Toric Mirror Symmetry

Hiroshi Iritani

(Kyoto University)

In the minicourse I will explain Hodge-theoretic mirror symmetry  and its global aspects in toric context.
The global picture explains phenomena of analytic continuation in  Gromov-Witten theory such as crepant resolution conjecture or LG/CY correspondence. These phenomena are closely related to equivalence of derived categories and I will explain that the Gamma class plays a crucial role there.


References:

1) Coates, Iritani, Tseng "Wall-crossings in toric Gromov-Witten theory I: crepant examples"

2) Katzarkov, Kontsevich, Pantev "Hodge theoretic aspects of mirror symmetry"

3) Iritani "An integral structure in quantum cohomology and mirror symmetry of toric
orbifolds"

4) Chiodo, Iritani, Ruan "Landau-Ginzburg/Calabi-Yau correspondence, global mirror
symmetry and Orlov equivalence"

5) Coates, Corti, Iritani, Tseng, "Mirror Theorem for Toric Stacks"

6) Galkin, Golyshev, Iritani "The Gamma classes and quantum cohomology of Fano
manifolds: Gamma conjectures"