Colloquium abstracts

Burt Totaro
University of California, Los Angeles, USA
December 2, 2020

The Hilbert scheme of points on affine space:  I will discuss the Hilbert scheme of d points in affine n-space, with some examples. This space has many irreducible components for n at least 3 and has been poorly understood. For n greater than d, we determine the homotopy type of the Hilbert scheme in a range of dimensions. Many questions remain. (Joint with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, Maria Yakerson.)