Presentations by our featured plenary speakers
Hortensia Soto from Colorado State University
Carl Yerger from Davidson College
This talk will begin with a brief discussion of motivations for conducting research in mathematics and why the presenter believes that graph pebbling is an appealing research area. It will continue with an introduction to graph pebbling. A survey of several streams of pebbling research, including cover pebbling, optimal pebbling and Class 0 graphs will be discussed. A number of accessible results (many involving undergraduates) and some open problems will also be presented. *Graph pebbling* is a combinatorial game played on an undirected graph with an initial configuration of pebbles. A pebbling move consists of removing two pebbles from one vertex and placing one pebbling on an adjacent vertex. The *pebbling number* of a graph is the smallest number of pebbles necessary such that, given any initial configuration of pebbles, at least one pebble can be moved to a specified target vertex.
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The work that you do changes the way that you think. Your problem-solving approach will shift dramatically over years of work studying math. In this session we’ll investigate how several groups of students and faculty with varying mathematical backgrounds approached solving the same problem (and you’ll get to try this fun puzzle for yourselves!). We’ll attempt to characterize some of the differences in their approaches. Then, we’ll take time to share our stories of how mathematics has shaped the way we think, learn, and interact in the world. Come ready to reflect on how you think and solve problems.
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Habitat fragmentation breaks continuous habitat into smaller patches separated by a less suitable “matrix.” For many species, persistence depends not only on births and deaths within a patch, but also on movement across patch boundaries and that movement can change when a patch becomes crowded. In this talk I’ll introduce a mathematical framework for fragmentation using reaction diffusion models. The reaction term describes local population growth, while diffusion captures movement that resembles random walk-like movement. We’ll begin by introducing diffusion (how a concentration spreads in space) and then translate the same idea into animal dispersal across a landscape. A key modeling choice is how individuals behave at habitat edges. We’ll discuss emigration (leaving a patch) and density-dependent emigration, where departure rates increase with local density. These assumptions lead to “rules at the boundary” (boundary conditions) that represent how animals cross edges which is an ingredient that strongly influences persistence predictions. We’ll end with a conservation-focused application to Northern Bobwhite quail: estimating a biologically meaningful minimum patch size needed for persistence. Using movement and demographic rates reported in field studies (and simple fitted components when needed), we’ll see how mathematics can test common rule-of-thumb recommendations and identify which movement assumptions matter most.
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In this presentation I will share on a research project where we explored how undergraduates, enrolled in an introductory linear algebra course, collectively created an assemblage of a shear using 3-D change of basis vectors. For this study, I used a theoretical perspective that falls under the umbrella of embodied cognition–inclusive materialism. This lens posits that learning is the invention of a new creation that manifests through imagination in unusual and unexpected ways. It describes mathematics as an assemblage between the body of participants and the body of their materials that give shape to an activity, where affective and aesthetic features contribute to the virtuality of the body of mathematics. Our findings suggest that the class created an assemblage of a shear by (a) introducing or catalyzing the new and (b) showcasing how aesthetics and affect inspire intra-actions. As part of my presentation, I will describe the students’ intra-actions with their own fabricated material.
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What makes a math metaphor land and what makes it crash? In this talk, I reflect on my journey as a mathematics educator through the lens of one of teaching's most powerful and perilous tools: the conceptual metaphor. We begin at the University of Illinois at Urbana-Champaign, where, as a graduate teaching assistant, I deployed some genuinely tortured metaphors with the full confidence only inexperience can provide. We then move to the University of Arizona, where as a postdoc I discovered the subtler danger of mixed metaphors, where individually reasonable analogies placed side by side can quietly undermine each other and students’ developing understanding. And finally, we arrive at Auburn University, where I stumbled upon a metaphor that actually worked beautifully, and found myself compelled to understand *why*. Along the way, I will draw lightly on cognitive theories of mathematics learning to ask: what is a metaphor really doing for a learner? What happens when the wrong one takes root? The talk will include penguins, binoculars, a poorly drawn summary of *The Terminator*, and a live encounter with the surprisingly rich metaphorical life of the equals sign. I will also invite the audience to consider a new and thought-provoking question: in an age of large language models that can generate metaphors fluently and instantly, what does that reveal about what makes a math metaphor genuinely *good*? This talk is equal parts a confession, an investigation, and a love letter to the craft of teaching. P.S. As a lifelong Swiftie, I could not resist naming this talk after a certain album. But I promise that the parallel is more than cosmetic.
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