BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yifeng Huang (The University of Southern California) DTSTART:20250618T020000Z DTEND:20250618T030000Z DTSTAMP:20260422T155159Z UID:HKUST-AG/77 DESCRIPTION:Title: High-rank motivic degree-zero Donaldson--Thomas theory on singular curve s\, and q-series\nby Yifeng Huang (The University of Southern Californ ia) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in 450 2 (Lifts 25/26).\n\nAbstract\nMy main point is that high-rank motivic degr ee-zero DT invariants on singular curves appear to give infinite products of Rogers--Ramanujan type. This is based on explicit computation of certai n Quot schemes\, which is where the new ideas and results lie\, but this s eems to be a new phenomenon that I cannot explain from physics or other co nceptual connection. For context\, the rank-1 case has been observed to re late to knot theory and Catalan combinatorics in the last decade (keyword: Oblomkov--Rasmussen--Shende conjecture). \n\nA down-to-earth statement th at captures all the essence is the following (stated for the singular curv e $y^2=x^3$): For a random $n\\times n$ matrix $A$ over a finite field $\\ mathbb{F}_q$\, what is the expected number of matrices $B$ such that $AB=B A$ and $A^3=B^2$? It turns out that as $n\\to \\infty$\, the limiting answ er is $\\prod (1-q^{-i})$ over all positive $i$ congruent to $1\,4$ mod $5 $\, the famous Rogers--Ramanujan infinite product. \n\nThe reported result s contain joint work with Ruofan Jiang (on the $y^2=x^n$ case) and joint w ork in progress with RJ and Alexei Oblomkov (on the $y^m=x^n$ case with $m \,n$ coprime).\n LOCATION:https://researchseminars.org/talk/HKUST-AG/77/ END:VEVENT END:VCALENDAR