BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tony Yue Yu (Caltech) DTSTART:20220318T190000Z DTEND:20220318T200000Z DTSTAMP:20260407T214749Z UID:agstanford/81 DESCRIPTION:Title: Non-archimedean Quantum K-theory and Gromov-Witten invariants\nby Tony Yue Yu (Caltech) as part of Stanford algebraic geometry seminar\n\n\n Abstract\nMotivated by mirror symmetry and the enumeration of curves with boundaries\, it is desirable to develop a theory of Gromov-Witten invarian ts in the setting of non-archimedean geometry. I will explain our recent w orks in this direction. Our approach differs from the classical one in alg ebraic geometry via perfect obstruction theory. Instead\, we build on our previous works on the foundation of derived non-archimedean geometry\, the representability theorem and Gromov compactness. We obtain numerical inva riants by passing to K-theory or motivic cohomology. We prove a list of na tural geometric relations between the stacks of stable maps\, directly at the derived level\, with respect to elementary operations on graphs\, name ly\, products\, cutting edges\, forgetting tails and contracting edges. Th ey imply the corresponding properties of numerical invariants. The derived approach produces highly intuitive statements and functorial proofs. Furt hermore\, its flexibility allows us to impose not only simple incidence co nditions for marked points\, but also incidence conditions with multiplici ties. Joint work with M Porta.\n\nThe synchronous discussion for Tony Yue Yu’s talk is taking place not in zoom-chat\, but at https://tinyurl.com /2022-03-18-ty (and will be deleted after ~3-7 days).\n LOCATION:https://researchseminars.org/talk/agstanford/81/ END:VEVENT END:VCALENDAR