BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bill Goldman DTSTART:20210810T134000Z DTEND:20210810T141000Z DTSTAMP:20260417T010124Z UID:MSR80/10 DESCRIPTION:Title: D ynamics and the classification of geometries on surfaces\nby Bill Gold man as part of International Conference on Discrete groups\, Geometry and Arithmetic\n\n\nAbstract\nMany interesting dynamical systems arise from th e classification of locally homogeneous\ngeometric structures and flat con nections on manifolds. Their classification mimics that of\nRiemann surfac es by the Riemann moduli space\, which identifies as the quotient of Teich mueller\nspace of marked Riemann surfaces by the action of the mapping cla ss group. However\, unlike\nRiemann surfaces\, these actions are generally chaotic. A striking elementary example is Baues's\ntheorem that the defor mation space of complete affine structures on the 2-torus is the plane wit h\nthe usual linear action of GL(2\,Z) (the mapping class group of the tor us). We discuss specific\nexamples of these dynamics for some simple surfa ces\, where the relative character varieties\nappear as cubic surfaces in affine 3-space. Complicated dynamics seems to accompany\ncomplicated topol ogies\, which we interpret as (possibly singular) hyperbolic structures on \nsurfaces.\n LOCATION:https://researchseminars.org/talk/MSR80/10/ END:VEVENT END:VCALENDAR