Alessio Figalli

Alessio Figalli is an Italian mathematician renowned for his profound contributions to the calculus of variations and partial differential equations. His work, particularly in optimal transport theory, Monge–Ampère equations, and interfacial dynamics, has resolved long-standing problems and forged new connections across mathematical analysis. Awarded the Fields Medal in 2018, he is recognized as one of the leading analysts of his generation, holding prestigious positions at institutions like the École Polytechnique Fédérale de Lausanne. Figalli's research combines deep theoretical insight with a remarkable ability to apply abstract techniques to concrete problems in geometry and mathematical physics.

Early life and education

Alessio Figalli was born in Rome and demonstrated an early aptitude for mathematics, eventually competing in the International Mathematical Olympiad. He pursued his undergraduate studies at the Scuola Normale Superiore di Pisa and the University of Pisa, graduating in 2006. For his doctoral research, he engaged in a unique joint supervision program between the University of Pisa and the École Normale Supérieure de Lyon, working under the guidance of Luigi Ambrosio and Cédric Villani. He earned his Ph.D. in 2007 with a thesis on optimal transport, a field where he would later make transformative contributions, building on the foundational work of pioneers like Leonid Kantorovich.

Career and research

Following his doctorate, Figalli held postdoctoral positions at the École Polytechnique Fédérale de Lausanne, the University of Paris-Sud, and the University of Texas at Austin, where he later became a full professor. In 2016, he returned to Europe as a professor at the University of Zurich before moving to the École Polytechnique Fédérale de Lausanne in 2019. His research portfolio is exceptionally broad, tackling central questions in nonlinear partial differential equations and geometric analysis. A landmark achievement was his work on the regularity theory for the Monge–Ampère equation, providing crucial insights into the Monge–Kantorovich problem. He has also made seminal contributions to the stability of functional inequalities, the optimal transportation on Riemannian manifolds, and the asymptotic behavior of evolution equations modeling crystal growth and phase transitions.

Awards and honors

Figalli's work has been recognized with numerous international prizes. He received the Caccioppoli Prize in 2011 and the EMS Prize from the European Mathematical Society in 2012. In 2015, he was awarded the Stampacchia Medal and the Feltrinelli Prize from the Accademia Nazionale dei Lincei. The pinnacle of his recognition came in 2018 when he was awarded the Fields Medal at the International Congress of Mathematicians in Rio de Janeiro for his contributions to the calculus of variations and optimal transport. He is also a member of several academies, including the Accademia Nazionale dei Lincei and the European Academy of Sciences.

Selected publications

Figalli's extensive publication record includes influential papers in journals such as the Annals of Mathematics, Inventiones Mathematicae, and the Journal of the American Mathematical Society. Notable works include "The Monge-Ampère equation and its link to optimal transportation" in the Bulletin of the American Mathematical Society and "A mass transportation approach to quantitative isoperimetric inequalities" in Inventiones Mathematicae. His research monographs, such as "The Monge-Ampère Equation and Optimal Transportation," co-authored with other leading analysts, have become standard references in the field, synthesizing complex theory with novel applications.

Personal life

Figalli is married and maintains a strong connection to his native Italy, often collaborating with mathematicians at institutions like the Scuola Normale Superiore di Pisa and the International School for Advanced Studies in Trieste. Known for his energetic and collaborative approach, he has supervised numerous Ph.D. students and postdoctoral researchers, fostering the next generation of analysts. Outside of mathematics, he has expressed a fondness for classical music and is an avid supporter of A.S. Roma, the football club from his hometown.

Category:1984 births Category:Living people Category:Italian mathematicians Category:Fields Medal winners Category:University of Texas at Austin faculty Category:École Polytechnique Fédérale de Lausanne faculty Category:University of Zurich faculty Category:Scuola Normale Superiore di Pisa alumni Category:University of Pisa alumni Category:École Normale Supérieure de Lyon alumni