BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yuuji Tanaka (Kyoto University) DTSTART:20210313T000000Z DTEND:20210313T010000Z DTSTAMP:20260407T214440Z UID:agstanford/42 DESCRIPTION:Title: On the virtual Euler characteristics of the moduli spaces of semistab le sheaves on a complex projective surface\nby Yuuji Tanaka (Kyoto Uni versity) as part of Stanford algebraic geometry seminar\n\n\nAbstract\n(wa rning: notice unusual time)\n\nI'll deliver an overview of studies on the virtual Euler \ncharacteristics of the moduli spaces of semistable sheave s on a complex \nprojective surface. The virtual Euler characteristic is a refinement of \nthe topological Euler characteristic for a proper scheme with a perfect \nobstruction theory，which was introduced by Fantechi and Goettsche\, and \nby Ciocan-Fontanine and Kapranov. Motivated by the work of Vafa and \nWitten in the early 90's on the S-duality conjecture in N=4 super \nYang-Mills theory in physics\, Goettsche and Kool conjectured tha t the \ngenerating function of the virtual Euler characteristics\, or othe r \nvariants\, of the moduli space of semistable sheaves on a complex \npr ojective surfaces could be written in terms of modular forms (and the \nSe iberg-Witten invariants)\, and they verified it in examples. I'll \ndescri be the recent progress around this topic\, starting by mentioning \nmore b ackground materials such as the studies on the topological Euler \ncharact eristics of the moduli spaces.\n LOCATION:https://researchseminars.org/talk/agstanford/42/ END:VEVENT END:VCALENDAR