Lagrangian Floer theory for trivalent graphs and HMS for curves

Abstract: The mirror of a genus g curve can be viewed as a trivalent configuration of 3g−3 rational curves meeting in 2g−2 triple points; more precisely, this singular configuration arises as the critical locus of the superpotential in a 3-dimensional Landau-Ginzburg mirror. In joint work with Alexander Efimov and Ludmil Katzarkov, we introduce a notion of Fukaya category for such a configuration of rational curves, where objects are embedded graphs with trivalent vertices at the triple points, and morphisms are linear combinations of intersection points as in usual Floer theory. We will describe the construction of the structure maps of these Fukaya categories, attempt to provide some motivation, and outline examples of calculations that can be carried out to verify homological mirror symmetry in this setting.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar