Member Seminar

Speaker: Houcine Ben Dali, Harvard CMSA

Title: Jack polynomials and enumeration of non-orientable maps

Abstract: A map is a graph embedded on a surface, which may be orientable or not. The representation theory of the symmetric group can be used to write the generating series of maps on orientable surfaces using Schur symmetric functions.

Several conjectures suggest that Jack polynomials—a one-parameter deformation of Schur functions—are related to the enumeration of non-orientable maps counted with a “non-orientability” weight. In this talk, I will discuss some of these conjectures and present recent progress in this direction.