BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nicolle González (University of California at Los Angeles) DTSTART:20201008T185000Z DTEND:20201008T195000Z DTSTAMP:20260423T005758Z UID:GPRTatNU/8 DESCRIPTION:Title: A Skein theoretic Carlsson-Mellit algebra\nby Nicolle González (Univ ersity of California at Los Angeles) as part of Geometry\, Physics\, and R epresentation Theory Seminar\n\n\nAbstract\nThe Carlsson-Mellit algebra ar ose for the first time in the proof of the shuffle conjecture\, which give s an explicit combinatorial formula for the Frobenius character of the spa ce of diagonal harmonics in terms of parking functions. Its polynomial rep resentation\, given by certain complicated plethystic operators over exten sions of the ring of symmetric functions\, plays a particularly important role as it encodes much of the underlying combinatorial theory. By various results of Gorsky\, Mellit and Carlsson it was shown that this algebra ca n be used to construct generators of the Elliptic Hall algebra in addition to having deep connections to the homology of torus knots. Thus\, a natur al starting point in the search to categorify these structures is the cate gorification of the Carlsson-Mellit algebra and its polynomial representat ion. \n\nIn this talk I will explain joint work with Matt Hogancamp where we constructed a purely skein theoretic formulation of this algebra and re alized its generators as certain braid diagrams on a thickened annulus. Co nsequently\, we used this framework to categorify the polynomial represent ation of the Carlsson-Mellit algebra as a family of functors over the deri ved trace of the Soergel category.\n LOCATION:https://researchseminars.org/talk/GPRTatNU/8/ END:VEVENT END:VCALENDAR