BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Daniele Alessandrini (Columbia University) DTSTART:20220921T190000Z DTEND:20220921T200000Z DTSTAMP:20260420T053230Z UID:NYC-NCG/106 DESCRIPTION:Title: Non commutative cluster coordinates for Higher Teichmüller Spaces\n by Daniele Alessandrini (Columbia University) as part of Noncommutative ge ometry in NYC\n\n\nAbstract\nIn higher Teichmuller theory we study subsets of the character varieties\nof surface groups that are higher rank analog s of Teichmuller spaces\,\ne.g. the Hitchin components\, the spaces of max imal representations and\nthe other spaces of positive representations.\n\ nFock-Goncharov generalized Thurston's shear coordinates and Penner's\nLam bda-lengths to the Hitchin components\, showing that they have a\nbeautifu l structure of cluster variety.\n\nWe applied a similar strategy to Maxima l Representations and we found new\ncoordinates on these spaces that give them a structure of non-commutative\ncluster varieties\, in the sense defi ned by Berenstein-Rethak. This is based on a joint\nwork with Guichard\, R ogozinnikov and Wienhard and one with Berenstein\, Rethak\,\nRogozinnikov and Wienhard.\n\nIn an project in progress we are generalizing these coord inates to the other\nsets of positive representations\, using some tools w e developed.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/106/ END:VEVENT END:VCALENDAR