Geometry/Physics Seminar

Title: Witten equation and quantum singularity theory
Speaker: Professor Yongbin Ruan
Speaker Info: University of Michigan
Brief Description:
Special Note:

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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