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Colloquium Rendiconti
Giovedì 26 marzo 2026, ore 17, aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Francois Golse (École Polytechnique, Paris)
An Invitation to Quantum Optimal Transport
Abstract.
Optimal
transport is an old branch of the calculus of variations whose origins
can be traced back to an important memoir of Monge in 1781, followed by
remarkable contributions due to Kantorovich in 1942, and in the last 50
years by R.L. Dobrushin, Y. Brenier, and many others. Among the
by-products of optimal transport is a family of distances metrizing the
weak topology of Borel probability measures on Euclidean spaces. The
analogy between Borel probability measures on phase space and the notion
of density operators used in quantum mechanics suggests defining a
notion of « pseudometric » which can be used to compare two (quantum)
density operators, or a density operator with a probability density in
phase space. The talk will discuss the main properties of this
pseudometric, and applications to some problems arising in quantum
dynamics (such as the classical limit, or the mean-field limit of large
particle systems…) This presentation is based on a series of works with
E. Caglioti, C. Mouhot and T. Paul.