Tuesday, June 7, 14:00, 7.527

Christian Kassel (Strasbourg / CNRS), The Hilbert scheme of $n$ points on a torus and modular forms.

Abstract:
In recent joint work with Christophe Reutenauer (UQAM), we explicitly computed the zeta function of the Hilbert scheme of $n$ points on a two-dimensional torus. The computation involves a family of polynomials with nice properties: they are palindromic, their coefficients are non-negative integers and their values at $1$ and at roots of unity of order $2, 3, 4$ and $6$ can be expressed in terms of well-known modular forms.