Seminar: Dynamics on Teichmüller space

Sommersemester 2019

Prof. Anna Wienhard, Prof. Peter Albers, Arnaud Maret, Mareike Pfeil

Announcement

Please register on Müsli in order to obtain mails concerning the seminar.

Time and Location

Thursdays, 9-11am, SR 3

Organizational meeting

Tuesday, 16.04.19, 10.45 am, Room 03.414, 3rd floor, Mathematikon

Description

Let S be a closed oriented surface of genus g at least 2. In this seminar, we learn about various aspects of dynamics on Teichmüller space T(S). We start with showing that the space of holomorphic quadratic differentials on a Riemann surface X can be identified with the cotangent space to T(S) at X. We then look at the SL(2,R)-action on T(S). Further topics will be decided during the course of the seminar.

Schedule

Date	Speaker	Topic
16.04.2019	-	Organizational meeting
25.04.2019	Arnaud	Introduction to Teichmüller space
02.05.2019	Arnaud	Coordinates on Teichmmüller space and deformation of complex structures
09.05.2019	Aarya	Grötzsch's problem
16.05.2019	Gabriele	Quadratic differentials and measured foliations
23.05.2019	Andy	SL(2,R)-action on moduli space
30.05.2019	-	Public Holiday
06.06.2019	Irene	Period Coordinates and Masur-Veech measure
13.06.2019	-	Workshop
20.06.2019	-	Public Holiday
27.06.2019	-	no seminar
04.07.2019	Arnaud	TBD
11.07.2019	-	no seminar
18.07.2019	-	no seminar
25.07.2019	Mareike	The results from Eskin, Mirzakhani and Mohammadi

Literature

[1] Benson Farb and Dan Margalit. A primer on mapping class groups. Vol 49 of Princeton Mathematical Series , Princeton University Press 2012.
[2] John Hamal Hubbard. Teichmüller theory and applications to geometry, topology, and dynamics. Vol. 1. Matrix Editions , 2006.
[3] Curtis T. McMullen. The moduli space of Riemann surfaces is Kähler hyperbolic. Ann. Of Math. (2) , 151(1):327-357, 2000.
[4] Alex Wright. Lecture notes on the SL(2,R)-action on moduli space.

Last update: 08.07.2019