BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alfredo Najera (UNAM-Oaxaca) DTSTART:20211022T140000Z DTEND:20211022T150000Z DTSTAMP:20260423T021052Z UID:LAGARTOS/31 DESCRIPTION:Title: Cluster algebras\, deformation theory and beyond\nby Alfredo Najera (UNAM-Oaxaca) as part of (LAGARTOS) Latin American Real and Tropical Geome try Seminar\n\n\nAbstract\nThe purpose of this talk is to explain a fruitf ul interaction of ideas/constructions coming from the theory of cluster algebras\, representation theory of quivers and deformation theory.\n\nTh e representation theory of quivers is a well developed branch of mathemat ics that has been very active for nearly 50 years. The theory of cluster algebras is much younger\, it was initiated by Fomin and Zelevinsky in 20 01. Various important developments in these theories have emerged in the last 15 years thanks to the deep relation that exists in between them. A fter a gentle introduction to this circle of ideas I will recall the cons truction of a simplicial complex K(A) -- the tau-tilting complex-- associa ted to a finite dimensional path algebra A. Then I will report on one asp ect of work-in-progress with Nathan Ilten and Hipólito Treffinger. We sh ow that if K(A) is a cluster complex of finite type then the associated cluster algebra with universal coefficients is equal to a canonically ide ntified subfamily of the semiuniversal family for the Stanley-Reisner rin g of K(A). Time permitting\, and depending on the audience's preference\, I will elaborate either on some aspects of the "non-cluster" case (name ly\, when K(A) is not a cluster complex) or on the interpretation of thes e results from the point of view of tropical geometry.\n LOCATION:https://researchseminars.org/talk/LAGARTOS/31/ END:VEVENT END:VCALENDAR