A Spectral Gap for Spinors on Hyperbolic Surfaces

Vortrag von Dr. Vikramaditya Giri

Datum: 25.02.26  Zeit: 13.30 - 14.30  Raum: ETH HG G 19.1

We'll recall the spectral theory of the Laplacian on functions on a hyperbolic surface and show that as the genus goes to infinity, one can't obtain a uniform spectral gap above 1/4 - the bottom of the \(L^2\) spectrum of the hyperbolic plane. We'll show that this obstruction goes away when one instead considers the spectrum of the Dirac operator on spinors on a hyperbolic surface with a choice of spin structure. We'll sketch a construction of these surfaces with such a uniform spectral gap and note that these surfaces can be taken to be arithmetic.

Based on joint work with Anshul Adve.