Richard P. Stanley Seminar in Combinatorics

*Note: Unusual time and location Speaker: Jennifer Morse (University of Virginia) Title: Macdonald polynomials have nine lives (Current Developments in Mathematics) Abstract: Macdonald polynomials arose in the late 1980s from orthogonal polynomials and constant term identities, and have since led many lives: in generating functions for tableaux, Dyck paths and parking functions; in the representation theory of symmetric groups and the geometry of Hilbert schemes; and in affine Schubert calculus and double affine Hecke algebras, among other places. These lectures trace how Macdonald’s construction and his surprising conjecture that certain coefficients should be counting something inspired several largely separate directions. We will finish with how recent proofs of long-standing conjectures led to a discovery that brings these threads back together and has the potential to set off a new burst of activity.