- Friday, September 20, 2019, 2:00pm, Physics 047, Number Theory Seminar
*Moments of half integral weight modular L–functions, bilinear forms and applications*

Alexander Dunn (University of Illinois Urbana-Champaign)- Given a half-integral weight holomorphic newform f, we prove an asymptotic formula for the second moment of the twisted L-function over all primitive characters modulo a prime. In particular, we obtain a power saving error term and our result is unconditional; it does not rely on the Ramanujan—Petersson conjecture for the form f. This gives a very sharp Lindelof on average result for L-series attached to Hecke eigenforms without an Euler product. The Lindelof hypothesis for such series was originally conjectured by Hoffstein. In the course of the proof, one must treat a bilinear form in Salie sums. It turns out that such a bilinear form also has several arithmetic applications to equidistribution. These are a series of joint works with Zaharescu and Shparlinski—Zaharescu.

- Friday, September 20, 2019, 3:15pm, 119 Physics, Algebraic Geometry Seminar
*The Moduli Space of Matroids*

Matt Baker (Georgia Tech, Mathematics)- I will begin with an introduction to hyperfields (originally introduced by Krasner for number-theoretic reasons), and then discuss a far-reaching generalization, Oliver Lorscheid’s theory of ordered blueprints. Two key examples are the sign hyperfield S and the tropical hyperfield T. I will discuss a common generalization, in this language, of Descartes' Rule of Signs (which involves polynomials over S) and the theory of Newton Polygons (which involves polynomials over T). I will then give a quick introduction to matroids and explain how the theory of ordered blueprints and ordered blue schemes allow us to construct a "moduli space of matroids", which can be viewed as an enhancement of the usual Grassmannian variety in algebraic geometry. This is joint work with Oliver Lorscheid.

- Friday, October 11, 2019, 12:00pm, Physics 119, Frontiers in Mathematics Seminar
*Frontiers in Mathematics Seminar*

Jessica Fintzen- TBA

- Friday, October 11, 2019, 3:15pm, 119 Physics, Number Theory Seminar
*Local Multiplicity for Spherical Varieties*

Chen Wan (MIT)- In this talk, I will discuss the local multiplicity problem for spherical varieties. I will start with the conjecture of Sakellaridis and Venkatesh. Then I will discuss the behavior of the multiplicity over the local L-packet. Finally I will explain how to use the trace formula method to study the multiplicity.

- Friday, October 18, 2019, 3:15pm, 119 Physics, Frontiers in Mathematics Seminar
*Frontiers in Mathematics Seminar*

Jessica Fintzen (University of Michigan / University of Cambridge) - Friday, October 25, 2019, 3:15pm, 119 Physics, Number Theory Seminar
*TBA*

Yunqing Tang (Princeton University) - Friday, December 6, 2019, 3:00pm, 119 Physics, Number Theory Seminar
*TBA*

Eyal Goren (McGill University)

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