Print

2023　Advanced courses in Analysis D

Font size  SML

Register update notification mail Add to favorite lecture list
Academic unit or major
Mathematics
Instructor(s)
Tanabe Masaharu 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Fri3-4(M-102(H115))  
Group
-
Course number
ZUA.C334
Credits
1
Academic year
2023
Offered quarter
4Q
Syllabus updated
2023/3/20
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

Lectures are a sequel to ''Advanced courses in Analysis C'' in the previous quarter. A Riemann surface is a two-real-dimensional manifold with holomorphic coordinate transformations. The moduli space of Riemann surfaces is a geometric space whose points represent classes of conformally equivalent Riemann surfaces. The Teichmüller space is a universal covering of the moduli space.
Each point in it is an isomorphism class of 'marked' Riemann surfaces. Ahlfors was the first to derive the complex structure of Teichmüller space. We will study his method. Topics include Teichmüller spaces, quasiconformal maps, Teichmüller’s theorem,
and the complex structure of Teichmüller space.

Student learning outcomes

At the end of this course, students are expected to:
-- be familiar with quasiconformal maps
-- understand Teichmüller’s theorem
-- understand Ahlfors' approach for the complex structure of Teichmüller space

Keywords

Riemann surfaces, moduli spaces of Riemann surfaces, Teichmüller spaces

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 Teichmüller spaces Details will be provided during each class session.
Class 2 Quasiconformal maps Details will be provided during each class session.
Class 3 The Teichmüller distance Details will be provided during each class session.
Class 4 Teichmüller modular groups Details will be provided during each class session.
Class 5 Quadratic differentials Details will be provided during each class session.
Class 6 Teichmüller’s theorem Details will be provided during each class session.
Class 7 Ahlfors' approach Details will be provided during each class session.

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

To enhance effective learning, students are encouraged to spend approximately 100 minutes reviewing class content afterwards for each class.

Textbook(s)

None

Reference books, course materials, etc.

H. M. Farkas and I. Kra, Riemann surfaces, GTM 71, Springer-Verlag
Y. Imayoshi and M. Taniguchi, An Introduction to Teichmüller Spaces, Springer-Verlag
L. V. Ahlfors, The complex analytic structure of the space of closed Riemann surfaces. In Rolf Nevanlinna et. al., editor, Analytic Functions, pages 45-66. Princeton University Press, 1960.

Assessment criteria and methods

Assignments (100%).

Related courses

  • ZUA.C333 ： Advanced courses in Analysis C

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

Understanding of topics in Advanced courses in Analysis C is required.

Page Top