Lewis lectures II - Continued fractions and the 4-color theorem
Richard Schwartz - Brown University
Location: Hill Center Room 705
Date & time: Wednesday, 09 November 2022 at 3:30PM - 4:30PM
Abstract: In this talk I'll explain some experiments I have been doing lately with solutions to the 4-color problem on triangulations of non-negative combinatorial curvature. According to work of Bill Thurston, these triangulations are essentially rational points inside a certain complex hyperbolic orbifold that is closely related to the Deligne-Mostow lattices. My goal is to understand how the 4-coloring solutions vary as a function on these moduli spaces. So far I have made only modest progress on this project, though I did discover a nice connection between continued fractions and some solutions to the 4-color theorem on these kinds of triangulations. I'll explain a bit of Thurston's theory in a very elementary and accessible way, explain the connection to continued fractions, and show some mesmerizing animations created with my software.