Hochschild Cohomology and Deformation Theory of Hilbert Schemes of Points on Surfaces

Explore the computation of Hochschild cohomology groups for Hilbert schemes of points on surfaces in this advanced mathematics lecture. Delve into the non-commutative method used to analyze symmetric quotient stacks of varieties in arbitrary dimensions. Discover how this approach leads to various consequences in deformation theory, generalizing and reproving results by Bottacin, Fantechi, and Hitchin. Gain insights into an amended version of Boissière's conjecture on twisted Hodge numbers of Hilbert schemes. Learn about the collaborative research conducted with Pieter Belmans and Andreas Krug, as presented in their arXiv paper 2309.06244.