Vanishing Cycles and Bilinear Forms

Vanishing Cycles and Bilinear Forms

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Will Sawin , Princeton University
IAS Room S-101

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.