Symmetric functions and Hodge polynomials (2017-2023)

Recent work by Hausel, Rodriguez-Villegas and Letellier on the moduli space M of stable Higgs bundles on Riemann surfaces contains a number of remarkable conjectures which suggest a deep connection between the mixed Hodge polynomial of M and the celebrated Macdonald polynomials from the theory of symmetric functions. This project aims to resolve some of these conjectures using ideas and methods from symmetric function theory, algebraic combinatorics and representation theory, and thus to explain the mysterious connection predicted by Hausel et al.