BEGIN:VCALENDAR VERSION:2.0 CALSCALE:GREGORIAN BEGIN:VEVENT SUMMARY:Alessio Figalli (ETH Zurich/FIM) DTSTART;VALUE=DATE-TIME:20200702T140000Z DTEND;VALUE=DATE-TIME:20200702T153000Z DTSTAMP;VALUE=DATE-TIME:20200812T032507Z UID:Sissa-Ictp/1 DESCRIPTION:Title: Generic Regularity in Obstacle Problems\nby Alessio Fig alli (ETH Zurich/FIM) as part of Joint SISSA-ICTP Webinar Colloquium\n\n\n Abstract\nThe classical obstacle problem consists of finding the equilibri um position of an elastic membrane whose boundary is held fixed and which is constrained to lie above a given obstacle. By classical results of Caff arelli\, the free boundary is $C^\\infty$ outside a set of singular points . Explicit examples show that the singular set could be in general $(n-1)$ -dimensional that is\, as large as the regular set. In a recent paper with Ros-Oton and Serra we show that\, generically\, the singular set has zero $\\mathcal{H}^{n-4}$ measure (in particular\, it has codimension 3 inside the free boundary)\, solving a conjecture of Schaeffer in dimension $n \\ leq 4$. The aim of this talk is to give an overview of these results.\n\nT he talk will be followed by a question/answer session.\n\nPre-registration is required at the following url: er/WN_ca93G01TQ6eO0zn99mkp-g\nAfter registering\, you will receive a confi rmation email containing information about joining the webinar.\n END:VEVENT END:VCALENDAR