Ian Marquette, School of Mathematics and Physics, University of Queensland, Brisbane, Australie

Title:Polynomial algebras and algebraic derivation of spectrum of superintegrable models.

Abstract: Quadratic and more generally finitely generated polynomial algebras appear to be naturally related with integrals of superintegrable models. These models have been connected with the full Askey scheme of orthogonal polynomials, exceptional orthogonal polynomials, Painlevé transcendents and equations classified by Chazy. I will review some of the recent year results on their classification and the connected algebraic structures and how it can be used to obtain the spectrum. In particular, I will review a recent work on a higher rank quadratic algebra with an embedded structure.