Vanishing cycles and bilinear forms

Joint IAS/Princeton University Number Theory Seminar
Topic:Vanishing cycles and bilinear forms
Speaker:Will Sawin
Affiliation:Princeton University
Date:Thursday, February 18
Time/Room:4:30pm - 5:30pm/S-101
Video Link:https://video.ias.edu/puias/2016/0218-Sawin

In joint work with Emmanuel Kowalski and Philippe Michel, we prove two different estimates on sums of coefficients of modular forms---one related to L-functions and another to the level of distribution. A key step in the argument is a careful analysis of vanishing cycles, a tool originally developed by Lefschetz to study the topology of algebraic varieties. We will explain why this is helpful for these problems.