Magdalena Zielenkiewicz

Title: The refined Hilbert scheme of points on C^2

Abstract: 
I will recall the basic properties of the Hilbert Scheme of points on C^2, and introduce 
its modified version - the refined Hilbert Scheme of points on the plane. This object was 
introduced by Nakajima and Yoshioka in https://arxiv.org/abs/0806.0463 to study perverse
coherent sheaves on the blow up of a projective surface. While being a simple modification 
of the Hilbert Scheme of points, the refined Hilbert Scheme is slightly more complicated and 
not as well explored. I will present some open questions regarding it's cohomology and partial
answers to them.