Bernoullis Tafelrunde: Giacomo Cozzi (Università di Padova)

Bernoulli Introduces Gradient Flows of Nonlocal Energies

The aim of this talk is to present the theory of gradient flows on metric space. Given a functional defined on a Hilbert space, its gradient flow is the curve minimizing the functional in the fastest way possible, namely, following the opposite direction of its gradient. Starting from the pioneristic work of De Giorgi, it became possible to give a meaning to gradient flows even in spaces where the definition of gradient is not natural (i.e., on spaces which are not Hilbert). An important application is the case of gradient flows defined on the space of probability measures endowed with the Wasserstein distance. Using this theory, we will discuss two examples in which the functionals to be minimized are nonlocal (namely, long range interaction) energies.

abstract

Veranstaltung übernehmen als iCal