Systolic inequalities in Reeb dynamics (B03)

• Subject Area: Mathematics
• Term: from 2017 to 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 281071066

The aim of this project is to investigate the contact systolic ratio and more broadly the relation between the action spectrum and the volume for Hamiltonian systems. Key questions we will continue to investigate concern upper bounds for the contact systolic ratio under convexity assumptions, or under global symmetry assumptions. Answers are expected to shed light on important open problems in symplectic topology, Riemannian and Finsler systolic geometry, convex geometry and billiard dynamics.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 191: Symplectic Structures in Geometry, Algebra and Dynamics
• International Connection: Netherlands
• Applicant Institution: Universität zu Köln
• Co-Applicant Institution: Ruhr-Universität Bochum
• Project Heads: Professor Dr. Alberto Abbondandolo; Professor Dr. Gabriele Benedetti, until 9/2021; Professor Dr. Barney Bramham; Professor Dr. Umberto Hryniewicz, Ph.D.