Seminar on Complex Analysis and Complex Geometry - Fall 2016

On Wednesday when no extramural speaker is listed, the members of the complex geometry group may meet for a working seminar. For more information, send an email to Gordon Heier.

THURSDAY, November 10, 2016, 3-4pm, SPECIAL ROOM: AH 9

Title: Level structures, abelian varieties, and Brauer groups of K3 surfaces

Speaker: Anthony Várilly-Alvarado, Rice University

Abstract: In 1922, Mordell showed that the set of rational points on an elliptic curve over Q has the structure of a finitely generated abelian group. Surprisingly, there are only 15 possibilities for the torsion part of this group; this is a spectacular result of Mazur from 1977. In this talk I will discuss some higher-dimensional generalizations of results along Mazur's theorem, including recent joint work with Dan Abramovich on abelian varieties, and work with Bianca Viray for K3 surfaces, where I will argue that a suitable analogue of the group of rational points is the Brauer group.