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Thursday, June 02, 2022
4:00 PM - 5:00 PM
Linde Hall 387

# Number Theory Seminar

Applied $\ell$-adic cohomology II: Bilinear sums of Kloosterman sums and applications
Philippe Michel, EPFL/TAN, Ecole Polytechnique Fédérale de Lausanne,

In this talk we will discuss further applications of $\ell$-adic cohomology to analytic number theory.

In particular we will see that a certain non-trivial bound for bilinear sums of hyper-Kloosterman sums (below the Polya-Vinogradov range) constitute the final ingredient towards the resolution of a longstanding problem concerning moments for twists of $GL_2$ $L$-functions. In turn, these results shed some light on some recent conjectures of Mazur-Rubin regarding the distribution of modular symbols.

These are joint works with V. Blomer, E. Fouvry, E. Kowalski, D. Milicevic and W. Sawin