## On Automorphy of Certain Galois Representations of GO_4 Type

**GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR**

Tong Liu

Purdue University; Member, School of Mathematics

February 24, 2011

**GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR**

Christopher Skinner

Princeton University; Member, School of Mathemtics

February 23, 2011

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.

Sonal Jain

New York University

February 17, 2011

Institute for Advanced Study

February 16, 2011

Toniann Pitassi

University of Toronto

February 15, 2011

Shachar Lovett

Institute for Advanced Study

February 14, 2011

Recently there has been much interest in polynomial threshold functions in the context of learning theory, structural results and pseudorandomness. A crucial ingredient in these works is the understanding of the distribution of low-degree multivariate polynomials evaluated over normally distributed inputs. In particular, the two important properties are exponential tail decay and anti-concentration.

Christine Taylor

Harvard University; Member, School of Mathematics

February 14, 2011

The basic ingredients of Darwinian evolution, selection and mutation, are very well described by simple mathematical models. In 1973, John Maynard Smith linked game theory with evolutionary processes through the concept of evolutionarily stable strategy. Since then, cooperation has become the third fundamental pillar of evolution. I will discuss, with examples from evolutionary biology and ecology, the roles played by replicator equations (deterministic and stochastic) and cooperative dilemma games in our understanding of evolution.

Ivan Corwin

Courant Institute of Mathematics, New York University

February 11, 2011

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

Eric Urban

Columbia University; Member, School of Mathematics

February 10, 2011

**GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR**