Speaker: Dr. William Ross, University of Richmond

Title: A complex analysis view of Bezout’s theorem.

Abstract: A 1799 result of E. Bezout says that if A and B are polynomials of respective degrees at most N and K, then there are unique polynomials R and S of respective degrees at most K - 1 and N – 1 such that A R + B S = 1. In this talk I will improve a classical result of J. J. Sylvester to obtain sharp estimates of the coefficients of R and S in terms of the coefficients of A and B. I will also discuss an application of Bezout’s theorem for orthogonal polynomials. This is joint work with E. Fricain, A. Hartmann, and D. Timotin.