Algebraic Combinatorics - Matthew Satriano

Thursday, June 15, 2023 1:00 pm - 1:00 pm EDT (GMT -04:00)

Title: Monomial ideals, Galois closures, and Hilbert schemes of points

Speaker: Matthew Satriano
Affiliation: University of Waterloo
Location: MC 5501 and Zoom - please contact Oliver Pechenik for the Zoom link

Abstract: Manjul Bhargava and the speaker introduced a functorial Galois closure operation for finite-rank ring extensions, generalizing constructions of Grothendieck and Katz-Mazur. In this talk, we use Galois closures to construct new components of Hilbert schemes of points, which are fundamental objects in algebraic geometry whose component structure is largely mysterious. We answer a 35 year old open problem posed by Iarrobino by constructing an infinite family of low dimensional components. This talk is based on joint work with Andrew Staal. No prior knowledge of Hilbert schemes will be assumed.