BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gregg Musiker (Minnesota) DTSTART:20210426T120000Z DTEND:20210426T130000Z DTSTAMP:20260710T044509Z UID:paris-algebra-seminar/45 DESCRIPTION:Title: Combinatorial Expansion Formulas for Decorated Super-Teichm üller Spaces\nby Gregg Musiker (Minnesota) as part of Paris algebra s eminar\n\n\nAbstract\nMotivated by the definition of super Teichmuller spa ces\, and Penner-Zeitlin's recent extension of this definition to decorate d super Teichmuller space\, as examples of super Riemann surfaces\, we use the super Ptolemy relations to obtain formulas for super lambda-lengths a ssociated to arcs in a bordered surface. In the special case of a disk\, w e are able to give combinatorial expansion formulas for the super lambda-l engths associated to diagonals of a polygon in the spirit of Ralf Schiffle r's T-path formulas for type A cluster algebras. We further connect our fo rmulas to the super-friezes of Morier-Genoud\, Ovsienko\, and Tabachnikov\ , and obtain partial progress towards defining super cluster algebras of t ype A. In particular\, following Penner-Zeitlin\, we are able to get formu las (up to signs) for the mu-invariants associated to triangles in a trian gulated polygon\, and explain how these provide a step towards understandi ng odd variables of a super cluster algebra. This is joint work with Nich olas Ovenhouse and Sylvester Zhang.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/45/ END:VEVENT END:VCALENDAR