# Members Seminar

## The Weil Conjectures, from Abel to Deligne

## Recent development of random matrix theory

In this seminar, we will discuss the recent work on the eigenvalue and eigenvector distributions of random matrices. We will discuss a dynamical approach to these problems and related open questions. We will discuss both Wigner type matrix ensembles and invariant ensembles.

## Small Height and Infinite Non-Abelian Extensions

## Conformal Dynamics in Pseudo-Riemannian Geometry: Around a Question of A. Lichnerowicz

In the middle of the sixties, A. Lichnerowicz raised the following simple question: “Is the round sphere the only compact Riemannian manifold admitting a noncompact group of conformal transformations?” The talk will present the developments which arose from Lichnerowicz's question. It will be an opportunity to see diverse aspects of conformal dynamics in Riemannian, as well as Lorentzian geometry

## Five Stages of Accepting Constructive Mathematics

## Random Matrices, Dimensionality Reduction, and Faster Numerical Linear Algebra Algorithms

## Collective Phenomena, Collective Motion, and Collective Action in Ecological Systems

## Homological Mirror Symmetry

## Toeplitz Matrices and Determinants Under the Impetus of the Ising Model

This is the first of two talks in which the speaker will discuss the development of the theory of Toeplitz matrices and determinants in response to questions arising in the analysis of the Ising model of statistical mechanics. The first talk will be largely historical and the second will describe the state of the art today, including recent results of the speaker and his colleagues Alexander Its and Igor Krasovsky.