Rutgers Math 492

Junior-Senior Honors Seminar
Spring 2011

The seminar will be based on the text

Mirrors and Reflections - The Geometry of Finite Reflection Groups
by Alexandre Borovik and Anna Borovik
Springer (Universitext series) ISBN 978-0-387-79065-7

Finite reflection groups are a cornerstone of modern algebra and geometry. The seminar will emphasize the intuitive geometric aspects of these groups, starting with two and three-dimensional kaleidoscopes and proceeding to Coxeter's classification of all n-dimensional mirror arrangements (root systems) that give finite reflection groups. The seminar meets weekly. The material is presented by the students under the direction of Professors Roe Goodman and Robert Wilson.

The paper

   Alice through looking glass after looking glass: The Mathematics of Mirrors and Kaleidoscopes

(American Mathematical Monthly, April 2004) by Prof. Goodman outlines the topics covered in the seminar. The models of 3-dimensional kaleidoscopes shown in this paper and other models illustrating mirror systems will also be used in the seminar.

Comments on this page should be sent to goodman "at" math "dot" rutgers "dot" edu

Last revised April 1, 2011