Members' Colloquium

Convergence of Unitary Representations and Spectral Gaps of Manifolds

Let G be an infinite discrete group. Finite dimensional unitary representations of G are usually quite hard to understand. However, there are interesting notions of convergence of such representations as the dimension tends to infinity. One notion — strong convergence — is of interest both from the point of view of G alone but also through recently realized applications to spectral gaps of locally symmetric spaces. For example, this notion bypasses (unconditionally) the use of Selberg's Eigenvalue Conjecture in obtaining existence of large area hyperbolic surfaces with near-optimal spectral gaps.

The talk is a discussion on these themes, based on joint works with W. 

Hide, L. Louder, D. Puder, J. Thomas.

Date & Time

January 29, 2024 | 2:00pm – 3:00pm

Location

Simonyi 101 and Remote Access

Event Series

Notes

Meeting ID: 874 6951 4935 

Passcode: 483357

Video link: https://www.ias.edu/video/convergence-unitary-representations-and-spect…