Explicit modular abelian surfaces

Frank Calegari (University of Chicago)
Fri 23 Feb 2018 at 11am in Peter Hall 107

This is the introductory talk for a working group focusing on abelian surfaces over $\mathbb{Q}$. The projects include:

  1. Finding explicit abelian surfaces $A$ with $End_C(A)=\mathbb{Z}$ that are provably modular.
  2. Finding infinitely many fake modular elliptic curves that are provably modular.
  3. Finding fake abelian $4$-folds $A$ over $\mathbb{Q}$ with $End_C(A)\otimes\mathbb{Q}=$ division algebra.