Algebra and Geometry Seminar

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