## Overview of the p-Adic Local Langlands Correspondence for $GL(2,Q_p)$

(Introduction to the Lecture Series and and overview for those unable to attend the whole Lecture Series)

Pierre Colmez

National Center for Scientific Research

October 7, 2010

(Introduction to the Lecture Series and and overview for those unable to attend the whole Lecture Series)

September 1, 2010

Frank Calegari

Northwestern University; Member, School of Mathematics

October 6, 2010

Frank Calegari

Northwestern University; Member, School of Mathematics

October 13, 2010

Swastik Kopparty

Institute for Advanced Study

September 28, 2010

Van Vu

Rutgers, The State University of New Jersey

September 27, 2010

The condition number of a matrix is at the heart of numerical linear algebra. In the 1940s von-Neumann and Goldstine, motivated by the problem of inverting, posed the following question:

(1) What is the condition number of a random matrix ?

During the years, this question was raised again and again, by various researchers (Smale, Demmel etc). About ten years ago, motivated by "Smoothed Analysis", Spielman and Teng raised a more general question:

(2) What is the condition number of a randomly perturbed matrix ?

Carnegie Mellon University; Institute for Advanced Study

September 21, 2010

In this talk I will insult your intelligence by showing a non-original proof of the Central Limit Theorem, with not-particularly-good error bounds. However, the proof is very simple and flexible, allowing generalizations to multidimensional and higher-degree invariance principles. Time permitting, I will also discuss applications to areas of theoretical computer science: property testing, derandomization, learning, and inapproximability.

Seth Moglen

Associate Professor of English and Co-Director of the South Side Initiative, Lehigh University; Member (2009–10), School of Social Science

April 28, 2010

Matthew Kahle

Institute for Advanced Study

October 5, 2010

In this talk I will overview two very different kinds of random simplicial complex, both of which could be considered higher-dimensional generalizations of the Erdos-Renyi random graph, and discuss what is known and not known about the expected topology of each. Some of this is joint work with Eric Babson and Chris Hoffman.

October 5, 2010