Please join the Department of Mathematics and Statistics, today, Monday, November 8th at 3:30pm in Votey Hall 209 for a fascinating combinatorics seminar featuring our very own Veronika Potter.
Higher Dimensional Ford Circles via Clifford Algebras
Veronika Potter, University of Vermont
Monday, November 8th, 3:30PM, Votey Hall 209
Abstract: Ford circles are a set of circles in the upper half of the complex plane. Ford defined each circle as being tangent to the real axis and with radius determined by this point of tangency. In his original paper, he proved these circles are internally disjoint and connected. Later work showed Ford circles are the images of the line y = i under integral Möbius transformations. We extend this classic notion of Ford circles to higher dimensions using Clifford algebras. We show that the collection of Ford spheres are connected and present a closed formula for their respective radii dependent on their point of tangency to the boundary. This is joint work with Spencer Backman, Taylor Dupuy, and Anton Hilado.
