Optimal transport and gradient flows: a brief overview

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Giuseppe Savaré
Università Bocconi
Thursday 22nd June 2023
Aula Consiglio VII piano - Dipartimento di Matematica
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Optimal transport theory studies the optimal strategies for transferring a given initial distribution of resources (mathematically represented by a measure) to a final configuration in a way that minimizes the cost of transport. First addressed mathematically by G. Monge in 1781, its first modern formulation (1942) earned L.V. Kantorovich the Nobel Prize in Economics in 1975. Later, thanks to many outstanding theoretical, applied and numerical contributions, the theory has been developed in many directions including, in addition to economics, linear and stochastic programming, statistics and probability, mean field models, functional analysis, PDEs, Riemannian geometry, machine learning. The seminar aims to give a quick overview of some of the classical results and more recent contributions, with applications to evolution problems. Contatto: marco.verani@polimi.it
Giuseppe Savaré started his scientific career as a researcher at the CNR Institute for Numerical Analysis in Pavia and has been Professor of Mathematical Analysis since 2000, first at the University of Pavia and then, since 2020, at Bocconi University in Milan. During 2019-2023 he was Hans-Fischer Senior Fellow at the Institute for Advanced Study of the Technical University of Munich. In 2011 he received the Ennio De Giorgi prize awarded by the Italian Mathematical Union. His research activity concerns variational methods for evolution problems, in particular gradient flows and rate-independent models, and their interplay with optimal transport, measure theoretic tools and analysis in metric spaces. In collaboration with Luigi Ambrosio and Nicola Gigli, he has written a monograph on Gradient Flows in Metric Spaces and in the Space of Probability Measures.