# MT A618 Course Schedule

## WEEK 1: 1/13 - 1/17

Discontinuous groups acting on manifolds.Examples of 1-,2-, and 3-manifolds.

## WEEK 2: 1/20 - 1/24

**No 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 - 1/31

The modular group: case study of how to finda fundamental domain and deduce group theoretic structure

## WEEK 4: 2/3 - 2/7

Dirichlet domainsPoincarĂ© Polyhedron Theorem

## WEEK 5: 2/10 - 2/14

Generalities on Coxeter diagrams and Coxeter groupsClassification of elliptic diagrams

## WEEK 6: 2/17 - 2/21

Hyperbolic Coxeter diagrams, realization of Gram matrices## WEEK 7: 2/24 - 2/28

Tetrahedral groups, circle packings## WEEK 8: 3/3 - 3/7

Thurston's proof of Andreev's Theorem## WEEK 9: 3/17 - 3/21

**Withdrawal deadline is Friday, March 21st**

Introduction to arithmetic groups, quaternion algebras

## WEEK 10: 3/24 - 3/28

Invariant trace field and quaternion algebra of a Kleinian group## WEEK 11: 3/31 - 4/4

**No class Friday, April 4th because of MAA meeting**

More on invariant trace field. Examples.

## WEEK 12: 4/7 - 4/11

More examples. Figure 8 knot. Links from Bianchi groups.## WEEK 13: 4/14 - 4/18

**No classes Friday, April 18th (Good Friday)**

Trace relations, computations for polyhedral groups.

## WEEK 14: 4/21 - 4/25

The Identification Theorem; Vinberg's version for Coxeter groups.## WEEK 15: 4/28 - 5/2

**Friday, May 2nd is the last day of classes**

Arithmetic subgroups of SO(3,1) and quaternion algebras.

Volume computations.