Jacob Bucciarelli, Kansas State University, will speak about

Cell Decompositions of Hilbert schemes

Abstract: Using Bialynicki-Birula cell decomposition, one can decompose the Hilbert scheme of points in a complex plane into affine cells, which can be studied combinatorially using young diagrams.

Given a monomial ideal I corresponding to a partition of m > n, we consider the subvariety of the Hilbert scheme of points in a complex plane consisting of ideals that contain I. Intersecting this subvariety with the Bialynicki-Birula cells yields subdivisions.

We pose the question: ``When do these subdivisions form a cell decomposition?''

We study this question for a series of concave partitions.