Apr 11 2019

### Fluctuations look like white noise

Speaker: Laure Saint-Raymond

2:00pm | Simonyi Hall 101
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?

Apr 09 2019

### Space-time correlations at equilibrium

Speaker: Laure Saint-Raymond

2:00pm | Simonyi Hall 101
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 help to analyze this...

Apr 08 2019

### Disorder increases almost surely.

Speaker: Laure Saint-Raymond

2:00pm | Simonyi Hall 101
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 reversible dynamics. Where...

Apr 06 2018

### Exceptional holonomy and related geometric structures: Dimension reduction and boundary value problems

Speaker: Simon Donaldson

2:00pm | Simonyi Hall 101
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 to zero. In another...

Apr 04 2018

### Exceptional holonomy and related geometric structures: Examples and moduli theory

Speaker: Simon Donaldson

2:00pm | Simonyi Hall 101
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 constructs a 7-manifold from “...

Apr 03 2018

### Exceptional holonomy and related geometric structures: Basic theory

Speaker: Simon Donaldson

2:00pm | Simonyi Hall 101
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 differential geometry. Here...

Feb 24 2017

### Folding papers and turbulent flows

Speaker: Camillo De Lellis

3:30pm | S-101
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, no matter how large it is...

Feb 23 2017

### Folding papers and turbulent flows

Speaker: Camillo De Lellis

3:30pm | S-101
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, no matter how large it is...

Feb 21 2017

### Folding papers and turbulent flows

Speaker: Camillo De Lellis

3:30pm | S-101
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, no matter how large it is...