Mercoledì 13 Marzo 2019, alle ore 15 precise, presso **Aula Beltrami, Dipartimento di Matematica**, il

dott. Hugo Lavenant, Institut de Mathématique d'Orsay Univ. Paris-Sud

terrà un seminario dal titolo:

Harmonic mappings valued in the Wasserstein space

nell'ambito del Seminario di Matematica Applicata (IMATI-CNR e Dipartimento di Matematica, Pavia),


Abstract. The Wasserstein space, which is the space of probability measures endowed with the so-called (quadratic) Wasserstein distance coming from optimal transport, can formally be seen as a Riemannian manifold of infinite dimension. We propose, through a variational approach, a definition of harmonic mappings defined over a domain of an Euclidean space and valued in the Wasserstein space. We will show how one can build a fairly satisfying theory which captures some key features of harmonicity and present a numerical scheme to compute such harmonic mappings. Other than a better understanding of the Wasserstein space, the motivation of such a study can be found in geometric data analysis.