An evening in honour of the Fields Medal

Alessio Figalli’s honorary lecture in the ETH Zurich Auditorium Maximum was fully booked in just 70 minutes. The event was transmitted to a second auditorium, which was also filled to capacity. And, more than 1250 times the live stream of the lecture was watched. This reflects the great interest among students, researchers and colleagues in seeing the Fields Medal winner and hearing about what drives him in his research.

ETH held an honorary lecture in celebration of the Italian’s outstanding achievement in winning the Fields Medal, which holds the same prestige in mathematics as the Nobel Prize in natural sciences. There were four Fields Medal winners in the Audi Max: Alessio Figalli, Artur Avila (University of Zurich), Cédric Villani (University Lyon 1) and Wendelin Werner (ETH Zurich).

The surprising thing about mathematics, said ETH President Lino Guzzella, who hosted the honorary event, is that mathematical findings – as abstract as they may be – invariably turn out to be extremely useful and effective for people and technology.

Differential equations, such as the Monge-Ampère equation, which plays a key role in Alessio Figalli’s research, describe movements and changes. They are a powerful tool in the natural and engineering sciences and an irreplaceable prerequisite for many technical achievements in modern society. Lino Guzzella, whose parents immigrated from Italy to Switzerland, delivered his congratulatory address in Italian.

The unifying power of mathematics

Alessio Figalli took to the stage and fulfilled the expectations of his audience. He sees this "unifying power” as the quality that sets mathematics apart. The same type of equations that, for example, describes how elastic membranes change their shape when they encounter an obstacle, also shows how ice melts in water. Figalli demonstrated this using a tennis racket and a footballer heading the ball.

The theory of optimal transport also has a vast scope for application in new fields – besides the traditional areas of urban development or distribution of resources, it covers questions relating to astrophysics and the expansion of the universe or the meteorological analysis of cloud movements in a large weather front. Figalli was awarded the Fields Medal in August for his original contributions to this theory and the application thereof.

On the shoulders of giants

Although mathematical breakthroughs do require individual excellence, they rarely occur in complete isolation: Alessio Figalli’s PhD supervisors, the Italian Luigi Ambrosio and Frenchman Cédric Villani, are also leading experts in the field of optimal transport, as Mete Soner, Head of the ETH Mathematics Department pointed out.

Cédric Villani won the Fields Medal in 2010 for his proofs in mathematical physics and he has written two reference works on optimal transport. Villani is a celebrity in France known for his penchant for period clothing. He is also involved in scientific policy: he is a member of the "La République en Marche” party and the French National Assembly, Vice-President of the Parliamentary Office for the Evaluation of Scientific and Technological Choices and author of a key report on the French strategy for artificial intelligence.

Luigi Ambrosio, winner of the Fermat Prize in 2003, also inspired entire generations of mathematicians through his groundbreaking contributions to the calculus of variations, geometric measure theory and the theory of optimal transport. He also played a big part in the emergence of a new style of mathematics at the Scuola Normale Superiore di Pisa, an alma mater of Alessio Figalli. The legendary mathematician Ennio di Giorgi represents the "soul” of this Italian tradition and his work in analysing this area was also a major influence on Alessio Figalli.

Responsibility and virginity

The trio held an animated discussion, moderated by ETH mathematics professor Peter Bühlmann, on what sets Alessio Figalli apart as a mathematician. Both PhD supervisors recalled how he stood out even as a young doctoral student through his amazing questions, thirst for knowledge and phenomenal ability to solve complex mathematical problems extremely quickly – he was given an assignment in the morning and had completed it by the afternoon.

Moreover, Alessio Figalli is also able to work with all types of researchers. Alessio Figalli praised the collaboration in mathematics with the University of Zurich as a strength of the location: "ETH and the University of Zurich work as if they were the same university."

The group of four also discussed the growing economic and scientific significance of mathematics and its consequences for teaching and education, i.e. going beyond simply relaying techniques to including the conceptual meaning. A member of the audience asked whether mathematics was about to lose its "virginity" due to artificial intelligence, as happened with physics when the atom bomb was made in the 1940s. "Mathematics is an eternal virgin", quipped Villani admitting at the same time that the specific application of artificial intelligence needs to be carefully reviewed in every instance.