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].
Understand the Teichmuller space from two viewpoints: hyperbolic structures and complex structures on the surface.
Teichmuller space. Hyperbolic structures. Complex structures.
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
Standard lecture course
|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.|
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.
「Teichmüller Theory and Quadratic Differentials」Frederick P. Gardiner
Exams and reports. Details will be provided in class.
Students are expected to have passed [Geometry I], [Geometry II] and [Topology].