Hyperbolic groups summer minicourse

This course took place in summer 2019, as part of a series of summer mini-courses for graduate students organized by Richard Wong. It was an introductory five-day course on hyperbolic groups, intended to be accessible for people without much background in the subject. Max Riestenberg was a guest lecturer on Day 2.

For most of the course, we followed the book Metric Spaces of Non-positive Curvature, by Martin Bridson and André Haefliger. I also referred to Geometric Group Theory by Cornelia Druţu and Michael Kapovich, as well as Brian Bowditch's paper Relatively Hyperbolic Groups.

Exercises: Day 1, Day 2 (Max), Day 3, Day 4, Day 5

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Schedule

Day 1

Quasi-isometries, the Milnor-Svarc Lemma, and a definiton of hyperbolic metric spaces

Day 2 (led by Max Riestenberg)

The Morse Lemma and the local-to-global principle in hyperbolic metric spaces

Day 3

Definition of the boundary of a hyperbolic metric space. The topology on the boundary, and the dynamics of hyperbolic group actions on their boundaries

Day 4

Algorithmic properties of hyperbolic groups: the word and conjugacy problems, the geodesic automaton

Day 5

Generalizations of hyperbolicity: semihyperbolic spaces (and groups), relatively hyperbolic groups