BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Milen Yakimov (Northeastern University) DTSTART:20210408T185000Z DTEND:20210408T195000Z DTSTAMP:20260423T010006Z UID:GPRTatNU/25 DESCRIPTION:Title: Root of unity quantum cluster algebras\nby Milen Yakimov (Northeaste rn University) as part of Geometry\, Physics\, and Representation Theory S eminar\n\n\nAbstract\nWe will describe a theory of root of unity quantum c luster algebras\, which cover as special cases the big quantum groups of D e Concini\, Kac and Process. All such algebras will be shown to be polynom ial identity (PI) algebras. Inside each of them\, we will construct a cano nical central subalgebra which is proved to be isomorphic to the underlyin g cluster algebra. It is a far-reaching generalization of the De Concini-K ac-Procesi central subalgebras in big quantum groups and presents a genera l framework for studying the representation theory of quantum algebras at roots of unity by means of cluster algebras as the relevant data becomes ( PI algebra\, canonical central subalgebra)=(root of unity quantum cluster algebra\, underlying cluster algebra). We will also present an explicit fo rmula for the corresponding discriminants in this general setting that can be applied in many concrete situations of interest\, such as the discrimi nants of all root of unity quantum unipotent cells for symmetrizable Kac-M oody algebras. This is a joint work with Bach Nguyen (Xavier Univ) and Kur t Trampel (Notre Dame Univ).\n LOCATION:https://researchseminars.org/talk/GPRTatNU/25/ END:VEVENT END:VCALENDAR