Alessio Figalli

Alessio Figalli is an Italian mathematician known for contributions to the theory of optimal transport, partial differential equations, and the calculus of variations. He has held positions at the Massachusetts Institute of Technology, ETH Zurich, and the University of Texas at Austin, and was awarded the Fields Medal in 2018. Figalli's work has influenced research in geometry, probability theory, mathematical physics, numerical analysis, and financial mathematics.

Early life and education

Figalli was born in Rome and grew up in Firenze before undertaking undergraduate and graduate studies at the University of Pisa and the Scuola Normale Superiore di Pisa. During his doctoral studies he worked under supervision connected to researchers at the Scuola Normale Superiore and collaborators from the International Centre for Theoretical Physics, engaging with mathematicians from institutions such as the Institute for Advanced Study, the European Mathematical Society, and the Courant Institute. His early influences included interactions with scholars associated with the University of Paris (Sorbonne), the École Normale Supérieure, the University of Bonn, and the University of Cambridge.

Research and career

Figalli's research program developed through postdoctoral work at the ETH Zurich and a faculty appointment at the University of Texas at Austin, followed by a professorship at the Swiss Federal Institute of Technology in Zurich (ETH Zurich) and later a chair at the Massachusetts Institute of Technology. He has collaborated with mathematicians from the Collège de France, the University of Oxford, the Université Paris-Saclay, the Princeton University, the California Institute of Technology, the Stanford University, and the University of Chicago. His publication record spans journals associated with the American Mathematical Society, the Society for Industrial and Applied Mathematics, the Royal Society, and the European Mathematical Society, addressing problems tied to results from the Monge–Kantorovich problem, the Monge–Ampère equation, the Isaac Newton Institute, and the Clay Mathematics Institute programs.

Major contributions and results

Figalli produced key results on regularity theory for solutions to the Monge–Ampère equation and the optimal transport problem, building on prior work by Gaspard Monge, Leonid Kantorovich, Cédric Villani, Yann Brenier, and Luis Caffarelli. He established stability and quantitative estimates that connect to the Sobolev inequality, the isoperimetric inequality, and the calculus of variations frameworks developed by Ennio De Giorgi and John Nash. Figalli proved sharp results on regularity and uniqueness for optimal transport maps linked to the Kantorovich duality and contributed to the study of nonlinear partial differential equations such as the Vlasov–Poisson equation, the Keller–Segel model, and problems arising in statistical mechanics, quantum mechanics, and general relativity. His work on quantitative stability for the isoperimetric problem and on the structure of solution sets influenced methods used at the Simons Foundation, the National Science Foundation, and the European Research Council.

Awards and honors

Figalli received the EMS Prize, the Bôcher Memorial Prize, and the Fields Medal in 2018, recognizing advances connected to the International Congress of Mathematicians and to the bodies such as the International Mathematical Union and the European Mathematical Society. He has been invited to give addresses at the International Congress of Mathematicians, the Joint Mathematics Meetings, the Heilbronn Institute, the Newton Institute, and the Institute for Advanced Study. Honors include membership or fellowships with the Academia Europaea, the Royal Swedish Academy of Sciences forums, and awards tied to the European Research Council and national academies like the Istituto Lombardo and the Accademia Nazionale dei Lincei.

Teaching and mentoring

In his roles at ETH Zurich, the Massachusetts Institute of Technology, and the University of Texas at Austin, Figalli has supervised doctoral students and postdoctoral researchers who have gone on to positions at institutions including the University of Cambridge, the Princeton University, the Courant Institute, the University of Michigan, and the University of Chicago. He has taught advanced courses connected to the Monge–Ampère equation, optimal transport, and functional analysis for programs at the European Mathematical Society Summer School, the Program for Women and Mathematics, the Mathematical Sciences Research Institute, and the Centre International de Rencontres Mathématiques. He has participated in collaborative efforts with research groups at the Institut des Hautes Études Scientifiques, the Max Planck Institute for Mathematics, and the Swiss National Science Foundation to mentor early-career researchers.

Category:Italian mathematicians Category:Fields Medalists