Hugo Lavenant

What happens to Wasserstein gradient flows if one uses entropic optimal transport instead of classical optimal transport? I will explain why it may be relevant to use Sinkhorn divergences, built on entropic optimal transport, as they allow the...

Optimal Transport theory emerged more than two centuries ago as an engineering problem posed by Gaspard Monge just before the French revolution. Its rich mathematical structure was first revealed by the Russian Nobel-prize winner Kantorovich during...

The Wasserstein space, which is the space of probability measures endowed with the so-called (quadratic) Wasserstein distance coming from optimal transport, can formally be seen as a Riemannian manifold of infinite dimension. We propose, through a...

Among modern numerical methods to solve the optimal transport problem, dynamical optimal transport (a.k.a. fluid dynamic formulation or Benamou-Brenier formulation) is one of the oldest: it consists in rewriting the problem in terms of convex...