# Paul Nelson

**Category: **Research Award Winners

**Affiliation: ** Aarhus University

A Clay Research Award is made to Paul Nelson in recognition of his groundbreaking contributions to the analytic theory of automorphic forms. His work has resulted in the first convexity-breaking bounds for a large class of L-functions on the critical line (including all the standard ones of GL(n)). This marks a significant advance in a field initiated one hundred years ago by Hermann Weyl in the context of the Riemann Zeta function. Nelson analyses L-values via certain associated automorphic periods. His powerful approach involves many ingredients, including a refinement of the orbit method that he developed in earlier work with Venkatesh, and an analysis of the geometric side of an appropriate Relative Trace Formula, which facilitates the use of Amplification.