$\displaystyle \min_{\gamma\in\Pi(\mu,\nu)}\int_{X\times Y} c(x,y)\,d\gamma$
$K_\varepsilon = e^{-c/\varepsilon}$
$\gamma=\mathrm{diag}(a)\,K\,\mathrm{diag}(b)$
$\displaystyle W_2^2(\rho_0,\rho_1)=\inf_{(\rho,v)}\int_0^1\!\!\int |v_t|^2\,d\rho_t\,dt$
$\displaystyle \sup_{\varphi\oplus\psi\le c}\int\varphi\,d\mu+\int\psi\,d\nu$
$\displaystyle \min_\pi\, H(\pi\,|\,R)$
$\displaystyle \min_{\gamma\in\Pi(\mu_1,\dots,\mu_N)}\int_{X_1\times\cdots\times X_N}\! c(x_1,\dots,x_N)\,d\gamma$
$(\pi_k)_{\#}\gamma=\mu_k,\ \ k=1,\dots,N$
$F_L[\rho]=\min_{\Gamma\mapsto\rho}\mathrm{Tr}(H\Gamma)$
$\nabla\varphi_{\#}\mu=\nu$
$\displaystyle \mathrm{OT}_\varepsilon=\langle c,\gamma\rangle+\varepsilon\,\mathrm{KL}(\gamma\,|\,\mu\otimes\nu)$
$\dfrac{d\gamma_\varepsilon}{d\varepsilon}=F(\gamma_\varepsilon)$
Luca Nenna
Maître de conférences, HDR · Applied Mathematics
Université Paris-Saclay (Laboratoire de mathématiques d'Orsay) · Inria ParMaJunior member, Institut Universitaire de France
Where to find me: Bâtiment 307, bureau 2F1 · 307 rue Michel Magat, 91405 Orsay ·
+33 (0)1 69 15 74 92
I am a maître de conférences (HDR) in applied mathematics at Université Paris-Saclay
(Laboratoire de mathématiques d'Orsay) and a junior member of the Institut Universitaire de France.
I defended my HdR in March 2024; before that I was a post-doc with
Mathieu Lewin ,
following a PhD (2016) under
Jean-David Benamou and
Guillaume Carlier .
My research develops generalized optimal transport models and methods, with
applications to mathematical physics, economics and numerical optimization (and sometimes PDEs).
I am the Principal Investigator of the ANR project GOTA PiQuantO KarMa (ParMa–Kantorovich Initiative, PIMS), and a member of the Inria–Saclay
team ParMa.
Optimal Transport
Mathematical Physics
Mathematical Economics
Numerical Optimization
News
2026 Awarded an Inria PiQ project, PiQuantO — Problems in Quantum Optimal Transport R. Lelotte . 2027 Co-organizing a workshop on Numerical Optimal Transport at the Newton Institute (Cambridge), within the semester programme on Optimal Transport. 2026 Co-organizing a workshop at the Fondation des Treilles with M. Laborde and P. Pegon.
Agenda
Semester on Optimal Transport — Isaac Newton Institute, Cambridge Mar 2027
Organising a workshop on Optimal Transport — Fondation des Treilles Sep 2026
Research visit — Brendan Pass, University of Alberta, Edmonton Jun 2026
Experience
Maître de conférences — Université Paris-Saclay, Orsay · délégation at Inria-Paris (Matherials), 2023 & 2024 Sep 2018 – present
Post-doc (CNRS) — PSL · Université Paris-Dauphine · supervisor: M. Lewin Sep 2017 – Aug 2018
A.T.E.R. — PSL · Université Paris-DauphineSep 2016 – Aug 2017
Education
HdR in Mathematics — Université Paris-Saclay2024
PhD in Applied Mathematics — PSL · Université Paris-Dauphine2016
MSc in Mathematical Engineering — Politecnico di Milano2013
Recent & upcoming talks
GdT Contrôle et Optimisation, INSA Rouen Oct 2026
Analysis Seminar, Nova University, Lisbon Apr 2026
SMAI–MODE, Université Côte d'Azur Mar 2026
International Congress of Basic Science, Beijing · plenary Jul 2025
All talks & seminars →
Distinctions & funding
Distinctions
Institut Universitaire de France Junior member · 2025–2030 Frontiers of Science Award (ICBS) 2024 — regularized transportation problems Young Researchers Prize Fondation Paris-Dauphine & Accuracy · 2017
Funding
PiQ — PiQuantO Quantum OT · PI · awarded 2026 · 2026–2030 · 475 k€ ANR GOTA PI · 2023–2027 · 253 k€ KarMa (ParMa–Kantorovich Initiative, PIMS) Co-PI · 2024– RIPEC C3 2024–2027 PGMO grants 2022–2026 H-code Paris-Saclay · PEPS CNRS · PEDR 2020–2024
Selected publications
Quantum / DFT
MMOT
A sparse approximation of the Lieb functional with moment constraints
V. Ehrlacher, L. Nenna
SIAM Journal on Mathematical Analysis , 2026
Published
MMOT
Computational OT
An ODE characterisation of multi-marginal optimal transport for pairwise costs
L. Nenna, B. Pass
IMA Journal of Numerical Analysis , 2025
Published
Computational OT
Entropic OT
Iterative Bregman projections for regularized transportation problems
J.-D. Benamou, G. Carlier, M. Cuturi, L. Nenna, G. Peyré
SIAM Journal on Scientific Computing , 2015
Frontiers of Science Award 2024
Quantum / DFT
MMOT
Grand-Canonical Optimal Transport
S. Di Marino, M. Lewin, L. Nenna
Archive for Rational Mechanics and Analysis , 2025
Published
Recent preprints
Ehrlacher, Lelotte, Nenna — A land of monotone plenty, bis repetita: from classical to weak optimal transport · 2026
Garatti, Nenna, Rota-Nodari, Tamanini — A PDE approach to the Benamou–Brenier formula for the Schrödinger problem · 2026
Bonnet-Weill, Ehrlacher, Nenna — A reduced-order model for parametrized optimal transport problems · 2026
Cancès, Nenna, Omarov, Pass — Ordinary differential equations for regularized variational problems involving semi-discrete optimal transport · 2026
Cancès, Mérigot, Nenna — A particle method for a nonlinear multi-marginal optimal transport problem · 2026
Nenna, Pegon, Tocquec — Convergence rates for regularized unbalanced optimal transport: the discrete case · 2025
Nenna, Omarov, Pass — Characterizing and computing solutions to regularized semi-discrete OT via an ODE · 2025
Casteras, Monsaingeon, Nenna — Large deviations for sticky-reflecting Brownian motion with boundary diffusion · 2025
All publications →
Teaching · 2025–2026
Optimisation et simulation numérique — M2 MSV Université Paris-Saclay
Service & responsibilities
Refereeing & reviewing
Journals JOTA · SIAM J. Math. Anal. · Math. of Oper. Res. · J. Global Optim. · SIAM J. Sci. Comput. · ESAIM: M2AN · M3AS · JFA Grant & panel reviewing DFG · Inria Quadrant (PiQ) · NSERC Seminar organisation Co-organiser, GdT Optimal Transport–PDE–ML (since 2021)
Committees & administration
Frontiers of Science Awards — committee Scientific computing section · 2025 & 2026 MCF hiring committee LMO, Université Paris-Saclay PhD juries R. Coyaud (2020) · X. Bacon (2022) SMAI-MODE board Elected member · 2021–2024 Erasmus co-coordinator Dept. of Mathematics, Université Paris-Saclay
