Noah Arbesfeld

Donaldson-Thomas theory and the Hilbert scheme of points on a surface

I will explain how to use Donaldson-Thomas theory, a certain enumeration of curves in threefolds, to deduce combinatorial identities involving Young diagrams. These identities can be interpreted geometrically in terms of vector bundles on the Hilbert scheme of points on a plane. I'll also explain how these identities can be used to study the Euler characteristics of tautological bundles over Hilbert schemes of points on general surfaces.