# School of Mathematics

## IWASAWA: Lecture 3

## Mathematical Conversations

## What We Can Do With Waves

## Automorphic Cohomology I (General Theory)

These two talks will be about automorphic cohomology in the non-classical

case.

## Automatizability and Simple Stochastic Games

## Some Equations and Games in Evolutionary Biology

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

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

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR