SectionGeometry and Topology
Geometry is concerned with spaces equipped with notions of distance, angles, areas, or related concepts. Typical examples consist of smooth manifolds equipped with Riemannian metrics and/or symplectic or contact structures. Symmetries of these space, for instance expressed by Lie group actions, give rise to rich dynamical systems. Conversely, geometrically or physically motivated dynamical systems typically lead to interesting geometric objects and questions. These symmetries resp. dynamical systems may be discrete or continuous.
Geometry and Dynamics in Heidelberg encompasses broadly speaking differential geometry, geometric group theory and symplectic and contact geometry. One focus lies on discrete subgroups of Lie group, corresponding representations varieties and deformation spaces of geometric structures. This has strong ties to hyperbolic geometry. Another focus lies on applying modern tools from symplectic geometry to Hamiltonian dynamical systems such as classical systems from celestial mechanics or magnetic systems but also to billiard type systems. To foster the various links and connections between these research directions we founded the Research Station Geometry & Dynamics at Heidelberg University. The aim of the Research Station is to facilitate fundamental research and to explore applications of geometry, topology and dynamics in other sciences. In this we closely collaborate the cluster of excellence STRUCTURES. With the Heidelberg Experimental Geometry Lab (HEGL), we create a research driven learning and teaching environment for students and strive to make our research accessible to a wide audience.