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From stochastic geometric mechanics to mass transportation problems

PTDC/MAT-­STA/0975/2014

Researchers

PhD students

Description

This project will develop a stochastic perturbation of Geometric Mechanics (in finite and infinite dimensions), from different perspectives. Up to now the main approach has been motivated by ideas inspired by Statistical Mechanics. We advocate another method, inspired by the quantization of classical dynamical systems. This approach became recently interesting for a wide range of problems around optimal transport theory and our team is made up of some of the researchers who brought together the fields of Stochastic deformation and Optimal transport. Our methods will involve ideas of Geometric Mechanics, Stochastic Analysis, Stochastic Control Theory and entropy minimization techniques as well as some deterministic and geometric tools used in PDE's.

The host institution is the Group of Mathematical Physics of the University of Lisbon. This is a research centre in Mathematics funded by the Portuguese Science Foundation (FCT). The project includes funding for two postdoctoral positions starting before the end of 2017. For a description of the conditions, deadlines, etc, please see the call for applications for the first one.

Time span: 15/05/2016-14/05/2019

Some relevant publications

M. Arnaudon, X. Chen, A.B. Cruzeiro
Stochastic Euler-­Poincaré reduction
J. Math. Phys. 55, 081507
C. Léonard
A survey of the Schrödinger problem and some of its connections with optimal transport
Discrete Cont. Dyn.Syst. A 34 (4), 1533-­1574
J.C. Zambrini
Variational processes and stochastic versions of mechanics
J. Math. Phys. 27, 2307