Speaker: Heather Lee

Title: Global homological mirror symmetry for genus two curves

Abstract: As a complex manifold, a genus-2 curve is a hypersurface in its Jacobian variety that is an abelian surface. Cannizzo's thesis proved a homological mirror symmetry (HMS) result for genus two curves, with their mirrors being Landau-Ginzburg models of the form (Y, W), where Y is a locally toric Calabi-Yau 3-fold and W: Y--> \mathbb C is a symplectic fibration with a singular fiber above 0. Cannizzo's thesis is for a 1-parameter family of complex structures on the genus two curve, and we extend her construction to prove a global HMS result that covers the entire 3-dimensional moduli space of complex structures on the genus-2 curve. This is a joint work with Haniya Azam, Catherine Cannizzo, and Chiu-Chu Melissa Liu.