EVENT DETAILS AND ABSTRACT

Title: Exceptional splitting of abelian surfaces.
Speaker: Ananth Shankar
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfa​ces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.