Univalent Circle Packing and the Fundamental Result
Nathaniel Howle
In 1985, William Thurston proposed circle packing as a means for discrete approximation of conformal mappings based on results from E. M. Andrew. Further, these packings provide a setting for many parts of complex analysis. This presentation will establish the Euclidean, Parabolic, and Hyperbolic types of circle packings, analyze the Discrete Uniformization Theorem for such metrics and its maximizing properties, and finally prove the Monodromy Theorem for simply connected complexes with labels.
Nathaniel Howle graduated from South Pointe High School in Rock Hill, South Carolina. He is currently a senior in mathematics. He works as a Medical Technician at Emerald Gardens Assisted Living home, as well as a mathematics tutor here at Lander.