BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Weihong Xu (Rutgers University) DTSTART:20201214T210000Z DTEND:20201214T220000Z DTSTAMP:20260423T035920Z UID:AGSAGS/13 DESCRIPTION:Title: Quantum K-theory of Incidence Varieties\nby Weihong Xu (Rutgers Univer sity) as part of American Graduate Student Algebraic Geometry Seminar\n\n\ nAbstract\nCertain rational enumerative geometry problems can be formulate d as intersection theory in the moduli space of stable maps M̅_{0\,m}(X\, d). This moduli space is well-behaved when $X$ is a projective homogeneous variety $G/P$. Non-trivial relations among solutions to these enumerative geometry problems (Gromov-Witten invariants) enable the definition of an associative product and in turn a formal deformation of the cohomology rin g called the quantum cohomology ring of $X$. Similarly\, a deformation of the Grothendieck ring $K(X)$ called the quantum K-theory ring of $X$ is de fined using sheaf-theoretic versions of Gromov-Witten invariants.\n\nAfter introducing relevant background\, we will focus on the quantum K-theory o f the projective homogeneous variety $Fl(1\,n-1\;n)$ (also called an incid ence variety)\, where I have found explicit multiplication formulae and co mputed some sheaf-theoretic Gromov-Witten invariants. These computations l ead to suspected rationality properties of some natural subvarieties of M ̅_{0\,m}(X\,d).\n LOCATION:https://researchseminars.org/talk/AGSAGS/13/ END:VEVENT END:VCALENDAR