Alessio Figalli

Regularity of interfaces in phase transitions via obstacle problems

11 November 2019



The so-called Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase change, for example ice melting to water. An important goal is to describe the structure of the interface separating the two phases. In its stationary version, 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 lie above a given obstacle. The aim of this talk is to give a general overview of the classical theory of the obstacle problem, and then discuss recent developments on the structure of interfaces, both in the static and the parabolic settings.

Alessio Figalli, born in Rome on 2 April 1984, is an Italian mathematician specializing in the calculus of variations and partial differential equations. He was awarded the 2018 Fields Medal for his work.

Professor Figalli received his Master’s degree in mathematics in 2006 from the Scuola Normale Superiore in Pisa. In 2007, he successfully defended his PhD thesis at the École normale supérieure in Lyon and was appointed as a researcher by the French National Center for Scientific Research (CNRS). He later joined the Laurent Schwartz Mathematics Center at Ecole Polytechnique as a Hadamard Professor. In 2009, he was hired by the University of Texas at Austin as an associate professor; he was promoted to full professor there in 2011 and was awarded the R. L. Moore Chair in 2013. He has been a professor at ETH Zurich since 2016.