Mathematical Physics Seminar

Abstract: In this talk I'll survey recent results on the asymptotics of Chebyshev and orthogonal polynomials associated with a class of generalized Julia sets on the real line. The Chebyshev polynomials are defined as monic polynomials minimizing the sup norm over a given set. Similarly, the orthogonal polynomials are minimizers of the $L^2$ norm. We will consider polynomials orthogonal with respect to the equilibrium measure of a given set. The main results concern with the asymptotics of the corresponding norms as the degree of the polynomials tends to infinity.