The Hilbert scheme of infinite 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 is poorly understood.  Nonetheless, in the limit where n goes to infinity, we show that the Hilbert scheme of d points in infinite affine space has a very simple homotopy type. In fact, it has the A^1-homotopy type of the infinite Grassmannian BGL(d-1). Many questions remain. (Joint with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, Maria Yakerson.)

https://mathseminars.org/talk/agstanford/3/