Jack polynomials and their (dual) combinatorics

Jack polynomials can be regarded as a deformation of Schur polynomials, a deformation which depends on one parameter. Their combinatorics was investigated by several prominent researchers, including RIchard Stanley. In 1996 Ian P. Goulden and David M. Jackson formulated several conjectures (which remain open until today) and which suggest that Jack polynomials are related to some deformation of the group algebras of the symmetric groups. During the talk I will present some recent results of Maciej Dołęga and Adam Burchardt.