Symplectic geometry is a relatively new branch of geometry.
However, a string theory-inspired duality known as “mirror symmetry” reveals
more about symplectic geometry from its mirror counterparts in complex
geometry. M. Kontsevich conjectured an algebraic version of mirror symmetry
called “homological mirror symmetry” (HMS) in his 1994 ICM address. HMS
results were then proved for symplectic mirrors to Calabi-Yau and Fano
manifolds. Those mirror to general type manifolds have been studied in more
recent years, including my research. In this talk, we will introduce HMS
through the example of the 2-torus T^2. We will then outline how it relates
to HMS for a hypersurface of a 4-torus T^4, in joint work with Haniya Azam,
Heather Lee, and Chiu-Chu Melissa Liu. From there, we generalize to
hypersurfaces of higher dimensional tori, otherwise known as “theta
divisors.” This is also joint with Azam, Lee, and Liu.
Joint with Geometry and Topology Seminar.