Abstract: Symplectic geometry plays a crucial role in string theory through the lens of mirror symmetry, a duality that connects it to complex geometry. This connection is formalized in M. Kontsevich’s celebrated 1994 ICM conjecture on homological mirror symmetry (HMS), providing a powerful algebraic framework to study these dualities. While HMS has been established for mirrors of Calabi-Yau and Fano manifolds, recent efforts have extended its scope to mirrors of general type manifolds, which are central to my research. In this talk, we’ll explore HMS through the classic example of the 2-dimensional torus T^2. Building on this, we’ll discuss its generalization to higher-dimensional tori, and then to new results for hypersurfaces of tori, known as “theta divisors”. This work is in collaboration with Haniya Azam, Heather Lee, and Chiu-Chu Melissa Liu.