Speaker: Sicheng Lu (Fudan University)
Time: 19:00-20:30, Sep 21, 22, 28, 29, 2022
Room: Room 5505, the Fifth Teaching Building
This is a short course of Teichmuller theory, in which we will focus on the concepts, the concrete objects and some basic examples from the viewpoint of geometric topology. The preliminary knowledge for it only consists of basic topology and manifold theory.
The aim of this lectures:
1. Introduce the hyperbolic geometry;
2. Introduce some basic facts about Teichmuller theory;
3. Introduce partial work of Ahlfors, Thurston and Mirzakhani if time permitting.
Lecture 1. Introduction
- A brief history of Teichmuller theory
- The tori, the first example
Lecture 2. Basic hyperbolic geometry
- Planar hyperbolic geometry and their models
- Hyperbolic surfaces and Fuchsian groups
Lecture 3. The concept of Teichmuller space
- Teichmuller space from hyperbolic geometry
- Coordinates for the Teichmuller space
Lecture 4. The geometry of Teichmuller space
- Teichmuller space from quasi-conformal mappings
- Quadratic differentials and measured foliations
- Other geometry structures
