Topics in geometry: geometric group theory

Geometric group theory is based on the idea that we can study discrete groups by looking at geometric objects on which they act. A single group can act on many different spaces, but all of these spaces share certain large-scale geometric properties and asymptotic behavior. In this course, we will introduce some of the techniques of geometric group theory and study their applications, especially hyperbolic groups and groups with nonpositive curvature.

Some Riemannian geometry, algebraic topology, and group theory.

• Instructor: Robert Young (ryoung@cims.nyu.edu)
• Office: WWH 601
• Office hours: by appointment

• C. Druţu, M. Kapovich, Geometric Group Theory
• B. Bowditch, A course on geometric group theory
• Clara Löh, Geometric Group Theory: an Introduction

• Lecture 1: Introduction to geometric group theory
• Lectures 2-3: The QI lens, Hyperbolic space and hyperbolicity
• Problem Set: hyperbolic geometry
• Lecture 4: QIs of hyperbolic spaces
• Lecture 5: Boundaries and quasi-isometries
• Lecture 6: Growth and asymptotic cones
• Problem Set 2