Groups were first invented to study symmetry. In this course, the connection between groups and geometry is initiated by the symmetry groups of the Platonic solids, and then extended to geometric reflection groups (spherical, Euclidean, hyperbolic). This naturally leads to beautiful spaces (called Coxeter complexes) tiled by polygons, polyhedra, and polytopes. Concrete geometric examples will continually motivate our ideas, as well as provide connections to topology, combinatorics, and physics. Format: lecture. Evaluation will be based primarily on problem sets and exams. Prerequisite: Mathematics 211 and either 312 or 315. No enrollment limit (expected: 12).

Hour: DEVADOSS