SYZ mirror symmetry and its applications (22frg503)


(Boston University)

Conan Leung (Chinese University of Hong Kong)


Mirror symmetry is a deep duality between symplectic geometry and complex geometry. It has made striking predictions on enumerative geometry, and has motivated amazing developments in algebraic and symplectic geometry. The Strominger-Yau-Zaslow approach to mirror symmetry has made a very successful progress in explaining mirror symmetry in terms of Lagrangian torus fibrations.

In this workshop, we will discuss new developments and applications of SYZ mirror symmetry by combining the various analytic and Floer theoretical techniques found in recent years, including mirror construction via Fukaya isomorphisms, mirror symmetry of pairings, equivariant Lagrangian Floer theory and Lagrangian correspondence, quiver algebroid stacks, hypertoric varieties. Moreover, we will investigate emerging links between noncommutative geometry and networks widely used in data science.