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Department of Mathematics

Upcoming Colloquia

Memorial Union on sunny day

Dehn surgery and homology cobordism

KIDD 364

Speaker: Ian Zemke

One very important object of study in low-dimensional topology is the homology cobordism group. The structure of this group is largely unknown, although it is abelian and it is known that it is very large (it contains an infinite rank summand). In this talk, we will review the basics of this group, as well as more recent developments. We will end with some results which can be derived from Hendricks and Manolescu’s theory of involutive Heegaard Floer homology, focusing on a formula for Dehn surgery due to Hendricks, Hom, Stoffregen and myself. Read more.

Loop-erased random walks and uniform spanning trees

KEC 1001

Speaker: Greg Lawler

I will discuss two related models that arise in statistical physics and give an overview of their properties and various methods used to understand them and their continuum limits. The methods are many: probabilistic, combinatorial, fractal geometry, Laplacians and their determinants, random geometry, conformal fields. This will be an introduction for a general mathematical audience: I do not expect people to have heard of these terms before. Read more.

A Stroll Through Geometric Ideas

KEC 1001

Speaker: Laura Schaposnik

During the first half of the talk, we will introduce Higgs bundles, their integrable system, and motivate why they become useful tools to further our understanding in different geometric settings. After describing some dualities they satisfy (not only from mirror symmetry but also via other correspondences such as low-rank isogenies), we will then focus on different methods to understand the Hitchin fibration and branes it contains, and especially its singular fibers (monodromy, transitional geometries, Cayley correspondences). Then, we shall move on to more applied realms and look at how geometric insights can be used to classify viruses, understand the spread of fake news, examine the relationship between COVID and dengue, and address other questions about the world. Read more.

TBA

KIDD 364

Speaker: William Leeb

Read more.