BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Semon Rezchikov DTSTART:20220315T150000Z DTEND:20220315T160000Z DTSTAMP:20260423T035750Z UID:Freemath/76 DESCRIPTION:Title: Holomorphic Floer Theory and the Fueter Equation\nby Semon Rezchikov as part of Free Mathematics Seminar\n\n\nAbstract\nThe Lagrangian Floer h omology of a pair of holomorphic Lagrangian submanifolds of a hyperkahler manifold is expected to simplify\, by work of Solomon-Verbitsky and others . This occurs in part because\, in this setting\, the symplectic action fu nctional\, the gradient flow of which computes Lagrangian Floer homology\, is the real part of a holomorphic function. As noted by Haydys\, thinking of this holomorphic function as a superpotential on an infinite-dimension al symplectic manifold gives rise to a quaternionic analog of Floer's equa tion for holomorphic strips: the Fueter equation. I will explain how this line of thought gives rise to a `complexification' of Floer's theorem iden tifying Fueter maps in cotangent bundles to Kahler manifolds with holomorp hic planes in the base. This complexification has a conjectural categorica l interpretation\, giving a model for Fukaya-Seidel categories of Lefshetz fibrations\, which should have algebraic implications for the study of Fu kaya categories. This is a report on upcoming joint work with Aleksander D oan.\n LOCATION:https://researchseminars.org/talk/Freemath/76/ END:VEVENT END:VCALENDAR