Abstract: |
I'll give an introduction to equivariant elliptic cohomology, elliptic genus, and wall-crossing. Then I'll talk about some forthcoming work. Abstractly, the main result is that if the exceptional loci of a wall-crossing satisfy a numerical condition, then elliptic genus is invariant when crossing the wall. Concretely, it is the vanishing of a residue of some ratio of theta functions. This is a surprisingly complicated calculation. I'll explain how to do it using a beautiful result called elliptic rigidity, and also Jeffrey-Kirwan integration. Finally, I'll give some applications to elliptic Donaldson-Thomas theory. |