## EVENT DETAILS AND ABSTRACT

**Geometry/Physics Seminar**
**Title:** Witten equation and quantum singularity theory

**Speaker:** Professor Yongbin Ruan

**Speaker Info:** University of Michigan

**Brief Description:**

**Special Note**:

**Abstract:**

A long standing problem in Gromov-Witten theory is to compute
higher genus Gromov-Witten invariants of compact Calabi-Yau manifold such as quintic 3-folds. The defining equation of these Calabi-Yau manifold has a natural interpretation in Landau-Ginzburg/singularity theory. More than 15 years ago, Witten proposed a PDE as a replacement of familiar Cauchy-Riemann equation in the Laudau-Ginzburg/singularity setting. Furthermore, he proposed two remarkable conjectures for his conjectural theory for ADE-singularity. In the talk, we will present a moduli theory of the solution spaces of Witten equation. As a consequence, we solve Witten's conjectures for quantum theory of ADE-singularities. In the end of talk, we will sketch a plan to compute higher genus GW-invariants of Calabi-Yau manifolds.

**Date:** Thursday, February 28, 2008

**Time:** 4:00pm

**Where:** Lunt 107

**Contact Person:** Prof. Gabriel Kerr

**Contact email:** gdkerr@math.northwestern.edu

**Contact Phone:** 773-936-6405

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