# Separation of variables, superintegrability and BÃ´cher contractions

## GAP Seminar

## Meeting Details

For more information about this meeting, contact Eyal Subag, Nigel Higson, Ping Xu, Mathieu Stienon.

**Speaker:** Willard Miller, University of Minnesota

**Abstract:** Quantum superintegrable systems are exactly solvable quantum eigenvalue problems. Their solvability is due to symmetry,
but the symmetry is often ``hidden''. The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under
commutation to define quadratic algebras, a generalization of Lie algebras. The irreducible representations of these algebras yields
important information about the eigenvalues and eigenspaces of the quantum systems. Distinct superintegrable systems
and their quadratic algebras are related by geometric contractions, induced by generalized InÃ¶nÃ¼-Wigner Lie algebra contractions
which have important physical and geometric implications, such as the Askey scheme for obtaining all hypergeometric orthogonal
polynomials as limits of Racah/Wilson polynomials. This can all be unified by ideas first introduced in the 1894 thesis of BÃ´cher to
study R- separable solutions of the wave equation.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 01/26/2016

**Time:** 2:30pm - 3:30pm