Macdonald Polynomials and Geometry

Mark Haiman

University of California, San Diego

March 5,
refreshments at 3:45pm


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)

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