Galois symmetries of the stable homology of integer symplectic groups

Akshay Venkatesh
Institute for Advanced Study
Tuesday, December 1, 2020 - 3:30pm to 4:30pm
Via Zoom ID 91514486597 (contact faculty for pw)

There are many natural sequences of moduli spaces in algebraic geometry whose homology approaches a "limit", despite the fact that the spaces themselves have growing dimension. If these moduli spaces are defined over a field K, this limiting homology carries an extra structure -- an action of the Galois group of K -- which is arithmetically interesting.

In joint work with Feng and Galatius, we compute this action (or rather a slight variant) in the case of the moduli space of abelian varieties. I will explain the answer and why I find it interesting. No familiarity with abelian varieties will be assumed -- I will emphasize topology over algebraic geometry.