## Weakly Commensurable Arithmetic Groups and Isospectral Locally Symmetric Spaces

University of Michigan; Member, School of Mathematics
February 27, 2012

## Complexity, Approximability, and Mechanism Design

University of California at Berkeley
February 28, 2012

## A Centre-Stable Manifold for the Energy-Critical Wave Equation in $R^3$ in the Symmetric Setting

Marius Beceanu
Rutgers, The State Unviersity of New Jersey
February 28, 2012

## Stein Structures: Existence and Flexibility

Kai Cieliebak
Ludwig-Maximilians-Universitat, Munich, Germany
February 29, 2012

This is a series of 3 talks on the topology of Stein manifolds, based on work of Eliashberg since the early 1990ies. More specifically, I wish to explain to what extent Stein structures are flexible, i.e. obey an h-principle. After providing some general background on Stein manifolds, the first talk will focus on the construction of plurisubharmonic functions with specific properties. Using these, I will in the second talk present the proof of Eliashberg's existence theorem for Stein structures.

## Stein Structures: Existence and Flexibility

Kai Cieliebak
Ludwig-Maximilians-Universitat, Munich, Germany
March 1, 2012

## The Tamagawa Number Formula via Chiral Homology

Dennis Gaitsgory
Harvard University
March 1, 2012

## Stein Structures: Existence and Flexibility

Kai Cieliebak
Ludwig-Maximilians-Universitat, Munich, Germany
March 2, 2012

## Global Existence of Surface Waves

Jalal Shatah
Courant Institute, NYU
March 2, 2012

## The Complexity of Distributions

Emanuele Viola
Northeastern University
March 5, 2012

Complexity theory, with some notable exceptions, typically studies the complexity of computing a function h(x) of a *given* input x. We advocate the study of the complexity of generating -- or sampling -- the output distribution h(x) for random x, given random bits.

In particular, we present first-of-their-kind lower bounds for generating distributions in various restricted computational models. We also discuss connections to succinct data structures and to randomness extractors.

Avi Wigderson