The classical obstacle problem is a free boundary problem that appears naturally in the study of the Stefan problem, the Frostman equilibrium measure, the Helle-Shaw flow, the Dam problem, or the pricing of American options. Caffarelli obtained in the 1970’s a fundamental breakthrough: he gave a robust sufficient condition that implies the local smoothness of the free boundary. Complementarily, in the last years we worked towards obtaining a more complete understanding of singularities. This has lead us to proving, in dimensions three and four, a conjecture of Schaeffer which asserts that for generic boundary data there are no singularities (although one can construct examples of boundary data and obstacles for which the singular set is as large as the regular set!).

Joaquim Serra (Barcelona 1986), ganador del Premio José Luis Rubio de Francia 2018, es Doctor en Matemáticas por la U. Politècnica de Catalunya. Ha recibido recientemente el Premio Antonio Valle de la SeMA y en 2016 recibió el premio Josep Teixidó de la Societat Catalana de Matematiques. Una vez finalizada su tesis doctoral en 2014 bajo la dirección de Xavier Cabré, realizó estancias posdoctorales en WIAS-Berlin y ETH-Zurich. Actualmente es SNF Ambizione Fellow en ETH-Zurich. Su campo de investigación son las ecuaciones en derivadas parciales elípticas.