Abstract

Plateau problem consists in finding a surface of minimal area among the ones spanning a given curve. It is among the oldest problem in the calculus of variations and its study lead to wonderful development in mathematics with influences in different fields.

In this talk I will survey its history and present some of the different approaches that has been devised in trying to solve it and I will conclude by presenting a series of new results obtained in the last years, together with some open problems.

Short Bio

Guido De Philippis received his Ph.D. in 2012 under the direction of L. Ambrosio (Scuola Normale Superiore, Pisa) and L. Caffarelli (University of Texas at Austin). After research experiences at the Hausdorff Center for Mathematics in Bonn, at the University of Zurich, at the École Normale Supérieure de Lyon, he was appointed as Professor at SISSA and, currently, also at the Courant Institute, New York University.

Guido De Philippis has made outstanding contributions to different topics in the Calculus of Variation and Partial Differential Equations, like optimal transport and Monge-Ampére equation, the Plateau problem, Mumford-Shah optimization.

Major distinctions for his work are:

• 2018 Stampacchia Medal.
• 2018 Invited Speaker ICM, Rio de Janeiro.
• 2016 “EMS Prize” European Mathematical Society.
• 2014 “Miranda Prize” of the Accademia di Scienze Fisiche e Matematiche di Napoli.
• 2012 “Iapichino Prize” of the Accademia Nazionale dei Lincei