Mirror symmetry is a duality between symplectic geometry and complex geometry. The homological mirror symmetry (HMS) conjecture was formulated by Kontsevich in 1994 to fully capture this phenomenon for compact Calabi-Yau manifolds. Since then, it has been extended to cover a much wider range of manifolds. In this talk, I will give a few illustrative examples of HMS, starting with HMS for 2-real dimensional tori. Part of this talk is based on joint work with Haniya Azam, Catherine Cannizzo, and Chiu-Chu Melissa Liu.
Zoom passcode: colloquium