2021 Advanced courses in Geometry C

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Academic unit or major
Mathematics
Instructor(s)
Masai Hidetoshi 
Course component(s)
Lecture    (その他)
Day/Period(Room No.)
Mon3-4(本館 H213セミナー室, Main Building , H213 Seminar Room)  
Group
-
Course number
ZUA.B333
Credits
1
Academic year
2021
Offered quarter
3Q
Syllabus updated
2021/3/19
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

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].

Student learning outcomes

Understand the Teichmuller space from two viewpoints: hyperbolic structures and complex structures on the surface.

Keywords

Teichmuller space. Hyperbolic structures. Complex structures.

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 Basics of hyperbolic and complex structures on surfaces(Definitions) Details will be provided during each class session
Class 2 Basics of hyperbolic and complex structures on surfaces(Properties) Details will be provided during each class session
Class 3 Definition of the Teichmuller space Details will be provided during each class session
Class 4 Fenchel-Nielsen coordinates Details will be provided during each class session
Class 5 Quasi-conformal maps Details will be provided during each class session
Class 6 Holomorphic quadratic differentials Details will be provided during each class session
Class 7 Teichmuller distance 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 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

Assessment criteria and methods

Evaluation will be based on exams and homework. Details will be provided during class sessions.

Related courses

  • MTH.B301 : Geometry I
  • MTH.B302 : Geometry II
  • ZUA.B301 : Geometry I
  • MTH.B341 : Topology
  • ZUA.B334 : Advanced courses in Geometry D

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

Students are expected to have passed [Geometry I], [Geometry II] and [Topology].

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