Calculus of Variations,
Optimal Transport,
Gradient Flows in the space of probability measures,
Density Functional Theory,
Numerics and approximation.

Brief Research Description



  • Calculus of Variations

    I am mainly interested in Fundamental theory of multi-marginal optimal transport (transport plans, densities, potentials, existence and regularity of transport maps); Shape and Potential Optimization; and Gamma-convergence.

     

  • Density Functional Theory

    The focus of my current research is to extend the accuracy of electronic density functional theory (DFT) to systems in which electronic correlation plays a prominent role. In particular using the SCE formalism in the study of ground state properties of many-electrons system (existence and next-order corrections of SCE DFT) and time-dependent DFT (1d).

  • Numerics and Approximation

    - Numerical aspects of multi-marginal optimal transport, including convergence and stability of the Entropic reg. meth.;
    - (Rigorous) Numerical approximation of the Hohenberg-Kohn functional in DFT;


Collaborators and Mentors


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Giuseppe Buttazzo (Pisa, Ph.D. advisor)
Simone Di Marino (SNS Pisa)
Paola Gori-Giorgi (Chemistry, Amsterdam)
Anna Kausamo (Jyväskylä)
Luca Nenna (Dauphine)
Tapio Rajala (Jyväskylä)
Berardo Ruffini (Montpellier)
Michael Seidl (Physics, Regensburg)
Robert van Leeuwen (Physics, Jyväskylä)
Bozhidar Velichkov (Grenoble)
Johannes Zimmer (Bath).