Marston Morse Lecture

Traditionally the Morse lectures have consisted of two or three one-hour talks to be given within a week, usually during the School’s second term. It is expected that they will present a broadly conceived exposition of a topic of current interest, usually in an area related to Marston Morse’s work.

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...
Mar 03 2018
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...

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