October 9, Maxim Zinchenko, Albuquerque UniversityMath Colloquium: Fri at 2:30pm-3:20pm, CH 443
Title. Asymptotics of Chebyshev Polynomials.
Abstract. Chebyshev polynomials are the unique monic polynomials that minimize
the sup-norm on a given compact subset of the complex plane. These
polynomials have important applications in approximation theory and
numerical analysis. H. Widom in his 1969 influential work initiated a
study of the Chebyshev polynomials on compact sets given by a finite
union 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 the Chebyshev
polynomials as well as recent progress on Widom's conjecture on the
large n pointwise asymptotics for the Chebyshev polynomials on finite
gap subsets of the real line and a new upper bound for the norms of
the Chebyshev polynomials on positive measure Cantor-type sets.
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- Andrew Sluss is the recipient of the 2015-2016 Warner Scholarship.
- Kaitlyn Lee was awarded the 2015-2016 Travis Wood Memorial Scholarship.
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- On January 21 Alzaki Fadlallah successfully defended his Ph.D. thesis Elliptic Equations and Systems with Nonlinear Boundary Conditions. His studies were directed by Dr. M. Nkashama.