BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Catherine Cannizzo (Simons Center) DTSTART:20201029T150000Z DTEND:20201029T160000Z DTSTAMP:20260423T024807Z UID:notts_ag/32 DESCRIPTION:Title: Towards global homological mirror symmetry for genus 2 curves\nby Ca therine Cannizzo (Simons Center) as part of Online Nottingham algebraic ge ometry seminar\n\n\nAbstract\nThe first part of the talk will discuss work in arXiv:1908.04227 [math.SG] on constructing a Donaldson-Fukaya-Seidel t ype category for the generalized SYZ mirror of a genus $2$ curve. We will explain the categorical mirror correspondence on the cohomological level. The key idea uses that a $4$-torus is SYZ mirror to a $4$-torus. So if we view the complex genus $2$ curve as a hypersurface of a $4$-torus $V$\, a mirror can be constructed as a symplectic fibration with fiber given by th e dual $4$-torus $V^\\vee$. Hence on categories\, line bundles on $V$ are restricted to the genus $2$ curve while fiber Lagrangians of $V^\\vee$ are parallel transported over $U$-shapes in the base of the mirror. Next we d escribe ongoing work with H. Azam\, H. Lee\, and C-C. M. Liu on extending the result to a global statement\, namely allowing the complex and symplec tic structures to vary in their real six-dimensional families. The mirror statement for this more general result relies on work of A. Kanazawa and S -C. Lau.\n LOCATION:https://researchseminars.org/talk/notts_ag/32/ END:VEVENT END:VCALENDAR