# School of Mathematics

## Counting Pattern Avoiding Permutations Via Integral Operators

Richard Ehrenborg
University of Kentucky; Institute for Advanced Study
November 23, 2010

## Modularity of Galois Representations

Chandrashekhar Khare
University of California, Los Angeles
November 22, 2010

In this expository talk, I will outline a plausible story of how the study of congruences between modular forms of Serre and Swinnerton-Dyer, which was inspired by Ramanujan's celebrated congruences for his tau-function, led to the formulation of Serre's modularity conjecture. I will give some hints of the ideas used in its proof given in joint work with J-P. Wintenberger. I will end by pointing out just one of the many interesting obstructions to generalising the strategy of the proof to get modularity results in more general situations.

## Implied Existence for 3-D Reeb Dynamics

Al Momin
Purdue University
November 19, 2010

## Perturbation Theory for Band Matrices

Sasha Sodin
Institute for Advanced Study
November 19, 2010

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

## Endoscopic Transfer of Depth-Zero Suprcuspidal L-Packets

Tasho Kaletha
Princeton University; Member, School of Mathematics
November 18, 2010

## Potential Automorphy for Compatible Systems of l-Adic Galois Representations

David Geraghty
Princeton University; Member, School of Mathematics
November 18, 2010

I will describe a joint work with Barnet-Lamb, Gee and Taylor where we establish a potential automorphy result for compatible systems of Galois representations over totally real and CM fields. This is deduced from a potential automorphy result for single l-adic Galois representations satisfying a `diagonalizability' condition at the places dividing l.

## Lecture 6

Pierre Colmez
National Center for Scientific Research; Member, School of Mathematics
November 18, 2010

## A New Approach to the Local Langlands Correspondence for $GL_n$ Over p-Adic Fields

Peter Scholze
University of Bonn
November 17, 2010