AEI-DFG: Celestial Mechanics, Hydrodynamics, and Turing Machines

• Applicants: Professor Dr. Kai Cieliebak; Professor Dr. Urs Frauenfelder
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 541525489

Over the past ten years, interesting new directions of research have emerged both in celestial mechanics and in hydrodynamics. In celestial mechanics, they were inspired by Hofer's "symplectic dynamics" program, which aims at applying methods of modern symplectic geometry such as the theory of holomorphic curves to problems of planetary motion and space mission design. In hydrodynamics, they were motivated by Tao's "Turing universality" program, which suggests that the Euler and Navier-Stokes equations may be capable of incorporating systems of arbitrary dynamical and computational complexity. Moreover, there has been growing evidence that the two research areas have many similarities and can benefit from one another. In this project we plan to combine our expertise in celestial mechanics and hydrodynamics in order to address a variety of questions in both fields such as the following: 1. Proving existence of a periodic orbit for each stationary Euler flow on the three-sphere. 2. Proving results on dynamical and computational complexity in hydrodynamics. 3. Investigating the possibility of dynamical and computational complexity in celestial mechanics. 4. Addressing questions on space travel with boosts. 5. Initiating a Floer theory on singular symplectic manifolds.

• DFG Programme: Research Grants
• International Connection: Spain
• Partner Organisation: Agencia Estatal de Investigación
• Cooperation Partners: Professorin Eva Miranda, Ph.D.; Professor Daniel Peralta-Salas