GOTA

Objectives

This project deals with generalizations and applications of optimal transport theory, with a particular focus on three topics: multi-marginal optimal transport, multi-population models, and multi-marginal entropic optimal transport.

The transition from the classical case to the multi-population setting carries difficulties that make these problems more delicate both theoretically and numerically. On the theoretical side, the main questions concern the dimension of the support of the solution, tools for analysing PDEs involving several populations, and the first-order expansion of the multi-marginal entropic regularized problem under mild assumptions on the cost. On the numerical side, the common objective across the three topics is to develop methods that overcome the so-called curse of dimensionality.

Members

• Luca Nenna — P.I., U. Paris-Saclay
• Maxime Laborde — U. Paris-Cité
• Paul Pegon — U. Paris-Dauphine
• Adrien Cancès — PhD, U. Paris-Saclay
• Élise Bonnet-Weill — PhD, ENPC
• Alessandro Cosenza — post-doc, U. Paris-Saclay
• Mattia Garatti — PhD, U. Paris-Saclay
• Louis Tocquec — PhD, U. Paris-Saclay

Collaborators

• Jean-Baptiste Casteras — U. Lisbon
• Luigi De Pascale — U. Florence
• Simone Di Marino — U. Genova
• Virginie Ehrlacher — ENPC, Cermics
• Mathieu Lewin — U. Paris-Dauphine, Ceremade
• Léonard Monsaingeon — GFM, Lisbon
• Brendan Pass — U. Alberta

Publications & preprints

1. M. Garatti, L. Nenna, S. Rota-Nodari, L. Tamanini. A PDE approach to the Benamou–Brenier formula for the Schrödinger problem. Preprint, 2026.
2. É. Bonnet-Weill, V. Ehrlacher, L. Nenna. A reduced-order model for parametrized optimal transport problems. Preprint, 2026.
3. A. Cancès, L. Nenna, D. Omarov, B. Pass. Ordinary differential equations for regularized variational problems involving semi-discrete optimal transport. Preprint, 2026.
4. A. Cancès, Q. Mérigot, L. Nenna. A particle method for a nonlinear multi-marginal optimal transport problem. Preprint, 2026.
5. A. Cancès, H. Leclerc. Unidimensional semi-discrete partial optimal transport. Preprint, 2025.
6. L. Nenna, P. Pegon, L. Tocquec. Convergence rates for regularized unbalanced optimal transport: the discrete case. Preprint, 2025.
7. L. Nenna, D. Omarov, B. Pass. Characterizing and computing solutions to regularized semi-discrete optimal transport via an ODE. Preprint, 2025.
8. J.-B. Casteras, L. Monsaingeon, L. Nenna. Large deviations for sticky-reflecting Brownian motion with boundary diffusion. Preprint, 2025.
9. S. Di Marino, M. Lewin, L. Nenna. Grand-Canonical Optimal Transport. Archive for Rational Mechanics and Analysis 249(1), 12, 2025.
10. S. Di Marino, M. Lewin, L. Nenna. The ground state energy is not always convex in the number of electrons. The Journal of Physical Chemistry A 128(49), 10697–10706, 2024.
11. L. De Pascale, L. Nenna. A variational formulation of a multi-population Mean Field Games with non-local interactions. Preprint, 2024.
12. J. Z. G. Hiew, L. Nenna, B. Pass. An ordinary differential equation for entropic optimal transport and its linearly constrained variants. Preprint, 2024.
13. R. Ducasse, M. Laborde. Long-time behavior of the heterogeneous SIRS epidemiological model. Preprint, 2024.
14. H. Ennaji, Q. Mérigot, L. Nenna, B. Pass. Robust risk management via multi-marginal optimal transport. Journal of Optimization Theory and Applications, 2024.
15. L. Nenna, P. Pegon. Convergence rate of entropy-regularized multi-marginal optimal transport costs. Canadian Journal of Mathematics, 2024.

Ph.D. & HDR thesis

• Luca Nenna. On some generalisations of the optimal transport problem. HDR, Université Paris-Saclay, 2024. ⟨tel-04554531⟩

Events

• "Generalized Optimal Transport and Applications", Fondation des Treilles — 21–25 September 2026.
• Optimal Transport session at PGMO Days — November 2025.
• Optimal Transport session at PGMO Days — 19–20 November 2024.
• Optimal Transport session at CANUM — 27–31 May 2024.
• Moka10 — 4–6 June 2024.