2021 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry C1
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Hidetoshi Masai
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Mon (ハイフレックス, 本館H213セミナー室, Main Building, H213 Seminar Room)
- Class
- -
- Course Code
- MTH.B407
- Number of credits
- 100
- Course offered
- 2021
- Offered quarter
- 3Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
The aim of this lecture course is to familiarize students with the basics of surface theory, especially with the theory of Teichmuller. This course will be succeeded by [ZUA.B334 : Advanced courses in Geometry D].
Course description and aims
Understand the Teichmuller space from two viewpoints: hyperbolic structures and complex structures on the surface.
Keywords
Teichmuller space. Hyperbolic structures. Complex structures.
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 | Basics of hyperbolic and complex structures on surfaces(Definitions) | Details will be provided in class. |
| Class 2 | Basics of hyperbolic and complex structures on surfaces(Properties) | Details will be provided in class. |
| Class 3 | Definition of the Teichmuller space | Details will be provided in class. |
| Class 4 | Fenchel-Nielsen coordinates | Details will be provided in class. |
| Class 5 | Quasi-conformal maps | Details will be provided in class. |
| Class 6 | Holomorphic quadratic differentials | Details will be provided in class . |
| Class 7 | Teichmuller distance | Details will be provided in class. |
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 required
Reference books, course materials, etc.
「Teichmüller Theory and Quadratic Differentials」Frederick P. Gardiner
Evaluation methods and criteria
Exams and reports. Details will be provided in class.
Related courses
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- ZUA.B301 ： Geometry I
- MTH.B341 ： Topology
- MTH.B408 ： Advanced topics in Geometry D1
Prerequisites
Students are expected to have passed [Geometry I], [Geometry II] and [Topology].