[PAST EVENT] Mathematics Colloquium: Brian Simanek (Vanderbilt University)
February 4, 2015
2pm - 3pm
Abstract: In 1885, Stieltjes showed that the zeros of certain Jacobi polynomials mark the equilibrium position of electrons confined to an interval. The proof relies on the fact that Jacobi polynomials solve a certain second order differential equation. In this talk, we will consider an analogous problem on the unit circle. The main tool we will use is paraorthogonal polynomials on the unit circle, and we will show that the zeros of such polynomials mark the equilibrium position of electrons confined to the unit circle under the influence of an external field. As in the case of an interval, the proof will depend on establishing these polynomials as solutions to second order differential equations.