Title: On the parity conjecture for Hilbert schemes of points on threefolds
Abstract: The Hilbert scheme of d points on a smooth surface is a vibrant, well-studied space; it is smooth of dimension 2d and has numerous connections to other areas of mathematics. On the other hand, the Hilbert scheme of d points on a smooth threefold is singular, reducible, and conjectured to be non-reduced for large d. However, the Hilbert scheme of a threefold does exhibit some "good" behavior analogous to the Hilbert scheme of a surface. In this talk, I will describe some results and conjectures related to this. In particular, I will focus on the tangent space to the Hilbert scheme of a threefold. This is joint work with Alessio Sammartano.