Description
Recently, a close parallel emerged between conformal field theory in general dimension and the theory of automorphic forms. I will review this connection and explain how it can be leveraged to make rigorous progress on central open problems of number theory, using methods borrowed from the conformal bootstrap. In particular, I will use the crossing equation to prove new subconvex bounds on L-functions. Based on work with Adve, Bonifacio, Kravchuk, Pal, Radcliffe, and Rogelberg: https://arxiv.org/abs/2508.20576.
