Instructor: Timothy Riley

Mondays & Wednesdays
8:40am–9:55am, MLT205

Office hours by appointment, MLT403

Synopsis

This course will provide an introduction to Geometric Group Theory in a seminar format, with many of the presentations delivered by the participants. Our source will be the book Office Hours with a Geometric Group Theorist, edited by Matt Clay & Dan Margalit. Here's the book's blurb:

Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincaré, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics. It's like having office hours with your most trusted math professors.

An essential primer for undergraduates making the leap to graduate work, the book begins with free groups—actions of free groups on trees, algorithmic questions about free groups, the ping-pong lemma, and automorphisms of free groups. It goes on to cover several large-scale geometric invariants of groups, including quasi-isometry groups, Dehn functions, Gromov hyperbolicity, and asymptotic dimension. It also delves into important examples of groups, such as Coxeter groups, Thompson's groups, right-angled Artin groups, lamplighter groups, mapping class groups, and braid groups. The tone is conversational throughout, and the instruction is driven by examples.

Accessible to students who have taken a first course in abstract algebra, Office Hours with a Geometric Group Theorist also features numerous exercises and in-depth projects designed to engage readers and provide jumping-off points for research projects.

Assessment. For any undergraduates requiring a formal grade on this course, in addition to the presentations, I may give occasional problem sets.

Support. Office hours are by appointment. Please do not interpret this as no office hours! The Mathematics Support Center in Malott 256 also provides free tutoring, but if you're an undergraduate taking this course, then you're probably one of the tutors. I hope the group of students taking the course will constitute a stimulating and supportive community.

Schedule

24, 29, 31 January, Tim, Groups, spaces, groups acting on trees

5, 7 February, Tim, Free groups and folding

12, 14 February, Teddy, Ping pong

26, 28 February. Jason. Automorphisms of free groups (incl. Vogtmann's survey)

5, 7 March, John, Quasi-isometries

12, 14 March, Shruthi, Hyperbolic groups

19, 21 March, Tim, Dehn functions

26, 28 March, Kimoi, Ends of groups

9, 11 April, John; Tim, Asymptotic dimension; more on Dehn functions

16, 18 April Tim; Kimoi, Growth of groups 12.1 & 12.2; Coxeter Groups

25, 27 April Max; Right-Angled Artin Groups

30 April, 2 May, Shruthi, Mapping Class Groups

7, 9 May, Jason, Lamplighters / Thompson's Group / Braid Groups