Back to Algebraic Geometry Seminar: Fall 2013
Algebraic Geometry Seminar
Date: Tuesday, Sep 10, 2013
Time: 3:30PM - 4:30PM
Location: LCB 225
Mark Shoemaker
University of Utah
Title |
A proof of the LG/CY correspondence via the Crepant Resolution Conjecture |
Abstract |
Given a homogeneous degree five polynomial W in the variables X_1, . . . , X_5, we may view W as defining a quintic hypersurface in P^4, or alternatively, as defining a singularity in [C^5/Z_5], where the group action is diagonal. In the first case, one may consider the Gromov-Witten invariants of {W=0}. In the second case, there is a way to construct analogous invariants, called FJRW invariants, of the singularity. The LG/CY correspondence conjectures that these two sets of invariants should be related. In this talk I will explain this correspondence, and its relation to a much older conjecture, the Crepant Resolution Conjecture (CRC). I will sketch a proof that the CRC is equivalent to the LG/CY correspondence in certain cases. This work is joint with Prof. Y.-P. Lee. |
Algebraic Geometry