August 4, 2018, 5:04 pm
Alessio Figalli, a newly minted Fields medalist, gave his ICM 2018 plenary talk in front of thousands mathematicians, young and old. Two of the audience members had a special interest in the plenary – fellow Italian Luigi Ambrosio and 2010 Fields medalist Frenchman Cédric Villani — the two men who mentored Figalli during his Ph.D.
Figalli was awarded the Fields medal on August 1 at ICM 2018 for ‘his contributions to the theory of optimal transport and his applications in partial differential equations, metric geometry, and probability’. The Italian mathematician has worked as a mathematics professor at ETH Zurich since 2016.
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Ambrosio, who gave his own plenary talk earlier in the day, had the honor of introducing Figalli to a packed house at Riocentro. “I’ve never met anyone who does math in such a thoughtless and painless way as Alessio does mathematics,” said Ambrosio, who has known Figalli (34) for 14 years.
Alessio Figalli
Shortly after winning the Fields Medal, Figalli recounted how he informed his former professor Cédric Villani, also a Fields medalist, and a French parliamentarian. Since entering politics last year, Villani had been slow to answer Figalli’s emails (the main way he communicates). But when Figalli emailed him about the good news some months back (of course not mentioning the Fields prize), Villani called Figalli within two hours. “I guess he knew what I was emailing him about,” Figalli said.
Figalli’s talk, ‘Regularity of interlace in Phase Transitions via Obstacle Problems’, addressed a classic mathematics problem. The Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase change, for example, ice melting into water. The Stefan problem can be reduced to the classical obstacle problem, which consists in finding the equilibrium position of an elastic membrane whose boundary is held fixed and which is constrained to like above a given obstacle.
Throngs of mathematicians surrounded Figalli after the plenary to take photos and ask questions. “Figalli’s presentation was a walk down material analysis,” Villani said. “He is extremely quick sharp and good at absorbing new theories. He is very social and has an extreme ability to collaborate with other people.”