Olof Rubin defends his PhD thesis entitled "Chebyshev Polynomials - Complexities in the complex plane"

Opponent: Klaus Schiefermayr (University of Applied Sciences Upper Austria)

Advisor: Jacob S. Christiansen (Lund University)

Examining Committee: Arno Kuijlaars (KU Leuven), Bernhard Beckermann (Université de Lille) and Małgorzata Stawiska-Friedland (American Mathematical Society)

Suppleant: Yacin Ameur (Lund University)

Thesis Abstract 

This thesis investigates Chebyshev polynomials in the complex plane which trace their origins to Chebyshev's foundational work in the mid-19th century and later extensions by Faber into the complex plane. The thesis begins with a historical review, highlighting key developments and results in the field. For this reason, the initial section provides a comprehensive overview of classical results. This recapitulation extends into the present day, highlighting several recent findings that have shed new light on classical research problems. The latter part focuses on original research conducted by the author together with collaborators. Our analysis encompasses Chebyshev polynomials on star graphs, lemniscates, and a comprehensive examination of weighted Chebyshev polynomials on the unit interval. A central aspect of the research presented in this thesis is based on the integration of numerical methods with rigorous mathematical proofs. Notably, several hypotheses presented in the research papers were formulated through insights gained from numerical experiments.