Number Theory Seminar | Peter Humphries (UVA)

Title: Equidistribution and Subconvexity

Abstract: 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. I will also discuss how various proofs of subconvexity reduce to understanding period integrals of automorphic forms.

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