Geometry and dynamics on hyperbolic surfaces

Sunday 26 - Friday 31 August 2018

Bruno Colbois, Prof. Dr., Université de Neuchâtel, Felix Schlenk, Prof. Dr., Université de Neuchâtel

Francoise Dal'Bo, Prof. Dr., Univ. de Rennes, Hugo Parlier, Prof. Dr., University of Luxembourg

The goal of this five day meeting is to learn basic notions of geometric dynamics on closed surfaces of constant negative curvature. This is a topic with elementary and less elementary parts.

Even the elementary ones are usually not taught in courses at our universities, but of great interest to PhD students in geometry or dynamics. The beauty of this topic is the interaction of ideas from geometry and dynamics. Though elementary, the notions and topics we will study build the basis of the spectacular works of Mirzakhani and Avila (Fields medalists 2014).

Our goal is to learn these key notions together: Each participant gives one or two talks, on a topic close to his main interest. The two specialists (Francoise Dal'Bo and Hugo Parlier) will give three talks and will guide us and help in the exercice classes.

Key words:

Geodesic flow, horocycles, Fuchsian groups, constructions (pair of pants), coding, symplectic and metric structure of Teichmüller space, counting closed geodesics (simple or non-simple)

Les Diablerets, Suisse

 http://members.unine.ch/felix.schlenk/CUSO2018LesDiablerets/

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