BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Junliang Shen (MIT) DTSTART:20210504T150000Z DTEND:20210504T160000Z DTSTAMP:20260423T021651Z UID:DerSem/23 DESCRIPTION:Title: Geometry of the Gopakumar-Vafa theory.\nby Junliang Shen (MIT) as part of Derived seminar\n\n\nAbstract\nMotivated by classical enumerative geom etry and mathematical physics\, counting curves in Calabi-Yau 3-folds has been studied intensively for decades\, including Gromov-Witten theory and Donaldson-Thomas theory. In recent years\, mathematical theory (by Hosono- Saito-Takahashi\, Kiem-Li\, Maulik-Toda etc) has been developed to realize the idea of Gopakumar and Vafa to recover the curve-counting invariants u sing the geometry of 1-dimensional sheaves. These developments shed new li ght on both enumerative geometry and the classical geometry of the relevan t moduli spaces. I will discuss 3 particular cases (1) Higgs bundles (2) K 3 surfaces\, and (3) CP^2\, where the Gopakumar-Vafa theory interacts wi th some other structures and conjectures in a surprising way.\n LOCATION:https://researchseminars.org/talk/DerSem/23/ END:VEVENT END:VCALENDAR