Vanishing cycles and bilinear forms

Will Sawin
February 18, 2016
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.