2021 Advanced topics in Geometry C1

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Academic unit or major
Graduate major in Mathematics
Masai Hidetoshi 
Course component(s)
Lecture    (その他)
Day/Period(Room No.)
Mon3-4(ハイフレックス, 本館H213セミナー室, Main Building, H213 Seminar Room)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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.


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 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.

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.


None required

Reference books, course materials, etc.

「Teichmüller Theory and Quadratic Differentials」Frederick P. Gardiner

Assessment criteria and methods

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

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

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