Equidistribution and Subconvexity

Number Theory
Wednesday, May 1, 2024 - 3:30pm for 1 hour (actually 50 minutes)
Skiles 005
Peter Humphries – University of Virginia – pclhumphries@gmail.comhttps://sites.google.com/view/peterhumphries/
Alex Dunn

A fundamental conjecture in number theory is the Riemann hypothesis, which implies the prime number theorem with an optimally strong error term. While a proof remains elusive, many results in number theory can nonetheless be proved using weaker inputs. I will discuss how one such weaker input, subconvexity, can be used to prove strong results on the equidistribution of geometric objects such as lattice points on the sphere. If time permits, I will also discuss how various proofs of subconvexity reduce to understanding period integrals of automorphic forms.