Department of

Mathematics


Seminar Calendar
for events the day of Monday, March 2, 2020.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, March 2, 2020

9:00 am in Altgeld Hall,Monday, March 2, 2020

Math Graduate Open House

Abstract: Visiting Day for students admitted to the Math PhD program and currently living in North America.

3:00 pm in 243 Altgeld Hall,Monday, March 2, 2020

Analytic torsions associated with the Rumin complex on contact spheres

Akira Kitaoka (University of Tokyo)

Abstract: The Rumin complex, which is defined on contact manifolds, is a resolution of the constant sheaf of $\mathbb{R}$ given by a subquotient of the de Rham complex. In this talk, we explicitly write down all eigenvalues of the Rumin Laplacian on the standard contact spheres, and express the analytic torsion functions associated with the Rumin complex in terms of the Riemann zeta function. In particular, we find that the functions vanish at the origin and determine the analytic torsions.

4:00 pm in 245 Altgeld Hall,Monday, March 2, 2020

Linear Analysis on Singular Spaces

Hadrian Quan

Abstract: As an undergraduate, one may be introduced to the 3 classic linear differential equations: Laplaceís equation, the heat equation, and the wave equation. Simply trying to solve these equations in different coordinate systems leads to a zoo of different solutions; such variation reflects the strong connection between the geometry of a space, and the behavior of solutions to these PDE on that space. Passing from Euclidean space to more general manifolds, these three equations can be studied whenever our manifold is equipped with the geometric structure of a Riemannian metric. In this talk I will highlight a few of the many surprising theorems exhibiting this connection between the geometry and topology of a manifold and the behavior of solutions to the Laplace, heat, and wave equation. Time permitting, Iíll highlight recent joint work with Pierre Albin of some new phenomena on certain singular spaces.