Time: Wednesday July 2, 13:30-15:30.

Venue: Room 29 at Quan Zhai, BICMR

Speaker: Professor Yongbin Ruan (University of Michigin and Peking University)

Abstract: The famous mirror symmetry conjecture asserts that the $J$-function of genus zero Gromov-Witten invariant of a Calabi-Yau 3-fold is the same as the period integral of its mirror family up to a so called "mirror map". There is a version for toric variety which identifies J-function of its Gromov-Witten invariants to the oscillatory integral of its mirror Landau-Ginzburg model. The proof of these conjectures requires a technique called Picard-Fuch equation/GKZ-system which governs the period/oscillatory integral. From a different point of view, both A and B-model corresponds to the same quantum D-module defined by these PF/GKZ-system.

In this talk, I will discuss Borisov-Horja's construction of better behaved GKZ-system and its application.