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In ricordo del Professor Ambrosetti

23 November 2020
Antonio Ambrosetti, world-class mathematician and professor at Normale and SISSA, died on Friday 20 November at the age of 75 in Venice

Antonio Ambrosetti was born in Bari on November 25, 1944. He obtained a degree in Mathematics from the University of Padua in 1966.

Soon after, he began his PhD (called "Perfezionamento" at Scuola Normale) at the Scuola Normale Superiore under the guidance of Giovanni Prodi, with whom he established a lasting collaboration and a deep friendship throughout his life. Ambrosetti remained an assistant professor at the Scuola Normale for some years, interacting profitably with the effervescent Pisan environment, in particular with De Giorgi, Stampacchia and the many mathematicians from all over the world who in those years attended Pisa. It was then that the fruitful collaboration with Paul Rabinowitz began. In 1975 he won the chair of Full Professor of Mathematical Analysis, and his first appointment brought him to Bologna, then moved to Ferrara and in 1978 to SISSA in Trieste, where he was one of the first three professors.

In the early years of SISSA the role of Ambrosetti was decisive in giving the nascent School the character of excellence that has since distinguished it. After a brief stint at the University of Venice, Ambrosetti was appointed professor at Scuola Normale Superiore in 1986, where he remained until 1998 contributing to the excellence and international renown of the school of Nonlinear Analysis. Finally, Ambrosetti moved back to SISSA, of which he had always closely followed the activities.

In his scientific work Ambrosetti has been interested in many questions of Mathematical Analysis, ranging from Dynamical Systems to Partial Differential Equations. At the end of the sixties and seventies, together with Prodi, he founded the Italian school of nonlinear analysis, developing general techniques such as bifurcation theory, variational and topological methods, theory of critical points. The simplicity and at the same time the power of the geometric ideas at the base of these tools has generated a subsequent great development of these topics and has allowed to successfully address a wide range of applications in different fields, including Differential Equations, Fluid Dynamics, Quantum Mechanics.

The originality of the approach has in some cases contributed to the creation of new disciplines, as was the case with the study of Hamiltonian systems through the theory of critical points from which Symplectic Topology took its first steps.

Among his many valuable works, famous are for example the Mountain Pass Theorem with Paul Rabinowitz and the Global Inversion Theorem with Singularity in collaboration with his teacher Giovanni Prodi.

With numerous international collaborations he authored more than one hundred and forty scientific publications including five monographs, as well as various popular textbooks. His broad vision and his clarity of explanation, in addition to his depth, have made him a point of reference for the scientific community and for his many collaborators and students, for whom he was a stimulating mentor, attentive and always available.

Among the numerous awards we can mention the conference on invitation to the International Congress of Mathematicians in Warsaw in 1983, the Caccioppoli Prize in 1985, the plenary conferences at the Equadiff conferences in 1982, 1995, 1999 and 2001, the National Congress of the UMI in 1987, the Lagrange Chair, 1991, the BBV Chair Autonomous University of Madrid, 1998, the IBERDROLA Chair Autonomous University of Madrid, 2001, the Degree Honoris Causa at the Univ. Autonomous of Madrid, 2005, the Ferran Sunyer i Balaguer award for the monograph written with Andrea Malchiodi, 2005, the Amerio 2007 award.

He was always very well regarded internationally and has significantly contributed to creating and keeping international relations in the Nonlinear Analysis community: he was visiting professor, among others, at the Universities of Bremen, ETH Zurich, EPFL Lausanne, Paris VI and Paris IX, Wisconsin-Madison, Chicago, Rutgers, Granada...

Elected in 1988 as a member of the Accademia Nazionale dei Lincei, he closely followed its activities, in particular as editor-in-chief of the journal Rendiconti Lincei - Matematica e Applicazioni, a role he held for several years. He was also a member of the Istituto Veneto di Lettere, Scienze ed Arti, of the Accademia delle Scienze di Torino, of the European Academy of Science.

He was also involved in editorial activities, as he was founder of the magazine Nodea, and member of the editorial board of numerous international magazines.