turkmath.org

In this talk I will explain the proof of homological mirror symmetry where the B-side is a ring or chain of stacky projective lines joined nodally, and where each irreducible component is allowed to have a non-trivial generic stabiliser, generalising the work of Lekili and Polishchuk. The key ingredient of the proof is to match categorical resolutions on the A- and B-sides by identifying them both with an intermediary category given by the derived category of modules of a gentle algebra. I will explain the strategy of constructing these resolutions on the A-- and B--sides, as well as how to deduce homological mirror symmetry from this.