2008-2009

Greg Knese

**Monday, October 13
Millikan 213
(Pomona College), 3:00 PM**

**Title: **Polynomials with
no zeros on the bidisk

Abstract: We will describe a detailed sums of squares formula for two variable polynomials with no zeros in the unit bidisk and discuss some of its applications which include quick proofs of Ando's inequality in operator theory and the Pick interpolation theorem on the bidisk, and a bounded analytic extension theorem for functions on a special class of algebraic curves called "distinguished varieties." Our method of proof involves studying two variable orthogonal polynomials on the torus with respect to a positive (not necessarily finite) Borel measure, and we hope to touch on some of this.