"Parking functions and bi-Hamiltonian structures"

Dr Vladimir Dotsenko (Trinity College, Dublin)

Abstract:
In this talk, I am going to relate combinatorics of parking functions and
especially prime parking functions to bi-Hamiltonian (that is, compatible
Poisson) structures. Though originally the bi-Hamiltonian operad was introduced
in order to understand better Mark Haiman's celebrated results on diagonal 
harmonics, the related representation theory of symmetric groups turns out to
be different. The talk is aimed to convince the audience that in spite of that
bi-Hamiltonian structures are related to Haiman's result.