Project description
Geometry of Wasserstein spaces under study
The transport theory that was formalised by the French mathematician Gaspard Monge in 1781 explores the optimal transport and allocation of resources. The theory has since then found application in a number of fields, including mathematical physics and probability theory. Funded by the Marie Skłodowska-Curie Actions programme, the GWFP project will study the metric structure of classical Wasserstein spaces (which provide a metric on a space of probability measures), with a strong emphasis on the classification of distance-preserving maps.
Objective
The proposed research is divided into two main work packages. The first one is the study of spaces of measures equipped with the optimal transport distance (Wasserstein distance) with a special emphasis on the structure of isometries (surjective distance-preserving maps) and isometric embeddings (not necessarily surjective transformations that preserve the distance) of these spaces. The second work package is devoted to the investigation of measures from the viewpoint of free probability theory. This work package covers three subtopics: the qualitative behaviour of the free convolution, new random matrix ensembles arising from tensor networks, and the study of free Wasserstein spaces.
Fields of science
Programme(s)
Funding Scheme
MSCA-IF-EF-ST - Standard EFCoordinator
3400 Klosterneuburg
Austria