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Lecture Notes

Winter 2016
TCC Course on Compactifications of Moduli spaces

Winter 2015
TCC Course on Outer space and Automorphisms of free groups

St. Andrews August 2013
Lectures on automorphism groups of right-angled Artin groups

Tokyo July 2014 Introduction to Outer space for free groups and RAAGs

Lecture 1, Lecture 2, Lecture 3

Geometric Group Theory Course Spring 2014

Outline of lecture contents

Week 1

January 6, 2014
January 7
January 9
Introduction, free groups and ping-pong,
fundamental groups and covering spaces

Week 2

January 13
January 14

The geometry of the hyperbolic plane: geodesics,
isometries and the metric.

Week 3

January 21
January 23
More geometry of hyperbolic plane and
introduction to the Cayley graph.

Week 4

January 27
January 28
January 30

Examples of Cayley graphs,
definitions of hyperbolic metric space,
hyperbolic group, quasi-isometry and quasi-geodesic.

Week 5

February 3
February 4
February 6

A space quasi-isometric to a hyperbolic space is hyperbolic.
Quasi-geodesics stay a bounded distance from geodesics.
The divergence function is exponential.

Week 6

February 10
February 11
February 13

Group-theoretic consequences of hyperbolicity,
Svarc-Milnor Lemma.

Week 7

February 17
February 18
February 20

Gromov product and the boundary of a
hyperbolic space.

Week 8

February 24
February 25
February 27

Boundary of a hyperbolic space, continued.
Bounded cancellation for free group automorphisms.

Week 9

March 3
March 6
Infinite cyclic subgroups of hyperbolic groups are quasi-geodesicis
in the Cayley graph.

Week 10

March 10
March 11
March 13

Dynamics of infinite-order elements of hyperbolic groups
Quasi-convex subgroups