Seminars and Colloquia by Series

Vanishing of Brauer classes on K3 surfaces under reduction

Series
Number Theory
Time
Wednesday, November 1, 2023 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Salim Tayou – Harvard University –

Given a Brauer class on a K3 surface over a number field, we prove that there exists infinitely many primes where the reduction of the Brauer class vanishes, under some mild assumptions. This answers a question of Frei--Hassett--Várilly-Alvarado. The proof uses Arakelov intersection theory on GSpin Shimura varieties. If time permits, I will explain some applications to rationality questions. The results in this talk are joint work with Davesh Maulik.

Magic functions for the Smyth-Siegel trace problem

Series
Number Theory
Time
Wednesday, September 20, 2023 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Naser Sardari – Penn State –

We study the Schur-Siegel-Smyth trace problem. We introduce a new linear programming problem that inclues Smyths' constraints, and we give an exact solution to it. This improves the best known lower bound on the Siegel trace problem which is based on Smyths' method. In a special case, we recover Siegel's original upper bound.  Our method unifies Siegel's and Smyth's work under the same framework. This is joint work with Bryce Orloski.

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