2025/2026

Geometric Group Theory

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

When: 1, 2 module

Open to: students of all HSE University campuses

Instructors: Alexey Golota

Language: English

Contact hours: 60

Course Syllabus

Abstract

Historically, the motivation for studying infinite groups came from geometry (e. g., the study of automorphism groups of geometric objects or fundamental groups of manifolds). On the other hand, geometric methods and constructions can be applied to the study of groups. A basic (and very important) example is the Cayley graph of a group with a fixed finite generating set, endowed with the word metric. This construction converts every finitely generated group into a metric space with a faithful action of the group by left multiplications, preserving the metric. The structure of this metric space is closely related to the properties of the group in question. Nowadays methods of geometric group theory are used in all areas of geometry and topology, as well as in many other areas of mathematics. The goal of this course is to give an introduction into basic methods and results of geometric group theory.