Abstract: We will define a Fukaya category for the symplectic fibration appearing in the speaker’s research described at the end. We will compute structure maps for this Fukaya category, on the cohomological level. This will set us up to discuss work from https://arxiv.org/abs/1908.04227 on a homological mirror symmetry result for a complex genus 2 curve. We will describe the geometric construction of the mirror. Then we will see the algebraic result on homogenous coordinate rings, i.e. the HMS result on the level of cohomology. The method involves first considering mirror symmetry for the 4-torus, then extending to a correspondence between a hypersurface genus 2 curve and a mirror Landau-Ginzburg model with fiber the mirror 4-torus. This was work from my thesis under my PhD advisor Professor Denis Auroux.