The Department of Mathematics is delghted to welcome Prof Jean-David Benamou as a visiting Nelder Fellow from 3 October until 2 December 2022. 

Professor Benamou will hold series of lectures on:

"Optimal transportation, modelling and numerical simulations" (Subject to change (reduced/expended) along the way.)

Date:  11, 18, 25 October and 15, 22, 29 November  2022

Time:  11:00 - 13:00

Location: Chemistry C660

 

 

Course description:

Optimal transport is a fascinating topic that has applications in a wide range of areas in engineering, medicine, communications, geophysical fluid dynamics, economics, statistics etc. After the first optimal transport problems were posed by Monge, the reformulation by Kantorovich led to tractable mathematical analysis and algorithms (as well as a Nobel prize). Mathematical optimal transport enjoyed a remarkable revival from the 1990s, becoming a flagship example of a research area where theoretical analysis can have a direct impact on high performance computations and from there through to applications.

Based on [1], the lecture series will present an overview of the basic theory, modern optimal transportation extensions and recent algorithmic advances. This is a multidisciplinary topic that connects with probability theory, functional analysis, numerical analysis and scientific computing. It has applications in medical image analysis, fluid dynamics, economics and finance, and data science. In the course, selected modelling and numerical applications will illustrate the impact of optimal transportation in numerical analysis.

This course targets academics, researchers and graduate students in the Statistics, Applied Math- ematics and Pure Mathematics sections, as well as students from relevant areas of Computer Science, Physics and Engineering.

[1] Jean-David Benamou. Optimal transportation, modelling and numerical simulations. Acta Nu- merica (2021)

Sessions' titles:

Session 1 (11/10) :  Fast Introduction of the basic formulations  (Monge problem, Kantorovich  and dual Kantorovich). Notations used in this course.  

Session 2 (18/10) :  Wasserstein distance and probability measures Barycenters,  a first incursion into Entropic regularisation and Sinkhorn Algorithm  to treat The discrete Barycenter problem.  

Session 3 (25/10) :  Multi-marginal OT as a time-discretized dynamic transport problem. Extension of Entropic regularisation and Sinkhorn  to this setting.  

Session 4 (15/11) :  Wasserstein Gradient Flows. Small temperature asymptotics of Entropic Optimal transport/Shroedinger problem.

Session 5 (22/11) :  Generalization to Mean-Field Games and the interpretation of Entropic regularization.

Session 6 (29/11) :  The generalized OT formulation of Arnold’s  Euler Geodesics (temptative).

I will be giving a seminar at UCL on December 14th, will likely speak about the numerical resolution of the
Semi-Geostrophic equations which are a ``Wasserstein Hamiltonian System’’.

Speaker's biography:

Jean-David Benamou is Directeur de Recherche at INRIA, leading MOKAPLAN, a joint INRIA/CNRS/Université Paris-Dauphine team developing develop numerical methods, algorithms and software towards variational problems related to optimal transport, as well as towards inverse problems in imaging science. Jean-David took his PhD in 1989-1992 with Yann Brenier at Université Paris Dauphine, producing the first rigorous analysis of the semigeostrophic equations of atmospheric motion as well as the renowned Brenier-Benamou fluid dynamics interpretation of optimal transport. During his career at INRIA Jean-David has contributed significantly to the design, rigorous analysis and software implementation of a number of very successful algorithms for solving optimal transport problems (and related problems in optimisation, geometric optics, wave propagation and numerical analysis), and has collaborated with practitioners in diverse applications including geophysical inverse problems, astronomy, freeform optics, marine satellite imaging, etc.