Quantum Cohomology of the Hilbert scheme of points on ADE resolutions -- Davesh Maulik

Given a smooth algebraic surface $S$, the Hilbert scheme of points on $S$ is a smooth variety parametrizing collections of points on the surface. The classical cohomology rings of these varieties have a rich and well-studied structure developed by Nakajima, Grojnowski, and many others. In this talk, we discuss how to study the quantum cohomology ring for the family of surfaces obtained by resolving the ADE surface singularities. We then explain the equivalence between this theory and the all-genus Gromov-Witten theory of the threefold $S\times\mathbf{P}^1$. If time permits, we will talk about generalizing this equivalence to other surfaces and applications to understanding Gromov-Witten theory for all toric threefolds. (Joint with A. Oblomkov)