## 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.

## Perturbation Theory for Band Matrices

Sasha Sodin
November 19, 2010

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

## Implied Existence for 3-D Reeb Dynamics

Al Momin
Purdue University
November 19, 2010

## Human-Made Climate Change: A Moral, Political, and Legal Issue

James E. Hansen
Columbia University
November 19, 2010

Observations of ongoing climate change, paleoclimate data, and climate simulations concur: human-made greenhouse gases have set Earth on a path to climate change with potentially dangerous consequences for humanity. James Hansen, climatologist and Adjunct Professor in the Department of Earth and Environmental Sciences at Columbia University, explains the urgency of the situation and discusses why he believes it is a moral issue that pits the rich and powerful against the young and unborn, against the defenseless, and against nature. He explores available options to avoid morally unacceptable consequences.

## Lecture 6

Pierre Colmez
National Center for Scientific Research; 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.

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

Tasho Kaletha
Princeton University; 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