2020 Advanced topics in Geometry G

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Academic unit or major
Graduate major in Mathematics
Masai Hidetoshi 
Course component(s)
Lecture    (ZOOM)
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Syllabus updated
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Course description and aims

In Geometric Group Theory, we study groups by their action on "nice" metrics spaces. The purpose of this lecture is to overview this vast developing theory. The fundamental idea of Geometric Group Theory comes from its relation to geometric structures on manifolds. In particular, it has a fruitful relationship with hyperbolic geometry. Therefore I will also spend a reasonable time on hyperbolic geometry.

Student learning outcomes

To understand basic properties Geometric Group Theory.
To be familiar with the basics of geometric structures on manifolds.


Geometric Group Theory, Hyperbolic Groups, Geometric Structures, Hyperbolic Geometry

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

standard lecture course

Course schedule/Required learning

  Course schedule Required learning
Class 1 Fundamental Groups and Universal Coverings Details will be provided during each class session
Class 2 Geometric Structures on Manifolds
Class 3 Presentations of Groups
Class 4 Group Actions
Class 5 Quasi-isometric Mappings
Class 6 Hyperbolic Geometry
Class 7 Teichmuler Space

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.



Reference books, course materials, etc.

Clara Loeh, Geometric Group Theory: An Introduction (Universitext)

Assessment criteria and methods


Related courses

  • MTH.B504 : Advanced topics in Geometry H

Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites.
Basic knowledge of groups and manifolds would help to understand this lecture.


The lecture plan might be changed

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