Title: Gromov Witten theory of quotient of quintic 3-fold via global mirror symmetry

Speaker: Professor Yongbin Ruan (University of Michigan)

Venue: Room 09 at Quan-Zhai (全斋), Beijing International Center for Mathematical Research, Peking University

Time: July 24, 2012, Tuesday, 2:00-4:00pm

Abstract: Suppose that $X$ is a quintic 3-fold defined by a quintic polynomial $W$. There are two outstanding conjectures:

(i) Landau-Ginzburg/Calabi-Yau correspondence governing the equivalence of Gromov-Witten theory of $X$ and the so called FJRW-theory of $(W, Z_5)$. (ii) The modularity of Gromov-Witten theory of $X$. Both problems are expected to be true for the finite quotient of $X$. In the talk, we describe a on-going program to solve the above conjectures for $X/Z^5_5$. We do so by the method of "global mirror symmetry" which consists of a rigorous construction of higher genus B-model theory of its Landau-Ginzburg mirror and two mirror theorems of all genera.

This is a joint work with Iritani, Milanov and Shen.