WiMiCC 2026

Abstract: “Topological algebra” is the process of assembling topological things into algebraic structures with the goal of seeing something new either from the topological or the algebraic perspective. This includes: thinking of braids as forming a group and applying tools from linear algebra to understand them; modeling the Temperley-Lieb algebra (originally from statistical mechanics) as a span of certain planar diagrams; or turning manifolds with boundary into a category, and constructing a functor from this category to vector spaces. This talk will center around these three examples and what we can and can't learn from them. (Disclaimer: despite being extremely descriptive, "topological algebra" is not standard nomenclature.)

Abstract: Einstein's theory of gravity has been a strong driving force for the current developments in both physics and mathematics. Among its wide applications, the theory successfully describes and predicts celestial objects, such as black holes, which were previously unknown. Over the past few decades, remarkable progress has been made using advanced techniques in geometry and analysis to resolve fundamental questions in general relativity, such as the positive mass theorem, which relates to the properties of total mass in spacetime. Furthermore, this advancement has led to the astonishing realization that black holes are governed by the same mathematical principles that govern everyday objects, such as soap films. In this talk, we will discuss the mathematical models of black holes and explore their intriguing interconnections to the positive mass theorem and other problems in geometry and physics.

Abstract: In a first course on discrete math, you typically meet Kruskal's algorithm, which is an efficient greedy algorithm for choosing a random spanning tree of a graph. To execute it, you typically pull random real-valued weights for the edges independently, then choose the tree of minimum total weight (by activating edges in order of weight, only rejecting those that form cycles). This certainly sounds to most people like it's equally likely to choose any spanning tree, but in fact the distribution on spanning trees is decidedly non-uniform for most graphs. I'll tell you more about what's known and not known about this basic problem, and will show you how to put a "designer distribution" on spanning trees.

Abstract: The symmetries of an object are widely understood to be the collection of motions that preserve that object, which forms a group under composition. The field of dynamical systems takes static mathematical objects and sets them in motion, watching them evolve over time. What are the symmetries of a dynamical system? I will discuss some of the history of the subject, which naturally highlights work of women in mathematics, as well as recent work of my own and others on an emerging program we call centralizer rigidity.

Abstract: Geometry threads through the natural and social worlds, shaping the dendritic arms of snowflakes, the icosahedral shells of viruses, and even the thresholds that govern how ideas and infections spread in society. In this colloquium, we’ll take a guided “stroll” across these settings, as well as through a Mathematician's Path, beginning with the classical problem of classification via moduli spaces and the notion of equivalence, then moving to local-rule models for crystal growth that recover familiar plate and dendrite morphologies in snow crystals. From there, we’ll see how symmetry organizes viral capsids into mathematically constrained configurations, and how simple compartmental and percolation models on networks reveal phase transitions in contagion. We’ll conclude by looping back to geometry proper (Higgs bundles and related moduli), highlighting how geometric structure provides a unifying language that spans from the microscopic to the macroscopic. The talk is aimed at a broad audience; no specialized background will be assumed, just curiosity about how a few geometric ideas can illuminate complex phenomena.