4:00 pm Thursday, February 16th, 2017

Maxim Zinchenko (University of New Mexico)

Abstract: Chebyshev polynomials are the unique monic polynomials that
minimize the sup-norm on a given compact set. These polynomials have
important applications in approximation theory and numerical analysis.
H. Widom in his 1969 influential work initiated a study of Szeg\H{o}-type
asymptotics of Chebyshev polynomials on compact sets given by finite
unions of disjoint arcs in the complex plane. He obtained several partial
results on the norm and pointwise asymptotics of the polynomials and
made several long lasting conjectures. In this talk I will present some of
the classical results on Chebyshev polynomials as well as recent progress
on Widom's conjecture on the large n asymptotics of Chebyshev
polynomials on finite and infinite gap subsets of the real line.