Joint IAS/Princeton University Number Theory Seminar

Cohomology of Arithmetic Groups and Endoscopy

How fast do Betti numbers grow in a congruence tower of compact arithmetic manifolds? The dimension of the middle degree of cohomology is proportional to the volume of the manifold, but away from the middle the growth is known to be sub-linear in the volume. I will explain how automorphic representations and the phenomenon of endoscopy provide a framework to understand and quantify this slow growth. Specifically, I will discuss how to obtain some explicit bounds in the case of unitary groups using Arthur’s stable trace formula.

Date & Time

February 11, 2021 | 4:30pm – 5:30pm

Location

Remote Access

Affiliation

Member, School of Mathematics

Event Series

Categories

Notes

Zoom link password hint: the three digit integer that is the cube of the sum of its digits.