Closed string mirrors of symplectic cluster manifolds

Abstract: Consider a symplectic Calabi Yau manifold equipped with a Maslow 0 Lagrangian torus fibration with singularities. According to modern interpretations of the SYZ conjecture, there should be an associated analytic mirror variety with a non Archimedean torus fibration over the same base. I will suggest a general construction called the closed string mirror which is based on relative symplectic cohomologies of the fibers. A priori the closed string mirror is only a set with a map to the base, but conjecturally under some general hypotheses it is in fact an analytic variety with its non Archimedean torus fibration. I will discuss joint work with Umut Varolgunes where we prove this in the case of four dimensional symplectic cluster manifolds.

differential geometrydynamical systemsgeometric topologysymplectic geometryspectral theory

Audience: researchers in the topic

Geometry and Dynamics seminar

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