Research
Main research interests
Calculus of Variations,
Optimal Transport,
Elliptic and parabolic PDEs,
Evolution equations, gradient flows, population dynamics,
Equilibrium problems, Game Theory, economical applications,
Numerics and approximation
Papers, on the CVGMT
website
List of publications (updated
June 2023)
Most recent topics
-
Fundamental theory of optimal transport (transport plans, densities,
potentials, existence and regularity of transport maps)
-
Mean Field Games: variational formulation, regularity, density
constraints
new: variational MFG with jumps
-
Gradient flows in Wasserstein spaces and the JKO scheme
new: Wp gradient flows
new: Lipschitz estimates in nonlinear diffusion
new: Aronson-Bénlian estimates in Keller-Segel
new: approximation of the JKO scheme (fully discrete, Sinkhorn...)
-
Optimal quantization of measures
Most regular collaborators
(besides my PhD students and postdocs, see the dedicated page)
Aymeric Baradat (Lyon)
Giuseppe Buttazzo
(Pisa)
Pierre
Cardaliaguet (Dauphine)
Guillaume
Carlier (Dauphine)
José Antonio
Carrillo de La Plata (Oxford)
Gigi De Pascale (Firenze)
Alessio Figalli
(ETH)
Chloé Jimenez (Brest)
Antoine
Lemenant (Nancy)
Bertrand Maury (Orsay)
Quentin Mérigot (Orsay)
Markus Schmidtchen (Dresden)
Xu-Jia Wang
(Canberra)
Qinglan Xia (UC Davis)