BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Catherine Cannizzo DTSTART:20200728T140000Z DTEND:20200728T150000Z DTSTAMP:20260423T021234Z UID:Freemath/13 DESCRIPTION:Title: Towards global homological mirror symmetry for genus 2 curves\nby Ca therine Cannizzo as part of Free Mathematics Seminar\n\n\nAbstract\nThe fi rst part of the talk will discuss work in https://arxiv.org/abs/1908.04227 on constructing a Donaldson-Fukaya-Seidel type category for the generaliz ed SYZ mirror of a genus 2 curve. We will explain the categorical mirror c orrespondence 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 the dual 4-torus V^. Hence on categories\, l ine bundles on V are restricted to the genus 2 curve while fiber Lagrangia ns of V^ are parallel transported over U-shapes in the base of the mirror. Next we describe ongoing work with H. Azam\, H. Lee\, and C-C. M. Liu on extending the result to a global statement\, namely allowing the complex a nd symplectic structures to vary in their real six-dimensional families. T he mirror statement for this more general result relies on work of A. Kana zawa and S-C. Lau.\n LOCATION:https://researchseminars.org/talk/Freemath/13/ END:VEVENT END:VCALENDAR