Macdonald Polynomials and Geometry

Mark Haiman

University of California, San Diego

March 5,
4:15pm
refreshments at 3:45pm
2-338

ABSTRACT 

The theory of Macdonald polynomials (certain remarkable symmetric functions) leads to difficult and profound positivity conjectures, which remain unproven. The conjectured positive quantities are expected to describe irreducible character multiplicities in certain graded modules that Garsia and I constructed some time ago. The natural setting for studying these modules is the geometry of the Hilbert scheme of points in the plane. I will explain the geometric conjectures which imply the Macdonald positivity conjecture, and outline their connections with some other interesting conjectures such as the McKay correspondence and the conjectured Cohen-Macaulay property of the variety of pairs of commuting matrices.


Speaker's Contact Info: mhaiman(at-sign)macaulay.ucsd.edu


Return to seminar home page

Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

Page loaded on March 01, 1999 at 05:45 PM. Copyright © 1998-99, Sara C. Billey. All rights reserved.