BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ben Davison (University of Edinburgh) DTSTART:20240111T073000Z DTEND:20240111T090000Z DTSTAMP:20260422T155204Z UID:HKUST-AG/29 DESCRIPTION:Title: Okounkov's conjecture via BPS Lie algebras\nby Ben Davison (Universi ty of Edinburgh) as part of Algebra and Geometry Seminar @ HKUST\n\nLectur e held in 4503.\n\nAbstract\nGiven an arbitrary finite quiver Q\, Maulik a nd Okounkov defined a new Yangian-style quantum group. It is built via the ir construction of R matrices on the cohomology of Nakajima quiver varieti es\, which in turn is constructed via their construction of stable envelop es. Just as in the case of ordinary Yangians\, there is a Lie algebra g_Q inside their new algebra\, and the Yangian is a deformation of the current algebra of this Lie algebra.\n\nOutside of extended ADE type\, numerous b asic features of g_Q have remained mysterious since the outset of the subj ect\, for example\, the dimensions of the graded pieces. A conjecture of O kounkov predicts that these dimensions are given by the coefficients of Ka c's polynomials\, which count isomorphism classes of absolutely indecompos able Q-representations over finite fields. I will present a recent result with Tommaso Botta: we prove that the Maulik-Okounkov Lie algebra g_Q is i somorphic to a certain BPS Lie algebra constructed in my previous work wit h Sven Meinhardt. This implies Okounkov's conjecture\, as well as essenti ally determining g_Q\, thanks to recent joint work of myself with Hennecar t and Schlegel Mejia.\n LOCATION:https://researchseminars.org/talk/HKUST-AG/29/ END:VEVENT END:VCALENDAR