School of Mathematics

Topology of resolvent problems

Benson Farb
University of Chicago
December 6, 2019

In this talk I will describe a topological approach to some problems about algebraic functions due to Klein and Hilbert. As a sample application of these methods, I will explain the solution to the following problem of Felix Klein: Let $\Phi_{g,n}$ be the algebraic function that assigns to a (principally polarized) abelian variety its $n$-torsion points. What is the minimal $d$ such that, after a rational change of variables, $\Phi_{g,n}$ can be written as an algebraic function of $d$ variables? This is joint work with Mark Kisin and Jesse Wolfson.

The nonlinear stability of the Schwarzschild metric without symmetry

Mihalis Dafermos
Princeton University
December 6, 2019

I will discuss an upcoming result proving the full finite-codimension non-linear asymptotic stability of the Schwarzschild family as solutions to the Einstein vacuum equations in the exterior of the black hole region. 


No symmetry is assumed. The work is based on our previous understanding of linear stability of Schwarzschild in double null gauge. Joint work with G. Holzegel, I. Rodnianski and M. Taylor.

Regularity lemma and its applications Part I

Fan Wei
Member, School of Mathematics
December 3, 2019

Szemeredi's regularity lemma is an important tool in modern graph theory. It and its variants have numerous applications in graph theory, which in turn has applications in fields such as theoretical computer science and number theory. The first part of the talk covers some basic knowledge about the regularity lemma and some of its applications, such as the graph removal lemma. I will also discuss some recent works related to the removal lemma. 

Constraint Satisfaction Problems and Probabilistic Combinatorics II

Fotios Illiopoulos
Member, School of Mathematics
November 26, 2019

The tasks of finding and randomly sampling solutions of constraint satisfaction problems over discrete variable sets arise naturally in a wide variety of areas, among them artificial intelligence, bioinformatics and combinatorics, and further have deep connections to statistical physics.

In this second talk of the series, I'll cover some results regarding random constraint satisfaction problems and their connection to statistical physics.