Bernt Ivar Utstøl Nødland (Oslo): Irreducibility of Hilbert schemes of points
Abstract: The Hilbert scheme of d points on a scheme X parametrize degree d finite subschemes of X. For a surface X, the Hilbert scheme of points will always be smooth, however for higher dimensional X it may even fail to be irreducible. For X=A^3 it was not known whether the Hilbert scheme of d points was irreducible for d from 11 to 77. We present, and sketch the proof of, the recent result that this is in fact irreducible for d=11. This is joint work with Theo Douvropoulos, Joachim Jelisiejew and Zach Teitler.