Joachim Jelisiejew Title: The Hilbert scheme of 11 points in A^3 is irreducible Abstract: We discuss singularities and irreducibility of the Hilbert scheme of r points on a smooth irreducible threefold X. For X = A^3 we construct rational curves on this scheme (so-called ray families) and sketch a proof of irreducibility for r <= 11. Irreducibility for 12 <= r <= 77 remains open, whereas for r >= 78 the scheme is reducible. This is a joint work with T. Douvropoulos, B.I. Ulstoer Noedland, and Z. Teitler.