Mirror symmetry relates complex and symplectic manifolds which come in mirror pairs, and homological mirror symmetry is an equivalence of categories on each - the Fukaya category of the symplectic manifold with the bounded derived category of coherent sheaves of the complex manifold. In forthcoming joint work [ACLL] with Haniya Azam, Heather Lee, and Chiu-Chu Melissa Liu, we prove an analogue of arXiv:1908.04227 globally, that is, homological mirror symmetry for all genus 2 curves. We consider genus 2 curves as hypersurfaces of abelian surfaces, on the complex side. In particular, the set-up for the abelian variety relates to works of Chan-Melo-Viviani arXiv:1207.2443 and Chan arXiv:1012.4539 on tropical abelian varieties.

In a follow-up paper [ACLL2], we allow the abelian variety to have arbitrary dimension, and hypersurfaces are now theta divisors. [ACLL2] will be the content of this talk.