# Galois symmetries of the stable homology of integer symplectic groups

HARVARD-MIT-BU-BRANDEIS-NORTHEASTERN

##### Speaker:

Akshay Venkatesh *- Institute for Advanced Study*

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.

Zoom: https://mit.zoom.us/j/98577860372