# From stochastic geometric mechanics to mass transportation problems

PTDC/MAT-STA/0975/2014

## Researchers

- Marc Arnaudon
- Giovanni Conforti
- Ana Bela Cruzeiro (PI)
- Diogo Gomes
- Rémi Lassalle
- Christian Léonard
- Davide Masoero
- Jean-Claude Zambrini

## PhD students

- Guoping Liu
- Luigia Ripani
- Alexandra Symeonides
- Luca Tamanini

## 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