Research

Main research interests

Problems

• Fundamental theory of optimal transport (transport plans, densities and potentials)
  new: summability of transport densities
  new: existence of optimal transport maps for non-strictly convex costs and for convexly constrained ones
  
• Branched Transport Structures
  variational formulations and regularity
  Landscape functions and applications to river basins
  new: elliptic approximation via a Modica-Mortola procedure
  new: a model à la Benamou-Brenier
  
• Curves of measures and measures on curves
• Incompressible Euler equations à la Brenier
• Gradient flows in Wasserstein spaces
• Trasport with Traffic Congestion in continuous settings
  equilibrium and convex optimization,
  divergence-constrained problems and degenerate elliptic PDEs,
  numerical algorithms from Fast Marching Computations
• Principal-agent problem with costless and undesired qualities (new)
• Applications of convex optimization to equilibria, regression...
• Optimal locations of facilities
• Models for the urban planning of residential and service areas
• Hotelling problem
• Minimization under length constraints
• Compliance optimization

Collaborators