Seminars Sorted by Series

In contrast to the two dimensional case, in dimension $d \geq 3$ averaging operators on the $d-1$-sphere using finitely many rotations, i.e. averaging operators of the form $Af(x)= |S|^{-1} \sum_{\theta \in S} f(s x)$ where $S$ is a finite subset of...

Understanding the structure of large graphs is a fundamental problem, as it can yield critical insights into topics ranging from the spread of diseases to how the brain works to patterns in the primes. Szemerédi's regularity lemma gives a rough...

A celebrated theorem of Roth from 1953 shows that every dense set of integers contains a three-term arithmetic progression. This has been the starting point for the development of an enormous amount of beautiful mathematics. In this talk, I will...

We describe a simple yet surprisingly powerful probabilistic technique that shows how to find, in a dense graph, a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently, this technique has had...

In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it...

In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it...

In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it...

In this lecture we will review the notion of the holonomy group of a Riemannian manifold and the Berger classification. We will discuss special algebraic structures in dimensions 6, 7 and 8, emphasising exterior algebra, and then go on to...

We will discuss the constructions of compact manifolds with exceptional holonomy (in fact, holonomy $G_{2}$), due to Joyce and Kovalev. These both use “gluing constructions”. The first involves de-singularising quotient spaces and the second...

By imposing symmetry on manifolds of exceptional holonomy we get a variety of differential geometric questions in lower dimensions. Related to that, one can consider “adiabatic limits”, where the manifold has a fibration and the fibre size is scaled...

Consider a system of small hard spheres, which are initially (almost) independent and identically distributed. Then, in the low density limit, their empirical measure $\frac1N \sum_{i=1}^N \delta_{x_i(t), v_i(t)}$ converges almost surely to a non...

Although the distribution of hard spheres remains essentially chaotic in this regime, collisions give birth to small correlations. The structure of these dynamical correlations is amazing, going through all scales. How combinatorial techniques can...

At leading order, the fluctuations around the typical dynamics are described by the second cumulant. They actually satisfy a stochastic PDE with time-space white noise. Can we say more using higher order cumulants?

The Riemann zeta function is the most important function of number theory, and a great part of modern research in number theory is dedicated to its study and the study of its relatives the L-functions. It was Riemann who revolutionized number theory...