Alternatively have a look at the program.

## The Hilbert scheme of points of affine 3-space

We describe the scheme structure of the Hilbert scheme of points of affine 3-space,

in terms of representations of the Jacobi algebra of a quiver with potential. This exhibits the Hilbert scheme of points as the critical locus of a regular function on a smooth variety.

We discuss the torus action on the Hilbert scheme and its Euler characteristic.

## Rational Cherednik algebras, Hilbert schemes and combinatorics

We will discuss the connection between cyclotomic rational Cherednik algebras at t=0 and the Hilbert scheme of points in the plane. In particular, we will explain how the spectrum of the centre of the rational Cherednik algebra is diffeomorphic to a certain component of the Hilbert scheme. Analyzing torus actions we will derive some combinatorial applications such as Bezrukavnikov and Finkelberg's proof of Haiman's conjecture about wreath MacDonald polynomials and a generalization of the q-hook formula.