Luigi Ambrosio

Luigi Ambrosio is an influential Italian mathematician renowned for his profound contributions to mathematical analysis and geometric measure theory. A student of the legendary Ennio De Giorgi, his research has significantly advanced the fields of calculus of variations, partial differential equations, and the theory of optimal transport. He holds a professorship at the prestigious Scuola Normale Superiore di Pisa and has been recognized with several of the highest awards in mathematics, including the Fermat Prize and the Feltrinelli Prize.

Biography

Born in Naples, he pursued his higher education at the Scuola Normale Superiore di Pisa, where he completed his doctoral studies under the supervision of Ennio De Giorgi, a towering figure in twentieth-century mathematics. His early academic career was shaped by this formative period in Pisa, a global center for mathematical research. He has held visiting positions at renowned institutions worldwide, including the Institut des Hautes Études Scientifiques in France and the University of California, Berkeley. Throughout his career, he has played a pivotal role in the international mathematical community, serving on editorial boards for leading journals like Annales de l'Institut Henri Poincaré and Archive for Rational Mechanics and Analysis.

Research and contributions

His work is central to modern calculus of variations and geometric measure theory, often bridging these areas with partial differential equations and metric geometry. A major contribution is his foundational work on the theory of functions of bounded variation in metric measure spaces, extending classical concepts from the Euclidean space setting. He developed, with Gianni Dal Maso, a comprehensive theory of integral functionals defined on these generalized functions, which is crucial for studying free discontinuity problems like those in the Mumford-Shah functional. In optimal transport, his collaborative research on gradient flows in the Wasserstein space, particularly with Giuseppe Savaré, has provided a robust analytic framework with applications to evolution equations and statistical physics. His investigations into mean curvature flow and minimal surfaces have also provided deep insights into geometric evolution problems.

Awards and honors

His research excellence has been acknowledged by numerous prestigious awards. He received the Caccioppoli Prize in 1998, awarded by the Italian Mathematical Union. In 2003, he was a co-recipient of the international Fermat Prize for his contributions to calculus of variations and optimal transport. The Czech Academy of Sciences awarded him the B. Bolzano Gold Medal for merits in mathematical sciences in 2011. A pinnacle of recognition came in 2012 with the Feltrinelli Prize for Mathematics, Mechanics, and Applications from the Accademia Nazionale dei Lincei. He is an elected member of several academies, including the Istituto Veneto di Scienze, Lettere ed Arti and the prestigious Accademia Nazionale dei Lincei.

Selected publications

His extensive body of work includes several highly cited monographs and research papers that have become standard references. Notable books include *Functions of Bounded Variation and Free Discontinuity Problems*, published in the Oxford Lecture Series in Mathematics and Its Applications. With Nicola Gigli and Giuseppe Savaré, he authored *Gradient Flows: In Metric Spaces and in the Space of Probability Measures*, a seminal text from Birkhäuser Verlag. Key research articles, often published in journals like Annals of Mathematics, Inventiones Mathematicae, and Communications on Pure and Applied Mathematics, cover topics such as minimal surfaces, geometric measure theory, and the Monge-Ampère equation.

Academic appointments

He has spent the majority of his career at the Scuola Normale Superiore di Pisa, where he is a full professor and has directed its doctoral program in mathematics. He has held long-term visiting professorships at institutions such as the École Polytechnique and the University of Paris-Sud. His leadership extends to directing the Centro di Ricerca Matematica Ennio De Giorgi, a research center named for his advisor, which fosters collaboration under the auspices of the Scuola Normale Superiore di Pisa. He has also served as a panel member for advanced grants from the European Research Council and has been involved in organizing major conferences like the International Congress of Mathematicians.

Category:Italian mathematicians Category:1963 births Category:Living people