Previous Conferences & Workshops

The classical Liouville theorem claims that any positive harmonic function in $R^n$ is a constant function. Nadirashvili conjectured that any non-constant harmonic function in $R^3$ has a zero set of infinite area. The conjecture is true and we will...

In these lectures, we will explore what insight can be gained into the arithmetic of Galois representations in a given dimension through the geometry of a higher-dimensional locally symmetric space near a boundary component. The starting point for...

We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem. Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured constant integrality...

This talk will survey ideas surrounding a conjecture in number theory about the structure of class groups of number fields. Each number field has associated to it a finite abelian group, the class group, and as long ago as Gauss, deep questions...

We show that the perfect matching problem in general graphs is in Quasi-NC. That is, we give a deterministic parallel algorithm which runs in polylogarithmic time on quasi-polynomially many processors. The result is obtained by a derandomization of...

For a formal group law G the group of automorphisms Aut(G) acts on the space of deformations Def(G). The invariants of this action miraculously recover an object of huge interest to algebraic topologists, and this connection led to much progress in...

In these lectures, we will explore what insight can be gained into the arithmetic of Galois representations in a given dimension through the geometry of a higher-dimensional locally symmetric space near a boundary component. The starting point for...

This will be an informal working group on aspects of microlocal analysis that are relevant to automorphic forms. We will try to study Archimedean zeta integrals (which are related to local L-functions) using tools from the geometric theory of...