BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dan Cristofaro-Gardiner (Maryland) DTSTART:20220407T185000Z DTEND:20220407T195000Z DTSTAMP:20260423T022834Z UID:GPRTatNU/49 DESCRIPTION:Title: The simplicity conjecture\nby Dan Cristofaro-Gardiner (Maryland) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstra ct\nIn the 60s and 70s\, there was a flurry of activity concerning the que stion of whether or not various subgroups of homeomorphism groups of manif olds are simple\, with beautiful contributions by Fathi\, Kirby\, Mather\, Thurston\, and many others. A funnily stubborn case that remained open wa s the case of area-preserving homeomorphisms of surfaces. For example\, fo r balls of dimension at least 3\, the relevant group was shown to be simpl e by work of Fathi from the 1970s\, but the answer in the two-dimensional case was not known. I will explain recent joint work proving that the gro up of compactly supported area preserving homeomorphisms of the two-disc i s in fact not a simple group\, which answers the ``Simplicity Conjecture ” in the affirmative. Our proof uses a new tool for studying area-prese rving surface homeomorphisms\, called periodic Floer homology (PFH) spectr al invariants\; these recover the classical Calabi invariant via a kind of Weyl law. I will also briefly mention a generalization of our result to compact surfaces of any genus.\n LOCATION:https://researchseminars.org/talk/GPRTatNU/49/ END:VEVENT END:VCALENDAR