Hugo Malamut

I am a 3rd-year Ph.D. student in Mathematics at Ceremade, Paris Dauphine PSL and Mokaplan, Inria Paris. I am advised by Jean-David Benamou and co-advised by Guillaume Carlier. From September 2025, I will be a postdoctoral researcher in the Map 5, financed by the ANR Socot, working with Nathael Gozlan. Before that, I studied at École Normale Supérieure de Paris and got my M.Sc. from the Mathematics of Modelling track of the Master Mathematics and Application (Sorbonne Université).

My research interests lie in (entropic or not) optimal transport, Euler and semigeostrophic PDEs, weak optimal transport and functional inequalities with both theoretical and computational aspects.

Email: malamut at ceremade dot dauphine dot fr

We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic equations as the entropic parameter vanishes. Convergence is also proved for discretizations that can be computed numerically in practice as shown recently in [6].

We study the convergence of the transport plans γϵ towards γ0 as well as the cost of the entropy-regularized optimal transport (c,γϵ) towards (c,γ0) as the regularization parameter ϵ vanishes in the setting of finite entropy marginals. We show that under the assumption of infinitesimally twisted cost and compactly supported marginals the distance W2(γϵ,γ0) is asymptotically greater than Cϵ√ and the suboptimality (c,γϵ)−(c,γ0) is of order ϵ. In the quadratic cost case the compactness assumption is relaxed into a moment of order 2+δ assumption. Moreover, in the case of a Lipschitz transport map for the non-regularized problem, the distance W2(γϵ,γ0) converges to 0 at rate √ϵ. Finally, if in addition the marginals have finite Fisher information, we prove (c,γϵ)−(c,γ0)∼dϵ/2 and we provide a companion expansion of H(γϵ). These results are achieved by disentangling the role of the cost and the entropy in the regularized problem.

The semigeostrophic equations are a frontogenesis model in atmospheric science. Existence of solutions both from the theoretical and numerical point of view is given under a change of variable involving the interpretation of the pressure gradient as an optimal transport map between the density of the fluid and its push forward. Thanks to recent advances in numerical optimal transportation, the computation of large scale discrete approximations can be envisioned. We study here the use of entropic optimal transport and its Sinkhorn algorithm companion.