27th Jyväskylä Summer School
and
MAnET-miniworkshop

Optimal mass transportation and related fields

Description - Courses - Workshop - Program - Contact

27th Jyväskylä Summer School and MAnET-miniworkshop

The 27th Jyväskylä Summer School will be organized 7th - 18th August, 2017. Both of the summer school weeks include a five day course on optimal mass transportation. In addition, a miniworkshop on optimal mass transportation and related fields will be held during the weekend between the summer school weeks on 12th August.

The mathematics and statistics courses at the summer school and the miniworkshop are mainly funded by the Marie Curie Inital Training Network Metric Analysis for Emergent Technologies.



       

Optimal mass transportation courses at the Summer School

A complete list of the summer school courses, registration to the summer school and other information can be found on
the official webpage of the summer school.

First week:

Optimal Mass Transportation and Geometric Inequalities
by Zoltán Balogh (Universität Bern)

Time:

7.-11.8.2017, 10h of lectures

Abstract:

Optimal mass transportation is a powerful tool to prove geometric inequalities in various settings of metric measure spaces. In this series of lectures I will indicate such applications in the setting of Euclidean, Riemannian and sub-Riemannian spaces. As a consequence we obtain Brunn-Minkowski, Borell-Brascamp-Lieb and entropy inequalities.


Second week:

Lectures on optimal entropic transport
by Christian Léonard (Université Paris Ouest)

Time:

14.-18.8.2017, 10h of lectures

Abstract:

An optimal transport problem consists of finding an interpolation between two probability distributions minimizing some average cost. Displacement interpolations resulting from standard optimal transport are basic tools
(i) for deriving several concentration and geometric inequalities, and
(ii) for developing the Lott-Sturm-Villani (LST) theory of curvature lower bounds of geodesic spaces.

Entropic optimal transport is a probabilistic version of the standard transport problem. It consists of finding most probable interpolations between two prescribed configurations described probability dsitributions, when one travels randomly, typically along Brownian diffusion processes on manifolds or random walks on graphs. In its original form, this optimization problem was addressed by Schrödinger in 1931 as a large deviation problem (the so-called Schrödinger problem) for a random particle system. Its solutions are called entropic interpolations.

We shall introduce both standard and entropic optimal transport problems, their interpretations in terms of large deviations of particle systems and their equations of motion. Some geometric and concentration inequalities will be proved by means of entropic interpolations. Otto's heuristic interpretation of the heat equation as the gradient flow of the entropy with respect to a transport distance will be investigated in light of Schrödinger's problem. Finally, the convergence of entropic interpolations to displacement interpolations on graphs will be investigated.

MAnET-miniworkshop

The purpose of the workshop is to give Ph.D. students and young researchers attending the summer school a possibility to communicate their research and to exchange ideas.

List of speakers

Augusto Gerolin (Jyväskylä)
Farhad Hatami (UAB)
Heikki Jylhä (UAB)
Shirsho Mukherjee (Jyväskylä)
Kinga Sipos (Bern)
Luca Tamanini (SISSA and Paris-Ouest)
Giulio Trigila (NYU)
Walter Andrés Ortiz (UAB)

Program

(The program will be added later.)

Contact

If you have questions regarding the summer school or if you are interested in participating in the workshop, please email me.

I hope to see you in Jyväskylä!

Last modified: 28.6.2017