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

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)

## The Completed Cohomology of Arithmetic Groups

Frank Calegari
Northwestern University; Member, School of Mathematics
October 6, 2010

## Topology of Random Simplicial Complexes

Matthew Kahle
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.

## STPM - Some Questions Regarding Arithmetic Circuits

Srikanth Srinivasan
I will discuss the problem of approximating a given positive semidefinite matrix A , written as a sum of outer products $vv^T$ , by a much shorter weighted sum in the same outer products. I will then mention an application to sparsification of finite undirected graphs.