Symplectic Structures in Geometry, Algebra and Dynamics
Collaborative Research Centre TRR 191
 
A1, A2, A3, A5, A6, A7
B1, B2, B3, B4, B5, B6, B7
C1, C2, C3, C4, C5
Algebra, Combinatorics & Optimization
C1: Symplectic capacities of polytopes
Abbondandolo, Albers, Vallentin
Abstract:
The aim of this project is to perform first steps into discrete symplectic geometry by developing and implementing algorithms to compute the Ekeland-Hofer capacity of convex polytopes in a symplectic vector space. These algorithms are based on the dual action principle of Clarke. There are several interesting symplectic and optimization questions connected to this. We expect these algorithms to give us insights into challenging open questions in symplectic topology, billiard dynamics and convex geometry.
Group:
 
Prof. Alberto Abbondandolo (PI)
mail: alberto.abbondandolo at rub.de
phone: 0234 / 322 3345
room: NA 4/33
Faculty of Mathematics
Ruhr-University Bochum
Prof. Peter Albers (PI)
mail: palbers at mathi.uni-heidelberg.de
phone: 06221 / 54 14230
room: 3.405
Mathematical Institute
Heidelberg University
Prof. Frank Vallentin (PI)
mail: frank.vallentin at uni-koeln.de
phone: 0221 / 470 6003
location: Weyertal 80
Mathematical Institute
University of Cologne
Impressum Institution of DFG, MI University of Cologne and FM Ruhr-University Bochum