School of Mathematics

Due to its importance in materials science where it models the slow relaxation of grain boundaries, multiphase mean curvature flow has received a lot of attention over the last decades.

In this talk, I want to present two theorems. The first one is...

Symplectic geometry, and its close relative contact geometry, are geometries closely tied to complex geometry, smooth topology, and mathematical physics. The h-principle is a general method used for construction of smooth geometric objects...

We develop a framework for graph sparsification and sketching, based on a new tool, short cycle decomposition -- a decomposition of an unweighted graph into an edge-disjoint collection of short cycles, plus a small number of extra edges. A simple...

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...

A random planar map is a canonical model for a discrete random surface which is studied in probability theory, combinatorics, mathematical physics, and geometry. Liouville quantum gravity is a canonical model for a random 2D Riemannian manifold with...

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 $\Phi_{g,n}$...

Given a polynomial in one variable, what is the simplest formula for the roots in terms of the coefficients? Hilbert conjectured that for polynomials of degree 6,7 and 8, any formula must involve functions of at least 2, 3 and 4 variables...

The classical regression problem seeks to estimate a function f on the basis of independent pairs $(x_i,y_i)$ where $\mathbb E[y_i]=f(x_i)$, $i=1,\dotsc,n$. In this talk, we consider statistical and computational aspects of the "uncoupled" version...

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...

Human memory is a multi-staged phenomenon of extreme complexity, which results in highly unpredictable behavior in real-life situations. Psychologists developed classical paradigms for studying memory in the lab, which produce easily quantifiable...