Algebraic Geometry Seminar
Kyungyong Lee
Purdue Univ.
Hilbert schemes of points
Abstract: The famous n! conjecture can be stated in an elementary
language. In fact it asserts that the dimension of the vector space
spanned by all derivatives of a certain bivariate analogue of the n by n
Vandermonde determinant is equal to n!. Earlier results of Haiman and
Garsia had shown that the n! conjecture implied the Macdonald positivity
conjecture. Later Haiman proved the n! conjecture, and the proof is
closely related to the algebraic and geometric properties of isospectral
Hilbert schemes of points on the plane. I'll discuss how some of the
results in the plane case can or cannot be generalized to the higher
dimensional case.
Thursday October 1, 2009 at 4:00 PM in SEO 636