Student Algebraic Geometry Seminar: The Geometry of Macdonald Polynomials (or The Combinatorics of Hilbert Schemes)

Seminar | February 27 | 4-5 p.m. | 891 Evans Hall

 Jeremy Meza, UC Berkeley

 Department of Mathematics

In 1988, Macdonald introduced his eponymous \(q,t\)-symmetric functions, which he conjectured were polynomials with non-negative integer coefficients. It was not until 2001 when Haiman proved this purely combinatorial conjecture using the underlying geometry subtly lurking in the background. In this talk I will outline Haiman's proof. Along the way, I will review symmetric function theory, introduce the Hilbert scheme of points in the plane, and see how the two are intimately connected.