A note on homological mirror symmetry over Novikov ring

Abstract: Homological Mirror symmetry is a symmetry between symplectic and complex geometries. In the symplectic side, Lagrangian Floer homology is the main object of the study. In most of the results on homological mirror symmetry in the literature, Lagrangian Floer homology is considered over the coefficient ring which is either a ground ring (such as Z, Q, C) or a Novikov field, where the formal parameter is inverted. Lagrangian Floer homology over Novikov ring is known to contain much more informations than one over Novikov field. In this talk, I will explain certain ideas and preliminary results to study homological Mirror symmetry over Novikov ring. I will explain how the notion of Gromov-Hausdorff convergence of A infinity category is used for this purpose.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar