Scope: This is a working seminar which takes inspiration from the paper by V. Fock and A. Goncharov "Moduli spaces of local systems and higher Teichmüller theory" As an intermediate interesting goal we propose to learn about: positivity of matrices, cluster algebras and their relation tropical geometry Teichmüller space as space of representations of fundamental groups of surfaces with boundary reinterpreting in tropical sense, changes of coordinates in Teichmüller space as to obtain its Thurston's compactification.

Speakers: 02.11.2006, Norbert A'Campo, Basel: High Teichmü'ller theory, after Fock and Goncharov 09.11.2006, Tobias Hartnick, ETH: 16.11.2006, Sebastian Baader, ETH: The modular complex of a surface 23.11.2006, Jonas Budmiger, Basel and Christian Graf, ETH: Some topics in classical Teichmüller theories 30.11.2006, François Labourie, Orsay: Configurations of flags, I 07.12.2006, Jinpeng An, ETH: Cluster algebras and total positivity 14.12.2006, François Labourie, Orsay: Configurations of flags, II 11.01.2007, François Labourie, Orsay: Mc Shane's identities and positive representations 18.01.2007, Mihai Halic, Basel: Positive structures on the higher Teichmüller spaces (Abstract: I shall explain the construction of a positive atlas and of a positive structure on the moduli space of framed G-local systems, that is the X-space in Fock & Goncharov's terminology). 25.01.2007, Maryam Mirzakhani, Princeton: TBA 01.02.2007,

Organization: The seminar takes place at ETH on Thursday afternoon, alternatively in the Hermann Weyl Zimmer (13h15-15h00) or in HG G19.2 (17h15-19h00). A reminder is sent a couple of days before the seminar.

For further informations or if you are interested in participating please contact either Sebastian Baader or Alessandra Iozzi.