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Giuseppe Buttazzo (Pisa, Ph.D. advisor) 
Guido Montúfar (UCLA & MPI) 
Research interests
Calculus of Variations,
Optimal Transport,
Gradient Flows in the space of probability measures,
Numerical methods and approximation,
Computational Chemistry,
 Density Functional Theory
 Onebody Reduced Density Matrix Theory
Mathematical Aspects of Machine learning theory
 Likelihoodfree 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 multimarginal optimal transport (transport plans, densities, potentials, existence and regularity of transport maps); Gammaconvergence. Computational realizations of Multimarginal Optimal Transport (MOT), Convex/Entropic regularization of MOT.

Computational Chemistry
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 manyelectrons system (existence and nextorder corrections of SCE DFT) and timedependent DFT (1d). I am also developing Noncommutative Optimal Transport methods to Onebody 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.