Florian Block

Introduction to Hilbert Schemes of Points

This talk is an introduction to the combinatorial aspects of Hilbert schemes of points. We will mostly focus on the already very rich planar case. Our goal (to be achieved in this or next week's talk) is to connected Hilbert schemes of points in the plane to symmetric functions and Macdonald polynomials via the n! conjecture (now a theorem) of Garsia and Haiman. No prior knowledge about Hilbert schemes will be assumed.