Title: Equivariant multiplicities and mirror symmetry for Hilbert schemes
Abstract: The global nilpotent cone of a smooth projective curve is an extremely singular variety; in particular, its irreducible components are not reduced. Multiplicities of so-called very stable components were computed by Hausel-Hitchin, using ideas from mirror symmetry. More curiously, they observed that these numbers can be naturally quantized. I will explain how to extend this quantization beyond the very stable components, and do a case study of Hilbert schemes of points on elliptic surfaces. Based on a joint work with F. Zivanovic.