Abstracts

Week of September 10, 2023

September 13, 2023
Colloquium Postdoc Mini-talks 4:00pm -
KT 219

Surya Raghavendran: Twisted supergravity and infinite-dimensional simple super-Lie algebras

Tamunonye Cheetham-West: Profinite completions of groups in low-dimensional geometry

Franco Vargas Pallete: Renormalized volume in hyperbolic geometry
September 14, 2023
Group Actions, Geometry and Dynamics Jordan and Cartan spectra in higher rank with applications to correlations 4:00pm -
KT801

The celebrated prime geodesic theorem for a closed hyperbolic surface says that the number of closed geodesics of length at most t is asymptotically e^t/t. For a closed surface equipped with two different hyperbolic structures, Schwartz and Sharp (’93) showed that the number of free homotopy classes of length about t in both hyperbolic structures is asymptotically a constant multiple e^{ct} /t^{3/2} for some 0<c<1. 

We will discuss the asymptotic correlations of the length spectra of convex cocompact manifolds, generalizing Schwartz-Sharp’s results. Surprisingly, it is helpful for us to relate this problem with understanding the Jordan spectrum of a discrete subgroup in higher rank. In particular, we will explain the source of the exponential and polynomial factors in Schwartz-Sharp’s asymptotic from a higher rank viewpoint.
 
We will also discuss the asymptotic correlations of the displacement spectra and  the ratio law between the asymptotic corrleations of the length and displacement spectra.  (This is joint work with Hee Oh).
 
 
Graduate Learning Seminar Learning seminar on D-modules 4:00pm -
WTS B31

This is the first talk in the seminar. Misha speaks on differential operators and basics of D-modules. 
September 15, 2023
Friday Morning Seminar Friday Morning Seminar 10:00am -
809 Commons

A relaxed-pace seminar on impromptu subjects related to the interests of the audience.

Everyone is welcome.

The subjects are geometry, probability, combinatorics, dynamics, and more!