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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Shiga Hiroshige
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Thr3-4(H137)
- Group
- -
- Course number
- MTH.C502
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 2Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
This course will give the fundamental theory of Teichmullar space, Kleinian groups, and their deformation spaces. The Teichmuller space is a deformation space of a Riemann surface and a Kleinian group is a discontinuous group of linear fractional transformations. The deformation space of a Kleinian group is a generalization of the Teichmuller space. Those theories are important for complex dynamics, topology as well as complex analysis. In this course, those theories will treated consistently by using quasiconformal maps.
This course is a succession of "Advanced Topics in Analysis E" in the previous quarter.
Student learning outcomes
At the end of this course, students are expected to:
-- understand the geometric meanings of the Beltrami equation and quasiconformal mappings.
-- understand Teichmuller space and the Bers embedding.
--understand fundamentals of complex structures of Teichmuller spaces and the deformation spaces of Kleinian groups.
Keywords
Riemann surfaces, quasiconformal mappings, Teichmuller spaces, Kleinian groups.
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course. Homework will be assigned occasionally
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Quasiconformal mappings (Part 1 : geometric definition and its applications) | Details will be provided in class. |
| Class 2 | Quasiconformal mappings (Part 2 : analytic definition, Beltrami equation) | Details will be provided in class. |
| Class 3 | Teichmuller space | Details will be provided in class. |
| Class 4 | A realization of Teichmuller space | Details will be provided in class. |
| Class 5 | Teichmuller space and holomorphic motions | Details will be provided in class. |
| Class 6 | The deformation space of Kleinian groups | Details will be provided in class. |
| Class 7 | Applications of Teichmuller theory | Details will be provided in class. |
| Class 8 | Comprehension check-up | Details will be provided in class. |
Textbook(s)
None required
Reference books, course materials, etc.
Ahlfors, "Lectures on Quasifoncormal mappings"
Hubbard, "Teichmuller Theory, Vol. 1"
Assessment criteria and methods
assignments 100%.
Related courses
- MTH.C501 ： Advanced topics in Analysis E
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None required
