School of Mathematics

Statistics for Families of Automorphic Representations

Sug-Woo Shin
Institute for Advanced Study
March 3, 2011

Let G be a connected reductive group over Q such that G(R) has discrete series representations. I will report on some statistical results on the Satake parameters (w.r.t. Sato-Tate distributions) and low-lying zeros of L-functions for families of automorphic representations of G(A). This is a joint work with Nicolas Templier.

 

Does Infinite Cardinal Arithmetic Resemble Number Theory?

Menachem Kojman
Ben-Gurion University of the Negev; Member, School of Mathematics
February 28, 2011

I will survey the development of modern infinite cardinal arithmetic, focusing mainly on S. Shelah's algebraic pcf theory, which was developed in the 1990s to provide upper bounds in infinite cardinal arithmetic and turned out to have applications in other fields.

This modern phase of the theory is marked by absolute theorems and rigid asymptotic structure, in contrast to the era following P. Cohen's discovery of forcing in 1963, during which infinite cardinal arithmetic was almost entirely composed of independence results.

Local Testing and Decoding of Sparse Linear Codes

Shubhangi Saraf
Massachusetts Institute of Technology
February 22, 2011

We study the local testabilty of sparse linear codes. This problem is intimately connected to the problem of tolerant linearity testing of Boolean functions under nonuniform distributions. We give linearity tests for several natural and interesting classes of distributions, and use this to show local testability for the corresponding codes.