Geometric Group Theory UFP

PCMI Summer 2012

UFP schedule: Week 1, Week 2, Week 3

PCMI Links

- Ning - weekly calendar, forums, etc
- Mladen's page - list of Graduate lecturers, lecture notes, link to research seminar schedule
- PCMI after hours - wiki with recreational info
- PCMI 2012 Participant List

REU Links

- NSF REU Program Overview
- NSF Site List
- Fairfield University (incl. knot theory)
- UNC Greensboro (Algorithmic combinatorics on words)
- UW Stout (incl. geometric group theory)
- Williams College (incl. ergodic theory, knot theory)

A few general GGT readings

- Bridson-Haefliger, Metric spaces of nonpositive curvature (high-quality searchable)
- Ruth Charney, An introduction to right-angled Artin groups
- Yann Ollivier, Invitation to random groups
- Henry Wilton, Non-positively curved cube complexes
- Drutu-Kapovich, Lectures on geometric group theory

Slides from UFP talks

- Tim Schroeder, The geometry and \(\ell^2\)-homology of Coxeter groups
- Greg Kelsey, The Grigorchuk group: An introduction to self-similar groups
- Greg Kelsey, Self-similar groups: Where are the fractals?"

References connected to talks -- \((\star)\) means available at PCMI

**Coxeter groups**- Mike Davis,
*The geometry and topology of Coxeter groups*\( (\star) \) - Davis and Okun, Vanishing theorems and conjectures for the \(\ell^2\)-homology of the right-angled Coxeter groups
- Beno Eckmann, Introduction to \(\ell^2\)-methods in topology \((\star)\)
- Tim Schroeder, Geometrization of 3-dimensional Coxeter orbifolds and Singer's conjecture

- Mike Davis,
**Braids**- Birman and Brendle, Braids: a survey
- Chapter 7 of Stillwell's book
*Classical topology and combinatorial group theory*. \((\star)\) -
Chapter 10 of Kunio Murasugi,
*Knot theory & its applications*. - Murasugi and Kurpita,
*A study of braids*.

**Knots**- Chapter 3 of Rolfsen,
*Knots and Links* - Chapter 11 of Lickorish,
*An Introduction to Knot Theory*\((\star)\)

- Chapter 3 of Rolfsen,
**Hilbert Geometries**- Pierre de la Harpe, On Hilbert's metric for simplices, Chapter 8 of Niblo-Roller, GGT \((\star)\)
- Karlsson and Noskov, The Hilbert metric and Gromov hyperbolicity
- Yves Benoist, A survey on divisible convex sets

**Curve complexes**- Saul Schleimer, Notes on the complex of curves
- Moon Duchin, The curve complex and its relatives (video lecture)

**Amenability**- Dave Witte Morris, What is an amenable group?