Discrete Geometry: Real and Complex Reflection Groups

Event Date: 

Wednesday, December 4, 2013 -
2:00pm to 3:00pm

Event Location: 

  • 4607B South Hall

Event Contact: 

Michael Dougherty

Email: dougherty@math.ucsb.edu

Speaker: Ben Coté

Title: Real and Complex Reflection Groups

Abstract: The study of regular polytopes in real two and three dimensional space is classical. Their higher-dimensional and complex cousins, along with the discrete groups generated by their symmetries, were studied and classified by Schläfli, Stott, Coxeter, Shephard, Todd, and Popov. In both the real and complex case, one can separate these groups into two categories: the finite and the infinite. Corresponding to each reflection group W (Coxeter group) is an Artin group, arising from the complexified hyperplane arrangement of W. The goal of this talk is to give a sample of what is known about these groups after discussing the history which led up to them.