# Members Seminar

## Counting Galois representations

Frank Calegari
University of Chicago
November 4, 2016
One of the main ideas that comes up in the proof of Fermat's Last Theorem is a way of "counting" 2-dimensional Galois representations over $\mathbb Q$ with certain prescribed properties. We discuss the problem of counting other types of Galois representations, and show how this leads naturally to questions related to derived algebraic geometry and the cohomology of arithmetic groups. A key example will be the case of 1-dimensional representations of a general number field.

## Word measures on unitary groups

Doron Puder
Member, School of Mathematics
February 29, 2016
*Please excuse the first 45seconds of video, due to technical issues, the video breaks up*