30. Sep 2021
The beauty of the beast: the Hilbert scheme of infinite affine space
ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR
Datum: 30. September 2021 |
Sprecher: Maria Yakerson, ETH Zürich
Veranstaltungsort: Heinzel Seminar Room, Office Building West, Ground floor
Various invariants have been computed for Hilbert schemes of surfaces, however our knowledge about Hilbert schemes (of points) of higher dimensional schemes is quite limited. In particular, Hilbert schemes of n-dimensional affine spaces have very complicated geometry for high n. In this talk we will discuss the homotopy type of the Hilbert scheme of infinite dimensional affine space, which turns out to be surprisingly simple. We will also mention the motivation for this result, coming from algebraic K-theory. Based on joint work with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, and Burt Totaro.