BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alessio Figalli (ETH Zurich/FIM) DTSTART:20200702T140000Z DTEND:20200702T153000Z DTSTAMP:20260404T111328Z UID:Sissa-Ictp/1 DESCRIPTION:Title: Generic Regularity in Obstacle Problems\nby Alessio Figalli (ETH Zurich/FIM) as part of Joint SISSA-ICTP Webinar Colloquium\n\n\nAbstr act\nThe classical obstacle problem consists of finding the equilibrium po sition of an elastic membrane whose boundary is held fixed and which is co nstrained to lie above a given obstacle. By classical results of Caffarell i\, the free boundary is $C^\\infty$ outside a set of singular points. Exp licit examples show that the singular set could be in general $(n-1)$-dime nsional 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 $\\m athcal{H}^{n-4}$ 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\nThe ta lk will be followed by a question/answer session.\n\nPre-registration is r equired at the following url: https://sissa-it.zoom.us/webinar/register/WN _ca93G01TQ6eO0zn99mkp-g\nAfter registering\, you will receive a confirmati on email containing information about joining the webinar.\n LOCATION:https://stable.researchseminars.org/talk/Sissa-Ictp/1/ END:VEVENT END:VCALENDAR