PRIN “Gradient flows, Optimal Transport and Metric Measure Structures” Grant 2017TEXA3H_002 (2019-2023)

“Gradient flows, Optimal Transport and Metric Measure Structures”

Principal Investigator:

Giuseppe Savaré,

Research team Bocconi unit:

Ugo Gianazza, Giuseppe Toscani, Stefano Lisini (Università di Pavia),
Andrea Marchese (Università di Trento),
Riccarda Rossi (Università di Brescia),
Ilaria Fragalà (Politecnico di Milano)

Research units:

Scuola Normale Superiore di Pisa (Luigi Ambrosio)
Università Bocconi (Giuseppe Savaré)
Università di Genova (Edoardo Mainini)
Università di Napoli Federico II (Nicola Fusco)
Università di Pisa (Giuseppe Buttazzo)
Università di Trento (Francesco Serra Cassano)

Abstract

This project stems out from the strong collaboration of several researchers that in recent years developed new ideas, techniques and methods in the study of gradient flows and evolution problems, optimal transport, metric analysis and geometric optimization problems.
All these topics are indeed strictly intertwined. Many evolution problems of interest in pure and applied Mathematics are energy-driven and the possibility to identify a gradient flow structure is of fundamental importance in the understanding of energy dissipation rates and of trends to equilibrium. In this respect, particularly in the last two decades, optimal transport has been a striking source of tools for studying evolution, due on one hand to the identification of new families of natural metrics, on the other hand to the possibility to lift the space dynamics to probability measures in the space of curves.
Since lack of smoothness is an intrinsic feature of many of these models, their analysis leads in a natural way to the investigation of metric measure structures, with the development of new calculus tools and synthetic theories for geometries that can also be very far from being Riemannian.

Grant 2017TEXA3H_002 (2019-2023) PRIN