Mirrors to surfaces and twisted derived categories

Abstract: Punctured surfaces are the simplest class of symplectic manifolds and there are many constructions of homological mirrors for them, i.e. constructions in algebraic geometry of a category equivalent to the Fukaya category of the surface. To make the Fukaya category Z-graded, not just Z/2-graded, you need to choose a line-field on the surface. I'll explain what this choice corresponds to in (some of) the mirror constructions, it leads to a kind of twisted derived category which doesn't seem to have been widely studied.

algebraic geometry

Audience: researchers in the topic

Derived seminar

Series comments: https://ed-ac-uk.zoom.us/j/89993982042

Password: a simply-connected two-dimensional variety with trivial canonical bundle (omit the space)