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 [MTH.B407 : Advanced topics in Geometry C1].
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 in class.|
|Class 2||Bers embedding(Definitions)||Details will be provided in class.|
|Class 3||Bers embedding(Properties)||Details will be provided in class.|
|Class 4||Stories-- relation to theory of 3-manifolds||Details will be provided in class.|
|Class 5||Weil-Petersson distance||Details will be provided in class.|
|Class 6||Compactifications of the Teichmuller space --part I||Details will be provided in class.|
|Class 7||Compactifications of the Teichmuller space --part II||Details will be provided in class.|
|Class 8||Evaluation of progress||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], [Topology] and [Advanced topics in Geometry C1].