MT A618 Course Schedule
WEEK 1: 1/13 - 1/17Discontinuous groups acting on manifolds.
Examples of 1-,2-, and 3-manifolds.
WEEK 2: 1/20 - 1/24No classes Monday, January 20th (MLK Day)
Last day to drop without a "W": Friday, January 24th
Introduction to "geometrization" of manifolds.
Elementary hyperbolic geometry in the plane.
WEEK 3: 1/27 - 1/31The modular group: case study of how to find
a fundamental domain and deduce group theoretic structure
WEEK 4: 2/3 - 2/7Dirichlet domains
Poincaré Polyhedron Theorem
WEEK 5: 2/10 - 2/14Generalities on Coxeter diagrams and Coxeter groups
Classification of elliptic diagrams
WEEK 6: 2/17 - 2/21Hyperbolic Coxeter diagrams, realization of Gram matrices
WEEK 7: 2/24 - 2/28Tetrahedral groups, circle packings
WEEK 8: 3/3 - 3/7Thurston's proof of Andreev's Theorem
WEEK 9: 3/17 - 3/21Withdrawal deadline is Friday, March 21st
Introduction to arithmetic groups, quaternion algebras
WEEK 10: 3/24 - 3/28Invariant trace field and quaternion algebra of a Kleinian group
WEEK 11: 3/31 - 4/4No class Friday, April 4th because of MAA meeting
More on invariant trace field. Examples.
WEEK 12: 4/7 - 4/11More examples. Figure 8 knot. Links from Bianchi groups.
WEEK 13: 4/14 - 4/18No classes Friday, April 18th (Good Friday)
Trace relations, computations for polyhedral groups.
WEEK 14: 4/21 - 4/25The Identification Theorem; Vinberg's version for Coxeter groups.
WEEK 15: 4/28 - 5/2Friday, May 2nd is the last day of classes
Arithmetic subgroups of SO(3,1) and quaternion algebras.