Locally symmetric spaces and transfer operators

• Applicant: Professorin Dr. Anke Pohl
• Subject Area: Mathematics
• Term: from 2014 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 264148330

Over the last few decades, mathematical quantum chaos on Riemannian manifolds has been studied using an ever increasing number of methods which focus on the dynamics of the manifolds rather than on their (static) geometry. Among these dynamical methods are transfer operator techniques whose potential is still far from being fully understood.The PI has advanced significantly the development of transfer operator techniques for Riemannian hyperbolic surfaces. For a wide range of noncompact surfaces they now provide, e.g., a purely dynamical characterization of Maass cusp forms, and hence show a deeper relation between these Laplace eigenfunctions and periodic geodesics than could be established by any other method. The main theme of this project is to use the insights gained to far to further extend the investigations for hyperbolic surfaces (in particular, to resonances, non-unitary twists, etc.), and to develop transfer operator methods for higher-dimensional hyperbolic spaces and also for some higher rank Riemannian locally symmetric spaces.

• DFG Programme: Research Grants