2020 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry G
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Hidetoshi Masai
- Class Format
- Lecture (Zoom)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Fri (Zoom)
- Class
- -
- Course Code
- MTH.B503
- Number of credits
- 100
- Course offered
- 2020
- Offered quarter
- 3Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
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.
Course description and aims
To understand basic properties Geometric Group Theory.
To be familiar with the basics of geometric structures on manifolds.
Keywords
Geometric Group Theory, Hyperbolic Groups, Geometric Structures, Hyperbolic Geometry
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
standard lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| 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 |
Study advice (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.
Textbook(s)
none
Reference books, course materials, etc.
Clara Loeh, Geometric Group Theory: An Introduction (Universitext)
Evaluation methods and criteria
Assignments
Related courses
- MTH.B504 ： Advanced topics in Geometry H
Prerequisites
No prerequisites.
Basic knowledge of groups and manifolds would help to understand this lecture.
Other
The lecture plan might be changed