Symplectic capacities of polytopes (C01)

• Subject Area: Mathematics
• Term: from 2017 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 281071066

The aim of this project is to continue our investigations in the novel field of discrete symplectic geometry by developing, analysing, and implementing algorithms to compute symplectic capacities of convex polytopes in a symplectic vector space. In the case of higher order capacities, this requires finding new combinatorial formulas based on Clarke's duality. We complement these algorithmic and theoretical parts by initiating a systematic study of symplectic capacities and related invariants for random polytopes.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 191: Symplectic Structures in Geometry, Algebra and Dynamics
• Applicant Institution: Universität zu Köln
• Co-Applicant Institution: Universität Münster ; Fachbereich 10 - Mathematik und Informatik; Mathematisches Institut; Ruhr-Universität Bochum
• Project Heads: Professor Dr. Alberto Abbondandolo; Professor Dr. Peter Albers, until 12/2020; Professor Dr. Christoph Thäle; Professor Dr. Frank Vallentin