Colloquia

UW Madison mathematics Colloquium is on Fridays at 4:00 pm.

January 10, 2022, Monday at 4pm in B239 + Live stream + Chat over Zoom, Reza Gheissari (UC Berkeley)

(reserved by the hiring committee)

Surface phenomena in the 2D and 3D Ising model

Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.

January 17, 2022, Monday at 4pm in B239 + Live stream + Chat over Zoom, Marissa Loving (Georgia Tech)

(reserved by the hiring committee)

Symmetries of surfaces: big and small

We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.

January 21, 2022, Friday at 4pm in B239 + Live stream + Chat over Zoom Nicholas Marshall (Princeton)

(reserved by the hiring committee)

Laplacian quadratic forms, function regularity, graphs, and optimal transport

In this talk, I will discuss two different applications of harmonic analysis to problems motivated by data science. Both problems involve using Laplacian quadratic forms to measure the regularity of functions. In both cases the key idea is to understand how to modify these quadratic forms to achieve a specific goal. First, in the graph setting, we suppose that a collection of m graphs G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given, and consider the problem of finding the 'smoothest' function f : V -> R with respect to all graphs simultaneously, where the notion of smoothness is defined using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we consider the problem of efficiently computing linearizations of 2-Wasserstein distance; here, the solution involves quadratic forms of a Witten Laplacian.

January 24, 2022, Monday at 4pm in B239 + Live stream, Rachel Skipper (Ohio State)

(reserved by the hiring committee)

From simple groups to symmetries of surfaces

We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.