Hyperbolicity in dynamics and geometry (B05)

• Subject Area: Mathematics
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 281071066

Hyperbolic structures play an important role in the theory of dynamical systems and in geometry. In the first two subprojects we study with the help of thermodynamical formalism pressure metrics and stretch metrics on the moduli space of Riemannian metrics with negative curvature as well as on the space of Anosov representation with the goal to establish global rigidity of the marked length spectrum and to study finer geometric structures on the space of representations. In the third project we like to visualize on a computer certain geometric structures of Anosov representations in low dimensions. Finally, we like to continue the investigation of non-compact harmonic manifolds with methods from hyperbolic geometry.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 191: Symplectic Structures in Geometry, Algebra and Dynamics
• Applicant Institution: Universität zu Köln
• Co-Applicant Institution: Ruhr-Universität Bochum
• Project Heads: Professor Dr. Gerhard Knieper; Professor Dr. Markus Kunze, until 10/2016; Professorin Dr. Maria Beatrice Pozzetti; Professorin Dr. Anna Wienhard