Department of

Mathematics


Seminar Calendar
for events the day of Thursday, February 14, 2019.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, February 14, 2019

12:00 pm in 243 Altgeld Hall,Thursday, February 14, 2019

Spectral Rigidity of q-differential Metrics

Marissa Loving (UIUC Math)

Abstract: When geometric structures on surfaces are determined by the lengths of curves, it is natural to ask which curves’ lengths do we really need to know? It is a classical result of Fricke that a hyperbolic metric on a surface is determined by its marked simple length spectrum. More recently, Duchin–Leininger–Rafi proved that a flat metric induced by a unit-norm quadratic differential is also determined by its marked simple length spectrum. In this talk, I will describe a generalization of the notion of simple curves to that of q-simple curves, for any positive integer q, and show that the lengths of q-simple curves suffice to determine a non-positively curved Euclidean cone metric induced by a q-differential metric.

2:00 pm in 347 Altgeld Hall,Thursday, February 14, 2019

An Introduction to Dyson Brownian Motion and Universality (Part 2)

Kesav Krishnan (UIUC Math)

Abstract: We will discuss the connections of Dyson Brownian Motion and the Totally Asymmetric Simple Exclusion Process (TASEP). This will be the first glimpse of the Kardar Parisi Zhang Universality class.

3:00 pm in 347 Altgeld Hall,Thursday, February 14, 2019

Quiver varieties and root multiplicities for symmetric Kac-Moody algebras

Peter Tingley   [email] (Loyola University, Chicago)

Abstract: We discuss combinatorial upper bounds on dimensions of certain imaginary root spaces for symmetric Kac-Moody algebras. These come from a realization of the infinity crystal using quiver varieties. The framework is quite general, but we only work out specifics for one special case. We conjecture that our bound is quite tight, and give both computational evidence and heuristic justification for this conjecture, but unfortunately not a proof.