. QTBD
7. Plenary

Composition of transseries, monotonicity, and analyticity — Vincenzo Mantova <v.l.mantova@leeds.ac.uk>

Transseries generalise power series by including exponential and logarithmic terms, if not more, and can be interpreted as germs of a non-standard Hardy field by composition (for instance, on surreal numbers). I'll discuss a few results that must 'obviously' be true, yet their proofs are not obvious: that composition is monotonic in both arguments, only proved by Edgar for LE-series, that it satisfies a suitable Taylor theorem and that in fact composition is 'analytic with large radius of convergence' (joint with V. Bagayoko), something which appeared before in various special forms, but not in full generality. I'll discuss briefly what I cannot prove yet (convexity!). I'll show how monotonicity and Taylor can be used to prove some fairly general normalisation results for hyperbolic transseries (joint with D. Peran, J.-P. Rolin, T. Servi).

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1. SumTopo
3. 2026
5. TC

Computability of Common Fixed Points of Isometries — Lucija Validžić <luc.validzic@gmail.com>

For a metric space $X$, the fixed points of $X$ are points that are fixed by all isometries of $X$. We will study computable properties of fixed points of compact subsets of $\mathbb{R}^n$. A natural question is: If $X$ is a computable subset of $\mathbb{R}^n$ whose set of fixed points is non-empty, is there a computable fixed point of $X$? The answer is negative and we will show an example of such $X$, but if the set of fixed points is finite, then the answer is positive. More generally, we will prove that the set of fixed points of a computable set is necessarily semicomputable. Additionally, we will show that the convexity of a computable set $X$ implies that the set of its fixed points is computable, so in that case $X$ contains computable fixed points.

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1. STDC
3. 2024
5. 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. STDC
3. 2026
5. Dynamics
7. 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. SumTopo
3. 2026
5. TC

Computable categoricity in Euclidean spaces — Patrik Vasung <patrik.vasung@grad.unizg.hr>

A computable metric space $(X, d)$ is computably categorical if every two effective separating sequences in $(X, d)$ are equivalent up to isometry. We investigate computable categoricity of effectively compact metric spaces. We prove that every effectively compact metric space whose isometry group has computable type is computably categorical. Using this result, we prove that every effectively compact subspace of $\mathbb{R}^n$ is computably categorical.

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1. SumTopo
3. 2026
5. TC

Computable inner approximation of topological graphs — Matea Čelar <matea.celar@math.hr>

In this talk, we will discuss conditions under which a metric space is inner approximated by its computable subspaces. We focus on (generalised) topological graphs, which are spaces obtained by gluing arcs and rays together at their endpoints. First, we show that every non-vertex point in a semicomputable topological graph has a neighbourhood which is a computable arc with computable endpoints. Using this, we show that every semicomputable topological graph is inner approximated by computable topological graphs with computable endpoints. This talk is based on joint work with Vedran Čačić, Marko Horvat and Zvonko Iljazović.

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1. SumTopo
3. 2025
5. Computing

Computing path homology chains by inductive construction — Matthew Burfitt <m.burfitt@bimsa.cn>

The path homology introduced by Grigor’yan, Lin, Muranov and Yau plays a central role in digraph topology and the emerging field of digraph homotopy theory more generally. Unfortunately, the computation of the path homology of a digraph is a two-step process, and until now no complete description of even the underlying chain complex has appeared in the literature. In particular, our understanding of the path chains is the primary obstruction to the development of fast path homology algorithms, which in turn would enable the practicality of a wide range of applications to directed networks. I will introduce an inductive method of constructing elements of the path homology chain modules from elements in the proceeding two dimensions. When the coefficient ring has prime characteristic the inductive elements generate the path chains. Moreover, in low dimensions the inductive elements coincide with naturally occurring generating sets up to sign, making them excellent candidates to reduce to a basis. Inductive elements provide a new concrete structure on the path chain complex that can be directly applied to understand path homology, under no restriction on the digraph. During the talk I will demonstrate how inductive elements yield the explicit structure of the dimension 3 path chains and enable the construction of a sequence of digraphs whose path Euler characteristic can differ arbitrarily depending on the choice of coefficients.

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1. STDC
3. 2025
5. 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. SumTopo
3. 2026
5. GSTT

Concentrated sets and the Hurewicz property — Valentin Haberl <valentin.haberl.math@gmail.com>

A set of reals $X$ is $\mathfrak{b}$-concentrated if it has cardinality at least $\mathfrak{b}$ and it contains a countable set $D\subseteq X$ such that each closed subset of $X$ disjoint from $D$ has size smaller than $\mathfrak{b}$. $\kappa$-concentrated sets play a crucial role in the investigation of combinatorial covering properties. It is independent of ZFC if all $\mathfrak{b}$-concentrated sets are Hurewicz. We present ZFC results about how structures of $\mathfrak{b}$-concentrated sets with the Hurewicz covering property can be characterized with the notion of being meager-unbounded, which we then use to get that such structures are productively Hurewicz. We obtain that assuming that the semifilter trichotomy holds each $\mathfrak{b}$-concentrated set is Hurewicz and even productively Hurewicz. In particular, in the Miller model $\mathfrak{b}$-concentrated sets are also productively Rothberger. We analyze the Laver model, where the behavior of Hurewicz $\mathfrak{b}$-concentrated sets differs from the one under the semifilter trichotomy. This is joint work with Piotr Szewczak (University of Warsaw) and Lyubomyr Zdomskyy (TU Vienna).

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1. STDC
3. 2025
5. 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. SumTopo
3. 2026
5. GGT

Conjugacy separability in free-by-cyclic groups — Monika Kudlinska <mak74@cam.ac.uk>

A group G is conjugacy separable if any pair of non-conjugate elements remain non-conjugate in a finite quotient of G. While the original motivation for studying conjugacy separability stems from applications to algorithmic problems in group theory, more recently it has been successfully leveraged to exhibit certain rigidity properties of manifolds. In my talk, I will briefly discuss the applications of conjugacy separability to topology, before discussing the new result that all free-by-cyclic groups - a family closely related to 3-manifold groups - are conjugacy separable. This is joint work with Francois Dahmani, Sam Hughes and Nicholas Touikan.

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1. STDC
3. 2026
5. 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. STDC
3. 2025
5. 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. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2026
5. GSTT

Constructions of crowded zero-dimensional Hausdorff P-spaces without the Axiom of Choice — Eliza Wajch <eliza.wajch@gmail.com>

#Constructions of crowded zero-dimensional Hausdorff _P_-spaces without the Axiom of Choice **Eliza Wajch** ***Institute of Mathematics, University of Siedlce, 3 Maja 54, 08-110 Siedlce, Poland*** The results presented here form part of the author's joint work with Eleftherios Tachtsis [2]. They are motivated by the question posed in [1]: is the existence of a non-discrete Tychonoff _P_-space provable in **ZF**? A topological space whose every _G__&delta;-set is open is called a _P_-space. Throughout, our set-theoretic framework is **ZF** or **ZFA**. Among several related results, we show that non-empty zero-dimensional crowded Hausdorff _P_-spaces exist in every permutation model of **ZFA** and in every model of **ZF** having an aleph of uncountable cofinality. A key ingredient in our analysis is the following construction of zero-dimensional Hausdorff spaces which, under additional hypotheses, yields _P_-spaces. Let _X_ be an infinite set, and let &Zscr; be a family of subsets of _X_ closed under finite unions and containing [_X_]^{&lt;*&omega;*}. For _x_ ∈ [X]^{&lt;*&omega;*} and _z_ ∈ &Zscr; with _x_ &cap; _z_ = &empty;, define _B_(_x_,_z_) = \{_y_ ∈ [_X_]^&lt;&omega; : _x_ ⊆ _y_ ⊆ _X_ \ _z_}. Let &Tscr; be the topology on [_X_]^{&lt;*&omega;*} such that, for each _x_ ∈ [_X_]^{&lt;*&omega;*}, the family {_B_(_x_,_z_): _z_∈ &Zscr; and _x_ &cap; _z_ = &empty;} forms a neighborhood base at _x_. The resulting space **S**(_X_, &Zscr;) = ([_X_]^{&lt;*&omega;*} , &Tscr;) is Hausdorff and zero-dimensional, and it is crowded whenever _X_ is not a member of &Zscr;. Assuming that &Zscr; is a bornology on _X_, we obtain that the space **S**(_X_, &Zscr;) is homogeneous, and if it is a _P_-space, then &Zscr; is a &sigma;-ideal. In particular, **S**(_X_, [_X_]^{&lt;*&omega;*}) is a _P_-space if and only if the set _X_ is quasi Dedekind-finite. The space **S**(*&omega;*₁, [*&omega;*₁]^{&le;*&omega;*}) is a _P_-space if and only if *&omega;*₁ has uncountable cofinality. Every denumerable family of non-empty finite sets admits a choice function if and only if, for every infinite set _X_, either _X_ is Dedekind-infinite or **S**(_X_, [_X_]^{&le;*&omega;*}) is a _P_-space. If every denumerable family of non-empty subsets of the real line &#8477; has a choice function, then there exists a topology &Tscr; on &#8477; such that (&#8477; &Tscr;) is a zero-dimensional, crowded Hausdorff _P_-space. The converse implication is false in the Basic Cohen Model of **ZF**. In fact, in the Basic Cohen Model, for every infinite set _X_, the space **S**(_X_, [_X_]^{&le;*&omega;*}) is a _P_-space. **References** - [1] K. Keremedis, A. R. Olfati, and E. Wajch, *On P-spaces and G_&delta;-sets in the absence of the axiom of choice*, Bull. Belg. Math. Soc. Simon Stevin 30 (2), 194–236 (2023). - [2] E. Tachtsis and E. Wajch, *Constructing crowded Hausdorff P-spaces in set theory without the axiom of choice*, submitted manuscript (2025), https://arxiv.org/abs/2510.11935

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1. SumTopo
3. 2026
5. CT

Continua that admit an inscribed polygon: the Euclidean and hyperbolic settings — Ulises Morales-Fuentes <ulises.morales@uaem.mx>

A plane continuum $X$ is said to admit an inscribed polygon, $P$, if every embedding of $X$ into $\mathbb{R}^2$ (the Euclidean plane) contains the vertices of a polygon similar to $P$. In this talk we adapt this definition to the hyperbolic geometry setting: A plane continuum quasi-inscribes a polygon $Q$ in the hyperbolic plane $\mathbb{H}$, if given any embedding $\gamma:X\hookrightarrow\mathbb{H}$, we have that for all $\varepsilon>0$, $\gamma(X)$ admits a polygon whose inner angular sum is $\varepsilon$-close to the sum in $Q$; and both polygons share geometric structure. In particular, we show that there is a wide class of continua that quasi-inscribe rectangles. We will also include some results, obtained in the Euclidean setting, regarding the inscription of squares and rectangles in continua, in this case we will focus on continua that are ray compactifications.

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1. SumTopo
3. 2026
5. TDS

Continuation of attractors for discrete semidynamical systems and applications to generalized Hopf bifurcations — Héctor Barge <h.barge@upm.es>

In this talk we shall study continuations of attractors of embeddings in manifolds. We shall introduce the abstract basin of attraction of such attractors and we shall see that if two attractors are related by continuation, their abstract basins are homeomorphic. Moreover, if this continuation is achieved by a small perturbation, then, the homeomorphism can be chosen to be the identity close to the original attractor. We shall make use of this rigidity property in order to characterize the Cech cohomology of the attractors expelled after a generalized Hopf bifurcation of an attractor. These results have been obtained in collaboration with J.J. Sánchez-Gabites

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1. STDC
3. 2024
5. 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. SumTopo
3. 2026
5. GSTT

Convergence with respect to a semitopogenous order on a complete lattice — Josef Slapal <slapal@fme.vutbr.cz>

A. Czaszar introduced the concept of a semitopogenous order as a binary relation on the power sets of a given set. We extend semitopogenous orders from power sets to arbitrary complete lattices and investigate their behaviour. In particular, we study convergence of generalized nets (upwards closed and centered subsets) with respect to a semitopogenous order and give conditions under which the convergence behaves analogously to the filter convergence in topological spaces. Separation and compactness with respect to a semitopogenous order are discussed, too.

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1. SumTopo
3. 2026
5. GGT

Convex cocompact groups with three-dimensional limit sets — Lorenzo Ruffoni <lorenzo.ruffoni2@gmail.com>

Given a discrete group of isometries of a real hyperbolic space, we can look at its limit set, i.e., the set of accumulation points of its orbits on the sphere at infinity. This is a compact metric space on which the group acts, and which enjoys many interesting geometric, topological, and dynamical features. For example, classical Kleinian groups provide many examples with limit sets that are quasicircles, Cantor sets, and Sierpinski carpets. In this talk, I will discuss how to construct examples whose limit sets are various low-dimensional trees of manifolds. In particular, we answer a question of M. Kapovich, by constructing convex cocompact groups of isometries of real hyperbolic spaces, whose limit sets are Čech cohomology 3-spheres not homeomorphic to S^3. These groups are right-angled Coxeter groups and our construction is flexible enough to produce infinitely many quasi-isometry classes. This is joint work with S. Douba, G.-S. Lee, and L. Marquis.

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1. STDC
3. 2024
5. 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. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2025
5. General/ST

Countable dense homogeneity and topological groups — Andrea Medini <andrea.medini@tuwien.ac.at>

All spaces are assumed to be separable and metrizable. A space X is countable dense homogeneous (CDH) if all countable dense subsets of X can be mapped onto each other by homeomorphisms of X. The fundamental theorem of countable dense homogeneity states that every "sufficiently homogeneous" Polish space is CDH. This result motivated a long-standing search for examples of non-Polish CDH spaces. We contribute to this line of research by exhibiting a non-Polish CDH topological group. This is joint work with Claudio Agostini and Lyubomyr Zdomskyy.

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1. STDC
3. 2026
5. 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. STDC
3. 2024
5. 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. STDC
3. 2024
5. 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. STDC
3. 2026
5. 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. STDC
3. 2026
5. 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. STDC
3. 2026
5. 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. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2026
5. QTBD

Cyclicity of piecewise linear centers — Rafel J. Prohens <rafel.prohens@uib.cat>

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1. STDC
3. 2024
5. 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. STDC
3. 2025
5. 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. STDC
3. 2024
5. 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. SumTopo
3. 2026
5. CT

Decomposability of inverse limits of positive entropy systems on the Gehman dendrite — Jakub Tomaszewski <tomaszew@agh.edu.pl>

The problem of the decomposability of inverse limits of dynamical systems on continua has been of long-standing interest to many researchers in topological dynamics. A cornerstone result by Barge and Martin ([1](https://doi.org/10.1090/S0002-9947-1985-0779069-7)) shows that if a topological dynamical system on a unit interval has positive entropy, then the inverse limit of this system must contain an indecomposable continuum. Since then, Ingram ([2](https://doi.org/10.1090/S0002-9939-1989-0984796-1)), Ye ([3](https://doi.org/10.1016/0166-8641(94)00035-0)), Mouron ([4](https://doi.org/10.1090/S0002-9939-2010-10783-9)), and others have carried out a number of studies, e.g., investigating maps exhibiting a local periodic behavior of a special kind on arc-like continua, and especially homeomorphisms of such spaces with positive entropy. A result by Darji and Kato ([5](https://doi.org/10.1016/j.aim.2016.09.012)) states that the inverse limit of a topological dynamical system on a graph-like continuum with positive entropy must contain an indecomposable continuum. In this talk, we will show that if we consider the Gehman dendrite, then it is possible to construct a system with arbitrarily large entropy whose inverse limit is hereditarily decomposable.

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1. SumTopo
3. 2025
5. Graphs

Decomposing $2$-cycles of graphs — Hein Van der Holst <hvanderholst@gsu.edu>

A $2$-cycle on a graph $G=(V,E)$ is a function $d: E\times E\to \mathbb{Z}$ such that for each edge $e$, both $d(e, \cdot)$ and $d(\cdot, e)$ are circulations on $G$. For an oriented cycle $C$ and an edge $e$ of $G$, define $C(e)=+1$ if $C$ traverses $e$ in forward direction, and $C(e)=-1$ if $C$ traverses $e$ in backward direction. Then examples of $2$-cycles are: take two vertex-disjoint oriented cycles $C$ and $D$ of $G$ and define $d(e,f) = C(e)D(f)$. Also on each $K_{3,3}$- and $K_5$-subdivision are $2$-cycles. In this talk, we show that each $2$-cycle on $G$ can be written as a sum of four types of special $2$-cycles. This is joint work with Serguei Norine and Robin Thomas.

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1. SumTopo
3. 2025
5. Graphs

Decomposition of Complete Graphs into Arbitrary Trees and Hamiltonian Cycles — Murugan Varadhan <murugan.v@vit.ac.in>

Decomposing the complete graph into arbitrary graph is a challenging and di cult problem in graph theory. In in this paper, we prove that the complete graph K4m+1 can be decomposed into 4m + 1 copies of an arbitrary tree with m edges and m copies of a Hamiltonian cycle whenever 4m+1 is a prime.

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1. STDC
3. 2026
5. 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. STDC
3. 2025
5. 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. STDC
3. 2025
5. 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. STDC
3. 2024
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2026
5. QTBD

Determining the local cycle locus of a vector field with a Hopf singularity — María Martín Vega <martinvega@imj-prg.fr>

Let $\xi$ be an analytic vector field at $0\in \mathbb{R}^3$ with a Hopf singularity, i.e. with eigenvalues $\pm i, c$ with $c\in \mathbb R$. We describe the germ of the subanalytic set $\mathcal{C}(\xi)$ defined by the union of the cycles on small neighborhoods of the singularity. We prove $\mathcal{C}(\xi)$ is the union of a finite number of surfaces or the complement of a curve of singularities of $\xi$. We also prove that the set $\mathcal{C}(\xi)$ is formally determined by any given formal normal form of $\xi$. This talk is based on a joint work with Nuria Corral and Fernando Sanz Sánchez.

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1. STDC
3. 2025
5. 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. STDC
3. 2025
5. 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. SumTopo
3. 2026
5. GSTT

Dimension under Dense Linear Mappings of Function Spaces — Krzysztof Zakrzewski <kzakrze@sgh.waw.pl>

### Dimension under Dense Linear Mappings of Function Spaces All topological spaces are assumed to be Tichonoff. For a space $X$, by $dim(X)$ we denote the covering dimension of the space $X$. For a topological space $X$, let $C_p(X)$ denote the space of real continuous functions on the space *X* endowed with the pointwise convergence topology. Let $\kappa$ be an infinite cardinal number. A normal space $X$ is called strongly $\kappa$-dimensional if it is a union of $\kappa$ many closed finite dimensional spaces. For $\kappa=\omega$, one obtains the well known class of strongly countable dimensional spaces. A space is called $\kappa$-compact if it is a union of $\kappa$ many its compact subspaces. We improve results concerning invariance of dimension-like properties under transformations of function spaces from [Za]. In particular we show that for a normal, strongly $\kappa$-dimensional space $X$ and a normal, metacompact, locally $\sigma$-compact space $Y$ if there exists a continuous linear operator $T:C_p(X)\xrightarrow[]{}C_p(Y)$ with dense image, then $Y$ is strongly $\kappa$-dimensional as well. The finite-dimensional case is examined as well. We also obtain a compactification theorem that may be of independent interest: every normal strongly $\kappa$-dimensional space admits a strongly $\kappa$-dimensional $\kappa$-compactification. Recall that for a space $X$, we have $dim\,(X)=dim\,(\beta X)$ and that there exist a normal, strongly countable dimensional space without strongly countable dimensional compactification [EP,Example 5.5]. 1. [EP] R. Engelking, E. Pol, _Countable-dimensional spaces: a survey_, Dissertationes Math. 216, (1983). 1. [Za] K. Zakrzewski, _Function spaces on Corson-like compacta_, Results Math. 80, 75 (2025).

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1. STDC
3. 2025
5. 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. SumTopo
3. 2026
5. QTBD

Discrete hyperbolic dynamical systems and surreal numbers — Dino Peran <dino.peran@pmfst.hr>

Determining the normal form of a map $f=\lambda z+\cdots$, where $\lambda>0$ and $\lambda\neq 1$, is a classical problem in dynamical systems. The goal is to "simplify" $f$ by finding a parabolic change of coordinates $\varphi=z+\cdots$ such that $\varphi^{-1}\circ f\circ\varphi=f_0$, where $f_0$ is a chosen normal form. This problem has been successfully solved in several settings, including analytic diffeomorphisms, various classes of real maps, Dulac maps, and logarithmic transseries. In this work, we investigate the normal form problem in the broader framework of surreal numbers. We review the main techniques used in existing normal form constructions and discuss how these methods can be extended to the surreal number setting. The study of normal forms in this context is connected with the dynamics of analytic planar vector fields because such objects arise as asymptotic expansions of Poincar\'e maps associated with hyperbolic and semi-hyperbolic polycycles of such fields. This is connected to the classical Dulac problem concerning the non-accumulation of limit cycles near polycycles of analytic planar vector fields. A deeper understanding of the formal dynamics of these asymptotic expansions may provide valuable insight into the dynamics of the corresponding Poincar\'e maps and could contribute to further progress on understanding of the Dulac problem. This is joint work in progress with V. Mantova, J.-P. Rolin, and T. Servi.

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1. STDC
3. 2025
5. 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. SumTopo
3. 2026
5. GGT

Divergence in groups with microsupported action — Dominik Francoeur <dominik.francoeur@uam.es>

Divergence is a quasi-isometry invariant of groups that measures how difficult it is to connect two elements in the Cayley graph of a group by a path that does not pass close to the identity element. It is related to the existence of cut points in the asymptotic cones of the group. In this talk, we will explore divergence in groups with microsupported actions, a class of groups that include interesting examples such as Grigorchuk's groups and Thompson's groups. This is joint work with Letizia Issini and Tatiana Nagnibeda.

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1. STDC
3. 2026
5. 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. STDC
3. 2025
5. 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. STDC
3. 2024
5. 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. STDC
3. 2026
5. 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. STDC
3. 2026
5. 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. STDC
3. 2024
5. 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. STDC
3. 2026
5. 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. STDC
3. 2024
5. 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. STDC
3. 2024
5. 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. SumTopo
3. 2026
5. TMAA
7. Plenary

Dynamics of unit groups of von Neumann's continuous rings — Friedrich Martin Schneider <martin.schneider@math.tu-freiberg.de>

In the 1930s, John von Neumann developed a continuous-dimensional analogue of finite-dimensional projective geometry. Inspired by conversations with Garrett Birkhoff as well as his collaboration with Francis Murray on rings of operators, von Neumann introduced and studied the notion of a continuous geometry, which is a complete complemented modular lattice possessing a certain continuity property. Among other remarkable results, von Neumann proved that every continuous geometry of order at least four can be coordinatized by some (up to isomorphism unique) ring, and that the continuous rings (i.e., rings corresponding to continuous geometries via this coordinatization theorem) are precisely those irreducible, regular rings which admit a complete rank function. The necessarily unique rank function of a continuous ring gives rise to a compatible metric and thus furnishes the ring with a natural topology. Unit groups of such continuous rings, equipped with the relative topology, constitute an interesting family of topological groups with many peculiar dynamical properties. The talk will provide an introduction to von Neumann's continuous geometry and discuss some of the latest advances concerning topological dynamics of unit groups of continuous rings.

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1. STDC
3. 2026
5. 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. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2026
5. TC

Effective Decomposability of Continua — David Tarandek <david.tarandek@gmail.com>

**Abstract.** We study effective decomposability of continua in computable metric spaces. A continuum $X$ is called **decomposable** if there exist proper subcontinua $A,B$ of $X$ such that $X=A\cup B$. We investigate when such a classical decomposition can be replaced by a computable one. We say that a continuum is **effectively decomposable** if it can be written as the union of two proper computable subcontinua. If $(X,d,\alpha)$ is itself a continuum, then in order to ask whether decomposability can be made effective, one must first require $X$ to be effectively compact. Even under this assumption, it is not known whether decomposability implies effective decomposability. Our first result gives one sufficient condition for effective decomposability. Let $(X,d,\alpha)$ be an effectively compact computable metric space such that $(X,d)$ is a continuum. If $X$ contains an open subset homeomorphic to $\mathbb{R}$, then $X$ is effectively decomposable. Consequently, arcs, topological circles and, in general, topological graphs exhibit effective decomposability in this setting. We also prove a result for chainable continua. If a semicomputable chainable continuum $S$ is decomposable, say $S=K_1\cup K_2$, then we use the fact that $S$ can be inner approximated by a computable subcontinuum $H$. This construction yields computable proper subcontinua $K_1\cup H$ and $K_2\cup H$, and hence an effective decomposition of $S$. Classically, decomposability is also characterized by the following condition: $$ \textbf{(Ch)}\qquad X \text{ is decomposable if and only if } X \text{ contains a proper subcontinuum with nonempty interior.} $$ Motivated by $\textbf{(Ch)}$, we discuss desirable effective versions of this characterization.

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1. STDC
3. 2025
5. 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. SumTopo
3. 2025
5. Computing

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. SumTopo
3. 2025
5. Dynamics/CT

Elliptic sectors and heteroclinic regions in real time holomorphic flows — Nicolas Kainz <nicolas.kainz@uni-ulm.de>

The geometric description of the phase space of holomorphic dynamical systems with real time is a crucial research field. In this context, the globalization of local structures is of particular interest. For example, the local structure of an equilibrium of order $m\in\mathbb{N}\setminus\{1\}$ has already been sufficiently investigated and characterized. Locally, there exist $2m-2$ elliptic sectors, all consisting of homoclinic trajectories tending to the equilibrium in both time directions. Now the question arises how this local structure can be globalized using analytical tools, as is the case, for example, with the basin of attraction of nodes and foci. I present a method to define a global elliptic sector based on so-called “sector-forming orbits” and show some topological properties for it: The global elliptic sector is open, flow-invariant, path-connected, and simply connected. Moreover, all orbits are nested inside each other, consistent with the intuitive notion of an elliptic sector. Furthermore, for the case $m\ge 3$, it coincides with the naively defined global elliptic sector, which merely contains all homoclinic trajectories with adjacent definite directions. This gives us an analytic precise definition of a globalization of a locally defined elliptic sector, together with important and useful topological properties. Moreover, it is possible to investigate the geometrical structure that can occur between two global elliptic sectors with no common boundary near the equilibrium. In this context, the question also arises as to how many so-called “heteroclinic regions” can appear between two such sectors.

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1. SumTopo
3. 2025
5. Graphs

Embedding Cartesian Products of Graphs on Surfaces — Christian Millichap <christian.millichap@furman.edu>

Determining how to build a minimal genus embedding of a graph is a classical and frequently challenging problem in topological graph theory. Here, we will be interested in Cartesian products of graphs where their fiber structures and symmetries can sometimes be leveraged to efficiently build embeddings and determine the genera of such graphs. More specifically, we will discuss work done towards a classification of all Cartesian products of graphs that embed on the torus where we leverage basic tools from combinatorial topology and determine the genera of certain graphs along the way. This work was part of an undergraduate summer research project with Beppy Badgett, and time permitting, we will briefly discuss ideas for future projects in this area that only requires some background in undergraduate graph theory and surface topology to get started.

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1. SumTopo
3. 2026
5. CT
7. Plenary

Embeddings of tree-like continua in the plane — Logan Hoehn <loganh@nipissingu.ca>

There are a number of interesting open problems in continuum theory that hinge on determining which tree-like continua can be embedded in the plane. Up to now, there are very few techniques available to show that a given tree-like continuum cannot be embedded in the plane. However, for a special class of tree-like continua, those which are inverse limits of simplicial inverse systems of trees, there is some hope that an algorithm may exist for checking planarity. I will describe this state of affairs, and pose some questions and computational challenges. At the same time, recent results are revealing that more tree-like continua can be embedded in the plane than perhaps were expected. I will discuss two such results: 1) Suppose $Y$ is any continuum of the form $Y = X \cup R$, where $X$ is an arc-like continuum, $R$ is a ray, $X \cap R = \emptyset$, and $\overline{R} \setminus R \subseteq X$. Then $Y$ can be embedded in the plane. 2) Suppose $Y$ is any continuum of the form $Y = K \cup \bigcup_{n=1}^\infty A_n$, where $K$ is a Knaster continuum and $\{A_n: n = 1,2,\ldots\}$ is a family of pairwise disjoint arcs, each intersecting $K$ in a single point, with $\mathrm{diam} A_n \to 0$. Then $Y$ can be embedded in the plane. This is joint work with Andrea Ammerlaan and Ana Anušić.

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1. STDC
3. 2026
5. GeoGT
7. 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. STDC
3. 2024
5. 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. SumTopo
3. 2026
5. GGT

Endomorphisms induced by self-maps in low dimensions — Christoforos Neofytidis <neofytidis.christoforos@ucy.ac.cy>

I will explain how residual finiteness and numerical invariants can be used to determine when all self-maps of non-zero degree induce an injective endomorphism or an automorphism of the fundamental group of a manifold in dimension three and in geometric settings in dimension four.

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1. STDC
3. 2024
5. 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. SumTopo
3. 2026
5. TDS

Entropy Maximizing Measures for Coded Shifts: Beyond Uniqueness — Tamara Kucherenko <tkucherenko@ccny.cuny.edu>

For transitive subshifts of finite type and sofic shifts, the measure of maximal entropy is unique. This fails for coded shifts, which form a natural generalization of these classes. While non-uniqueness is often viewed as pathological, it is still possible to obtain a detailed description of entropy maximizing measures in this setting. We discuss coded shifts that are not intrinsically ergodic and show that an ergodic measure of maximal entropy can be associated with a generator for which it is Bernoulli. This perspective provides a unified framework for understanding both uniqueness and non-uniqueness of entropy maximizing measures and yields explicit descriptions even in non-intrinsically ergodic settings.

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1. SumTopo
3. 2025
5. Dynamics/CT

Equivalence of equicontinuity and distality for real non-autonomous systems — Sushmita Yadav <yadav.34@iitj.ac.in>

This talk will focus on the topological dynamics of a non-autonomous dynamical system $(X,\mathbb{F})$, where $X$ is a compact metric space and $\mathbb{F}=\{f_1,f_2,\ldots\}$ is a sequence of continuous surjective functions on $X$. In particular we will discuss equicontinuity and distality for non-autonomous systems on the interval. We will discuss the distality of the system using the enveloping cover $E_0(X)=\overline{\{\omega_k:k\in \mathbb{Z} \}}$ (where $\omega_n=f_n \circ f_{n-1}... \circ f_1$). We use analytical tools to establish the equivalence of distality and equicontinuity for non-autonomous systems on the interval.

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1. SumTopo
3. 2026
5. GSTT
7. Plenary

Equivariant Means and Extension Properties — Natalia Jonard Pérez <nat@ciencias.unam.mx>

An $n$-mean on a topological space $X$ is a symmetric continuous operation $p:X^n\to X$ satisfying $p(x,\dots,x)=x$ for every $x\in X$. The existence of continuous means is closely related to several classical questions in topology, particularly in connection with retract theory and extension properties. In this talk, we discuss equivariant means associated with group actions on topological spaces and their connections with equivariant absolute extensors. Particular attention will be given to involutions (that is, $\mathbb Z_2$-actions) acting on spaces equipped with compatible lattice structures. We will present some existence results and applications in this setting, and explain how they relate to a classical open problem of Anderson. This is a joint work with Ananda López Poo.

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1. STDC
3. 2025
5. 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. STDC
3. 2025
5. 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. STDC
3. 2025
5. 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. SumTopo
3. 2026
5. TC

Escape problems for semigroup actions on effective topological spaces — Eike Neumann <e.f.neumann@swansea.ac.uk>

A wide range of fundamental systems verification tasks, such as liveness and safety verification for stochastic or quantum automata, can be modelled as instances of the general problem of deciding whether a point escapes a set under the action of a given semigroup. Theoretical computer scientists traditionally study such problems from a symbolic algebraic perspective: all data is assumed to be provided by exact symbolic means, for example in terms of exact algebraic numbers. In this framework, questions of the above kind become undecidable very quickly. For example, threshold problems for stochastic automata are undecidable in general, and threshold problems for quantum automata are decidable if and only if the inequality with the threshold is taken to be strict. Further, real-world systems are in general not known exactly, but only to some fixed finite accuracy. In this talk, I will advocate for the study of verification problems such as the above from the perspective of effective topology and second-order computability, where we model the input data as points in effective topological spaces. This allows us to naturally model systems that are known only to finite accuracy. Regarding decidability, we will have to make concessions: if an input lies on the boundary of a decision problem, it is trivially impossible for any second-order algorithm to make a correct decision in finite time. The natural question to ask is hence whether there exists a sound decision procedure that halts on the entire complement of the boundary. On the positive side, excluding the boundary instances will often naturally yield a large set of instances where problems of interest do become decidable. I will give a sound decision method for the problem of detecting whether a given point in an effectively locally compact space escapes given a set under a given action of a compactly generated topological semigroup. I will show that this method is complete (in the sense of halting on the complement of the boundary instances) when the space is either (weakly) locally contractible or totally disconnected. I will further give examples of effectively locally compact spaces where there exists a complete method, but my "generic" method fails to be complete, and examples where there is no complete decision method at all.

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1. SumTopo
3. 2026
5. GSTT

Examining Properties of Selective Divergence — Christopher Caruvana <chcaru@iu.edu>

We discuss the properties of being discretely selective and selectively highly divergent, as well as close variants. We give a variety of examples separating the notions and note their equivalence in rings of continuous real-valued functions. Some relations to hyperspaces of finite subsets are also considered.

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1. STDC
3. 2026
5. GeoTop
7. 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. STDC
3. 2025
5. 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. SumTopo
3. 2026
5. TMAA

Extension of maps into equivariant hulls of convex sets — Sergey Antonyan <antonyan@unam.mx>

We will establish the following equivariant extension theorem. Let $G$ be a compact Lie group, $L$ a locally convex metrizable linear $G$-space, and $V$ a closed convex subset of $L$. Denote $G(V):=\{gv\mid g\in G, v\in V\}$ -- the equivariant hull of $V$. Then any $G$-equivariant map $f:A\to G(V)$ defined on a closed invariant subset of a metrizable $G$-space $X$, extends to a $G$-equivariant map $F:U\to G(V)$ over some invariant neighborhood $U$ of $A$ in $X$. If, in addition, $V$ contains a $G$-fixed point, the extension can be taken over the whole space, i.e. $U=X$. In particular, any continuous map $f:A\to G(V)$ from a closed subset of a metrizable space $X$, extends to a continuous map $F:U\to G(V)$ over some neighborhood $U$ of $A$ in $X$. Several applications will be discussed.

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1. SumTopo
3. 2025
5. Computing

Facets in the Vietoris--Rips complexes of hypercubes — Ziqin Feng <zzf0006@auburn.edu>

In this talk, we'll discuss the facets (maximal simplices) of the Vietoris--Rips complex $\mathrm{VR}(Q_n; r)$ where $Q_n$ denotes the $n$-dimensional hypercube. We are particularly interested in those facets which are somehow independent of the dimension $n$. Using Hadamard matrices, we prove that the number of different dimensions of such facets is a super-polynomial function of the scale $r$, assuming that $n$ is sufficiently large. We show also that the $(2r-1)$-th dimensional homology of the complex $\mathrm{VR}(Q_n; r)$ is non-trivial when $n$ is large enough, provided that the Hadamard matrix of order $2r$ exists.

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1. STDC
3. 2025
5. 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. STDC
3. 2026
5. Applied & Data
7. 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. STDC
3. 2026
5. 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. STDC
3. 2026
5. Dynamics
7. 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. STDC
3. 2024
5. 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. STDC
3. 2025
5. 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. SumTopo
3. 2025
5. Graphs

Flowers of knots — Kouki Taniyama <taniyama@waseda.jp>

An $(n,k)$-flower $F(n,k)$ is the shadow of the closure of an $n$-braid $(\sigma_{1}\sigma_{2}\cdots\sigma_{n-1})^{k}$.\\ C. Lamm and V. O. Manturov independently showed the following: Let $K$ be a knot and $n\geq \mathrm{braid}(K)$. Then $K$ has $F(n,k)$ as its shadow for some $k$. We show the following: Let $K$ be a knot and $k\geq \mathrm{bridge}(K)$. Then $K$ has $F(n,k)$ as its shadow for some $n$. As a corollary, we show $\mathrm{bridge}(K)=\mathrm{lr}(K)$ where $\mathrm{lr}(K)$ is the left-right number of $K$. This gives us a new definition of the bridge number of a knot.

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1. SumTopo
3. 2025
5. Graphs

Forbidden complexes for the 3-sphere — Makoto Ozawa <w3c@komazawa-u.ac.jp>

A simplicial complex is said to be critical (or forbidden) for the 3-sphere $S^3$ if it cannot be embedded in $S^3$, but becomes embeddable upon removing the open star of any simplex in its second barycentric subdivision. We classify all critical complexes for $S^3$ that decompose as $(G \times S^1) \cup H$, where $G$ and $H$ are graphs whose intersection $G \cap H$ consists solely of vertices of $H$. This is a joint work with Mario Eudave-Munoz.

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1. STDC
3. 2024
5. 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. SumTopo
3. 2025
5. Plenary

Formalizing Braid Groups — Hannah Fechtner <hfechtne@andrew.cmu.edu>

I will discuss the formalization, in Lean, of braid groups : from their definition to the ongoing implementation and verification of a polynomial-time algorithm for the braid isotopy problem (Patrick Dehornoy’s subword reversing). Braids, inherently physical objects, were first abstracted to a nascent sort of topology by Vandermonde in the 18th century, and then to a proto-algebraic structure by Gauss in the 19th. More modern authors, from Artin to Markov (Jr.) to Dehornoy, have wrestled with the notion of rigor in this setting, as the associated visual imagery can suggest intuitive leaps. I will discuss one such example, and present a novel, formalized proof, which forms part of the work for the braid isotopy problem.

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1. STDC
3. 2025
5. 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. STDC
3. 2026
5. 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. SumTopo
3. 2026
5. TMAA

Frechet derivative is of first Baire class — Eva Kopecka <eva.kopecka@uibk.ac.at>

Let $X$ and $Y$ be Banach spaces, $G\subset X$ an open set and $f:G \to Y$ a mapping. We show that the Fr\'echet derivative $f'$ of $f$ is of first Baire class on the (possibly empty) set $D\subset G$ where it is defined.

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1. SumTopo
3. 2025
5. General/ST

Frechet spaces and M-separable (selectively separable) spaces — Alan Dow <adow@charlotte.edu>

Frechet spaces are selectively separable. Finite products of countable Frechet spaces need not be Frechet but it is independent as to whether they are selectively separable. We will review some recent results on this topic and, at the moment, think we have a new one.

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1. STDC
3. 2024
5. 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. STDC
3. 2026
5. Applied & Data
7. Plenaries

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

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1. SumTopo
3. 2026
5. TDS

From Dust to Fences — Udayan Darji <ubdarj01@gmail.com>

Homeomorphisms of the Cantor set (“dust”) play a fundamental role in topology, dynamical systems, and descriptive set theory, where they are studied from different perspectives. Recently, various properties of so-called fence-like objects have attracted attention. These include the Lelek fan (from topology), the hairy Cantor set and Cantor bouquet (from dynamical systems), and the Fraïssé fence (from model theory). Several recent works investigate both the structure of these spaces and the dynamics of homeomorphisms defined on them. In this work, we develop a general technique that allows one to transfer—or lift—the dynamics of a given homeomorphism of the Cantor set to a homeomorphism of a fence of the types described above.

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1. SumTopo
3. 2026
5. TMAA
7. Plenary

From group theory to topological data analysis: asymptotic dimension and the Gromov–Hausdorff distance — Nicolò Zava <nicolo.zava@ist.ac.at>

In his seminal work on finitely generated groups, Gromov established that such groups possess a well-defined large-scale metric structure induced by the word metric of a finite generating set. This perspective transformed geometric group theory by introducing quasi-isometric invariants, a prominent example of which is the asymptotic dimension—a large-scale analogue of the Lebesgue covering dimension. A parallel milestone in this geometric framework was the proof of Gromov's polynomial growth theorem, which characterises groups with polynomial growth, utilising the Gromov–Hausdorff distance to quantify dissimilarities between metric spaces. Almost a decade later, Topological Data Analysis (TDA), a field at the interplay of computational geometry, computer science, and algebraic topology, emerged to study the shape of data. The main tools are topology-inspired invariants, such as persistent homology, used to extract geometric features from datasets. Within this framework, both classic metric notions found new, independent utilities. The Gromov–Hausdorff distance became a standard tool for comparing datasets and evaluating the stability of invariants. The asymptotic dimension was used to analyse the spaces of these invariants, thereby bounding the unavoidable information loss incurred during their vectorisation, a necessary step to integrate them into statistical and machine learning pipelines. In this talk, we discuss how the asymptotic dimension and the Gromov–Hausdorff distance, originally introduced in the realm of topological methods to study algebraic structures, have gained a crucial role in TDA, and present recent results that bridge these notions by determining the asymptotic dimension of the Gromov–Hausdorff space.

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1. STDC
3. 2025
5. 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. SumTopo
3. 2026
5. GSTT

Function spaces on separable compact lines — Kacper Kucharski <k.kucharski6@uw.edu.pl>

A compact line is any linearly ordered compact topological space. During the talk we will provide a complete isomorphism classification of the spaces of real-valued continuous functions endowed with the topology of pointwise convergence $C_p(K)$ for separable compact lines $K$ of weight $\omega_1$, under the assumption of the Baumgartner's axiom BA. In particular, we will show that, up to linear homeomorphism, there are exactly two function spaces $C_p(K)$, for such $K$. This result should be compared with the recent work by Korpalski, Koszmider and Marciszewski in which it was proved that under the assumption of BA, whenever $K$ and $L$ are separable compact lines of weight $\omega_1$, then the Banach spaces $C(K)$ and $C(L)$ are isomorphic. We will also go over a construction of a ZFC example of a separable compact line $K$ of weight $2^{\omega}$, whose spaces of continuous functions with the pointwise convergence topology $C_p(K)$ and the weak topology $C_w(K)$ are not homeomorphic to their squares.

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1. SumTopo
3. 2026
5. GSTT

Fundamental properties and characterizations of new classes of δ− β* continuous mappings in m-Polar Neutrosophic Topological Spaces — Lorenzo Affè <lorenzo.affe1@gmail.com>

We introduce and study two classes of neutrosophic continuous mappings: the neutrosophic irresolute $\delta$-$\beta^\*$-continuous mappings (NIr $\delta$-$\beta^\*$ CM) and the $\delta$-$\beta^\*$-neutrosophic contra $\delta$-$\beta^\*$-continuous mappings (NC $\delta$-$\beta^\*$ CM). We establish their fundamental properties and provide characterizations in terms of preimages of $\delta$-$\beta^\*$-open and $\delta$-$\beta^\*$-closed sets. The role of each notion related to the other is shown and analyzed through implication chains, (non-)equivalences under mild hypothesis and stability result under composition, subspaces, and products. Then an extended framework to the $m$-polar setting is shown; in particular, the definitions of the $m$-polar neutrosophic irresolute $\delta$-$\beta^\*$-continuous mappings (MPNIr $\delta$-$\beta^\*$ CM) and $m$-polar neutrosophic contra $\delta$-$\beta^\*$-continuous mappings (MPNC $\delta$-$\beta^\*$ CM) are given. Moreover, this framework shows how core properties lift to the $m$-polar case and where new phenomena arise. Also examples and counterexamples are provided in order to separate the classes and to justify and illustrate the sharpness of the obtained results.

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1. SumTopo
3. 2026
5. GSTT

Further Observations on Locally Antisymmetric Spaces — Filiz YILDIZ <yfiliz@hacettepe.edu.tr>

Within the framework of asymmetry of the $T_0$-quasi-metric spaces [1], antisymmetric functions are appeared [3] as in some sense opposite to metric functions and studied [4] in detail. Following that in a previous study [2], the locality status of the $T_0$-quasi-metric spaces constructed with antisymmetric functions is described under the name local antisymmetricness. Hence, we are now in a position to ask that how local antisymmetric spaces behaves for subspaces, finite products and intersections-unions. Accordingly, some theorems and counterexamples will be presented about these observations in the context of $T_0$-quasi-metric spaces. Specifically, the question whether the images of locally antisymmetric spaces under an isometry have the same property or not, will be discussed as another problem worth examining.

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1. STDC
3. 2026
5. Continua