Lorentz and contact geometry

• Applicants: Professor Dr. Alberto Abbondandolo; Professor Dr. Stefan Nemirovski; Professor Dr. Stefan Suhr
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 575291291

The goal of this project is on the one hand to use ideas from contact geometry for advancing our understanding of Lorentzian geometry and, on the other hand, to study some of the fundamental objects of contact geometry from a Lorentzian perspective. The project is subdivided into the following three subprojects. A. Morse-Uhlenbeck theories and Lagrangian Floer homology. The goal is to relate Uhlenbeck's Morse theories for causal geodesics on globally hyperbolic spacetimes to suitable Lagrangian Floer theories. B. Causality and Lorentz-Finsler geometry of Sp(2n) and Cont(M). The goal is to study the natural causal structure and Lorentz-Finsler structure on the infinite dimensional group of contactomorphisms and on its finite dimensional counterpart given by the linear symplectic group. C. Spaces of null geodesics for relativistic models. The goal is to consider several concrete cosmological models, such as the Kerr-type spacetimes, and study the topological and contact topological properties of their spaces of null geodesics.

• DFG Programme: Research Grants