Intersection cohomology for the moduli of sheaves and Gopakumar-Vafa theory

Seminar: 
Geometry, Symmetry and Physics
Event time: 
Monday, March 22, 2021 - 4:30pm
Location: 
https://yale.zoom.us/j/92811265790 (Password is the same as last semester)
Speaker: 
Junliang Shen
Speaker affiliation: 
MIT
Event description: 

We explore some surprising symmetries for intersection cohomology of certain moduli of 1-dimensional sheaves and moduli of Higgs bundles, motivated by Gopakumar-Vafa theory concerning enumerative geometry for Calabi-Yau 3-folds. More precisely, we show that, for these moduli spaces, the intersection cohomology is independent of the choice of the Euler characteristic. This confirms a conjecture of Bousseau for P^2, and proves a conjecture of Toda in the case of local toric Calabi-Yau 3-folds. In the proof, a generalized version of NgĂ´'s support theorem refining the decomposition theorem plays a crucial role. Based on joint work with Davesh Maulik.