Analysis Seminar - 16/9/2015

Wednesday, 16 September 2015, 2:00 p.m.

Lecturer: Leonard Monsaingeon, CAMGSD-IST

Title: "A new optimal transport distance between nonnegative measures"

Local: Room 1.6, Edifício VII

Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: In this talk, I will introduce a new distance between nonnegative finite Borel measures in Rd. The distance is constructed by a Lagrangian approach (minimization of an action functional), which is similar to the celebrated Benamou-Brenier formula (dynamical representation of the quadratic Kantorovich-Rubinstein-Wasserstein distance between probability measures). Compared to the classical theory of optimal transportation of probability measures, our new distance has the advantage of allowing for mass changes, and the theory does not require any finite moments or decay at infinity. I will present several topological and geometrical properties of the metric space. If time permits, I will discuss the application to a fitness-driven model of population dynamics: once suitably interpreted as a gradient flow with respect to our metric, we show that the model satisfies exponential convergence to the unique steady state with explicit rates. This is joint with D. Vorotnikov and S. Kondratyev (Univ. Coimbra).