Wall-crossing in genus zero Landau-Ginzburg theory

Seminar: 
Algebraic and Tropical Geometry
Event time: 
Thursday, March 27, 2014 - 12:30pm to 1:30pm
Location: 
431 DL
Speaker: 
Dusty Ross
Speaker affiliation: 
University of Michigan
Event description: 

To any isolated singularity defined by a quasi-homogeneous polynomial W, we can associate certain Fan-Jarvis-Ruan-Witten invariants which are conjecturally equivalent to the Gromov-Witten invariants of the hypersurface defined by W. In nice cases, FJRW invariants are defined in terms of intersection numbers on moduli spaces of stable d-spin curves, ie. stable curves along with d-th roots of the log canonical bundle. In this talk, I will introduce a `weighted’ generalization of FJRW invariants obtained by working over weighted stable d-spin curves (weighted in the sense of Hassett). These weighted moduli spaces have a natural wall and chamber structure and I’ll discuss a wall-crossing formula which relates the genus zero invariants as we vary the weights. As a very special case of the wall-crossing formula, I’ll explain how we recover the Landau-Ginzburg mirror theorem along with a new enumerative interpretation of the mirror map. This is joint work with Yongbin Ruan.