MATH 415 Geometric Group Theory (Not offered 2006-2007; to be offered 2007-2008) (Q)
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.
Prerequisites: Mathematics 211 and either 312 or 315 or 317. No enrollment
limit (expected: 12).