BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yifeng Huang (University of British Columbia) DTSTART:20230302T233000Z DTEND:20230303T003000Z DTSTAMP:20260422T054358Z UID:SFUQNTAG/88 DESCRIPTION:Title: Matrix points on varieties and punctual Hilbert (and Quot) schemes\n by Yifeng Huang (University of British Columbia) as part of SFU NT-AG semi nar\n\nLecture held in K-95095.\n\nAbstract\nModuli spaces often have inte resting enumerative properties. The goal of this talk is to introduce some enumerative results on solutions of matrix equations and zero-dimensional sheaves over singular curves. To motivate them\, I first discuss several moduli spaces in general\, which I put onto the "unframed" side and the "f ramed" side. The unframed side includes the commuting variety AB=BA of n x n matrices\, the variety of commuting matrices satisfying polynomial equa tions (the titular "matrix points on varieties")\, and the moduli stack of zero-dimensional coherent sheaves on a variety. The framed side includes the Hilbert scheme of points on a variety\, or more generally\, the Quot s cheme of zero-dimensional quotients of a vector bundle on a variety. The e numerative properties to be considered are point counts over finite fields and the motive in the Grothendieck ring of varieties\, which essentially keep track of the combinatorial data of a stratification of the space in q uestion. I will explain some general connections within and between the tw o sides\, and known results for smooth curves and smooth surfaces. Finally \, I will discuss recent results on singular curves. This talk is based on joint work with Ruofan Jiang.\n\nIn the pre-seminar\, I plan to talk abou t a super fun combinatorial construction\, which we call “spiral shiftin g operators”\, used in the proof of one of our results.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/88/ END:VEVENT END:VCALENDAR