IAS Physics Group Meeting

This group meeting will be presented in-person in Wolfensohn Hall at the IAS.

For contact-tracing purposes all off-campus attendees must register for this seminar: 
REGISTRATION FORM

All in-person attendees must be fully vaccinated and masks are required in all indoor spaces. Additionally, all off-campus attendees are required to upload proof of vaccination via the IAS CrowdPass App . 

Abstract: I will explain how the conformal bootstrap can be adapted to place rigorous bounds on the spectra of automorphic forms on locally symmetric spaces. A locally symmetric space is of the form H\G/K, where G is a non-compact semisimple Lie group, K the maximal compact subgroup of G, and H a discrete subgroup of G. If we take G = SL(2,R), then spaces of this form are precisely hyperbolic surfaces and hyperbolic 2-orbifolds. Automorphic forms then come in two types: modular forms, and eigenfunctions of the hyperbolic Laplacian, also known as Maass forms. The bootstrap constraints arise from the associativity of function multiplication on the space H\G, and are very similar to the usual correlator bootstrap equations, with G playing the role of the conformal group. For G=SL(2,R), I will use this method to prove upper bounds on the lowest positive eigenvalue of the Laplacian on all closed hyperbolic surfaces of a fixed genus. The bounds at genus 2 and genus 3 are very nearly saturated by the Bolza surface and the Klein quartic. This is based on an upcoming work with P. Kravchuk and S. Pal.