SPEAKER: Sarah Post
TITLE: The Askey scheme of orthogonal polynomials and contractions of
superintegrable systems

ABSTRACT: In the first week, I will give a brief introduction to
orthogonal polynomials in general and focus on the Askey scheme of
hypergeometric orthogonal polynomials in particular. This scheme
details the relations between the classical orthogonal polynomials and
singular limits between the families.

The Askey scheme can be directly obtained from irreducible
representations of the symmetry algebras generated by superintegrable
systems and their contractions. I will discuss these maximally
symmetric Hamiltonians and explain how a generic superintegrable
system on the two sphere is related exactly to the most general
polynomials in the hierarchy-the Wilson polynomials. The entire Askey
scheme is then obtained from singular limits of this system. These
limits can be seen in the geometry of the systems and have the effect
of contractions of the symmetry algebras. This interpretation of the
Askey scheme in terms of the physical systems will be the subject of
the second week.