Rigidity of Lagrangian tori in K3 surfaces

Abstract: A Kahler-type form is a symplectic form compatible with an integrable complex structure. Sheridan and Smith previously proved, using deep methods of homological mirror symmetry, that for any Maslov-zero Lagrangian torus L in a K3 surface M equipped with a Kahler-type form of a *particular kind*, the integral homology class of L has to be non-zero and primitive. I will discuss how to extend this result to *arbitrary* Kahler-type forms on M using dynamical properties of the action of the diffeomorphism group of M on the space of such forms. These dynamical properties are obtained using a version of Ratner's theorem. This is a joint work in progress with M.Verbitsky.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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