School Seminars and Colloquia

MacDonald polynomials

Statistical Mechanics/Combinatorics Seminar

by Robin Langer


Institution: The University of Melbourne
Date: Thu 21st June 2007
Time: 3:15 PM
Location: Russell Love Theatre, Richard Berry building

Abstract: When MacDonald first introduced his polynomials in 1988, he conjectured
that the coefficient of their expansion in terms of a transformed
version of the Schur basis are qt-polynomials with positive integer
coefficients. This conjecture has since been proved, using methods from
algebraic geometry and representation theory, but it remains an open
problem to give an elementary combinatorial proof. In this talk I will
introduce the modified MacDonald polynomials and survey recent work by
Haglund, Haiman and Loehr which gives an explicit combinatorial formula
for the modified MacDonald polynomials in the basis of monomial symmetric functions.

For More Information: Dr Jan de Gier Phone: +61 3 8344 6603 J.Degier@ms.unimelb.edu.au