BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Daniel Litt (University of Toronto) DTSTART:20230915T150000Z DTEND:20230915T161500Z DTSTAMP:20260423T022734Z UID:CIRGET/100 DESCRIPTION:Title: Hodge theory\, braid groups\, and some questions about 2x2 matrices\n by Daniel Litt (University of Toronto) as part of CRM - Séminaire du CIRG ET / Géométrie et Topologie\n\nLecture held in PK-5115.\n\nAbstract\nLet $X_n$ be the set of conjugacy classes of n-tuples of 2x2 matrices whose p roduct is the identity matrix--equivalently\, the character variety of a n -punctured sphere. There is a natural braid group action on $X_n$\, whose study goes back to work of Markoff in the late 19th century. The most basi c question one can ask about this action\, which dates to work of Painlev é\, Fuchs\, Schlesinger\, and Garnier in the beginning of the 20th centur y\, is: what are the finite orbits? I'll explain the history of this quest ion\, as well as some recent work\, joint with Lam and Landesman\, in whic h we give a complete classification of such finite orbits\, by algebro-geo metric methods\, when at least one of the matrices in question has infinit e order.\n LOCATION:https://researchseminars.org/talk/CIRGET/100/ END:VEVENT END:VCALENDAR