**Date & Time:** Tuesday, March 17, 2009, 16:30-17:30.

**Venue:** Ramanujan Hall

**Title:** Bezoutians, Euclidean Algorithm and Orthogonal Polynomials

**Speaker:** Piotr Pragacz, Polish Academy of Sciences

**Abstract:** We prove a quadratic expression for the Bezoutian of two
univariate polynomials in terms of the remainders
for the Euclidean algorithm. In case of two polynomials of the
same degree, or of consecutive degrees, this allows us to interpret
their Bezoutian as the Christoffel-Darboux kernel for a finite
family of orthogonal polynomials, arising from the Euclidean
algorithm. We give orthogonality properties of remainders, and
reproducing properties of Bezoutians.