## A Conversation with Shimon Attie

Shimon Attie
February 18, 2011 - 5:30pm

Shimon Attie, an internationally renowned visual artist, presents and discusses a variety of his work, from his early site-specific installations across Europe through his more recent artworks that involve multiple-channel immersive video installations. He also discusses his new piece, MetroPAL.IS., an eight-channel video installation in-the-round, filmed with members of the Israeli and Palestinian communities of New York. MetroPAL.IS.

## Heuristics for lambda Invariants

Sonal Jain
New York University
February 17, 2011 - 4:30pm

The $\lambda$-invariant is an invariant of an imaginary quadratic field that measures the growth of class numbers in cyclotomic towers over the field. It also measures the number of zeroes of an associated $p$-adic L-function. In this talk, I will discuss the following question: How often is the p-adic $\lambda$-invariant of an imaginary quadratic field equal to $m$? I'll explain how one can model this question by statistics of $p$-adic random matrices, and show one can test this model by computing $\lambda$-invariants rapidly.

## Mathematical Conversations

February 16, 2011 - 5:30pm

## Automatizability and Simple Stochastic Games

Toniann Pitassi
University of Toronto
February 15, 2011 - 10:30am

The complexity of simple stochastic games (SSGs) has been open since they were defined by Condon in 1992. Such a game is played by two players, Min and Max, on a graph consisting of max nodes, min nodes, and average nodes. The goal of Max is to reach the 1-sink, while the goal of Min is to avoid the 1-sink. When on a max (min) node, Max (Min) chooses the outedge, and when on an average node, they take each edge with equal probability.

## Some Equations and Games in Evolutionary Biology

Christine Taylor
Harvard University; Member, School of Mathematics
February 14, 2011 - 2:00pm

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.

## An Elementary Proof of Anti-Concentration of Polynomials in Gaussian Variables

Shachar Lovett
February 14, 2011 - 11:15am

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.

## The KPZ Universality Class and Equation

Ivan Corwin
Courant Institute of Mathematics, New York University
February 11, 2011 - 2:00pm

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

## Eisenstein Congruences and Euler Systems

Eric Urban
Columbia University; Member, School of Mathematics
February 10, 2011 (All day)

GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR

## Completed Cohomology of Shimura Curves and a p-Adic Jacquet-Langlands Correspondence

James Newton
Member, School of Mathematics
February 9, 2011 - 2:15pm

In this talk, I will describe a construction of a geometric realisation of a p-adic Jacquet-Langlands correspondence for certain forms of GL(2) over a totally real field. The construction makes use of the completed cohomology of Shimura curves, and a study of the bad reduction of Shimura curves due to Rajaei (generalising work of Ribet for GL(2) over the rational numbers). Along the way I will also describe a p-adic analogue of Mazur's principle in this setting.

## The Isoperimetric Inequality

Larry Guth
University of Toronto; Member, School of Mathematics
February 9, 2011 (All day)