The aim of this lecture course is to familiarize students with the basics of surface theory, especially with the theory of Teichmuller.
This course is a continuation of [ZUA.B333 : Advanced courses in Geometry C].
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 | Teichmuller distance(Properties) | Details will be provided during each class session |
Class 2 | Bers embedding(Definitions) | Details will be provided during each class session |
Class 3 | Bers embedding(Properties) | Details will be provided during each class session |
Class 4 | Stories-- relation to theory of 3-manifolds | Details will be provided during each class session |
Class 5 | Weil-Petersson distance | Details will be provided during each class session |
Class 6 | Compactifications of the Teichmuller space --part I | Details will be provided during each class session |
Class 7 | Compactifications of the Teichmuller space --part II | Details will be provided during each class session |
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
「Teichmüller Theory and Quadratic Differentials」Frederick P. Gardiner
Evaluation will be based on exams and homework. Details will be provided during class sessions.
Students are expected to have passed [Geometry I], [Geometry II], [Topology] and [Advanced courses in Geometry C].