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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Masai Hidetoshi
- Class Format
- Lecture (ZOOM)
- Media-enhanced courses
- Day/Period(Room No.)
- Fri5-6(Zoom)
- Group
- -
- Course number
- MTH.B503
- Credits
- 1
- Academic year
- 2020
- Offered quarter
- 3Q
- Syllabus updated
- 2020/9/18
- Lecture notes updated
- -
- Language used
- English
- Access Index
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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.
Keywords
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.
Textbook(s)
none
Reference books, course materials, etc.
Clara Loeh, Geometric Group Theory: An Introduction (Universitext)
Assessment criteria and methods
Assignments
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.
Other
The lecture plan might be changed
