- Docente: Stefano Francaviglia
- Credits: 6
- SSD: MAT/03
- Language: English
- Moduli: Stefano Francaviglia (Modulo 1) Luca Marchese (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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from Feb 22, 2023 to Mar 30, 2023
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from Apr 05, 2023 to May 25, 2023
Learning outcomes
The student will learn the theory of Teichmuller spaces. The main viewpoint will be that of abelian differentials on Riemann surfaces and traslation surfaces, with links to hyperbolic surfaces. Some dynamical aspects such as geodesic and horocyclic flows will be studied in detail.
Course contents
Geometry of the hyperbolic plane in the half plane model and action of SL(2,R). Geodesic flow and horocyclic flow. Fuchsian groups and their quotients. Teichmuller space. Ergodic theory and invariant measures. Introduction to Ratner theory.
Readings/Bibliography
Einsiedler, Ward: "Ergodic Theory with a view towards number theory", Springer, 2011
Beardon: "The geometry of discrete groups", Springer, 1983.
Teaching methods
Classical frontal lessons
Assessment methods
Oral exam
Teaching tools
Use of online platforms as Virtuale, with dedicated forums, online material etc.
Office hours
See the website of Stefano Francaviglia
See the website of Luca Marchese