## Topology of Random Simplicial Complexes

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.

## STPM - Some Questions Regarding Arithmetic Circuits

Srikanth Srinivasan
Institute for Advanced Study
September 30, 2010

## STPM - Sparce Approximation of PSD Matrices

Nikhil Srivastava
Institute for Advanced Study
September 30, 2010

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.

## STPM - Torsion-Freeness of Certain Cohomology Groups of PEL-Type Shimura Varieties

Junecue Suh
Institute for Advanced Study
September 30, 2010

## STPM - L^p Concentration of Semiclassical Quasimodes

Melissa Tacy
Institute for Advanced Study
September 30, 2010

## STPM - The Spectrum of the Critical Almost Mathieu Operator

Mira Shamis
Institute for Advanced Study
September 29, 2010