The closed string mirror construction

Abstract: Consider a 2n-dimensional symplectic Calabi Yau manifold equipped with a Maslov 0 Lagrangian torus fibration with singularities over a base B. According to modern interpretations of the SYZ conjecture, there should be an associated analytic mirror variety with a non Archimedean torus fibration over B. 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. I will discuss work in progress on some general hypotheses for when it is in fact an n-dimensional rigid analytic variety with a non Archimedean torus fibration. I will touch on the relation to enumerative and homological mirror symmetry.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar