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Giuseppe Buttazzo (Pisa, Ph.D. advisor)
Guido Montúfar (UCLA & MPI)
Calculus of Variations,
Gradient Flows in the space of probability measures,
Numerical methods and approximation,
- Density Functional Theory
- One-body Reduced Density Matrix Theory
Mathematical Aspects of Machine learning theory
- Likelihood-free Variational Inference and Generative Modelling
- Normalizing flows
- Generative Adversarial Networks
- Statistical Learning Theory
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); Gamma-convergence. Computational realizations of Multi-marginal Optimal Transport (MOT), Convex/Entropic regularization of MOT.
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). I am also developing Non-commutative Optimal Transport methods to One-body Reduced Density Matrix (1RDM) functional theory.
Mathematical and Computational Aspects of Machine Learning
I am developing tools to improve the understanding of density estimation and generation in GANs, VAES and Normalizing Flows; and developing novel deep learning methods for Computational Chemistry.
Collaborators and Mentors