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
Dynamics & Variational Methods
B3: Systolic inequalities in Reeb dynamics
Abbondandolo, Bramham
Abstract:
The aim of this project is to extend some notions from classical systolic geometry to Reeb dynamics. In particular, we would like to carry out a thorough study of the ratio of the n-th power of the minimal action of a closed characteristic by the contact volume. Typical questions which we would like to address are, Is this ratio bounded from above on meaningful classes of contact forms? Is the maximum achieved? Although not a symplectically invariant notion, convexity seems to play a special role, why? Answers to these questions are expected to shed some light on important open problems in symplectic topology, Riemannian and Finsler systolic geometry, convex analysis and billiard dynamics.
Group:
 
Prof. Alberto Abbondandolo (PI)
mail: alberto.abbondandolo at rub.de
phone: 0234 / 32 23345
room: 1.6 (Wasserstr.)
Faculty of Mathematics
Ruhr-University Bochum
Prof. Barney Bramham (PI)
mail: barney.bramham at rub.de
phone: 0234 / 32 24179
room: NA 5/32
Faculty of Mathematics
Ruhr-University Bochum
Dr. Murat Saglam (pd)
mail: murat.saglam at rub.de
phone: 0234 / 32 23343
room: 1.1 (Wasserstr.)
Faculty of Mathematics
Ruhr-University Bochum
David Bechara Senior (ds)
mail: david.becharasenior at rub.de
phone: 0234 / 32 23343
room: 1.1 (Wasserstr.)
Faculty of Mathematics
Ruhr-University Bochum
Lorenzo Rigolli (ds)
mail: lorenzo.rigolli at rub.de
phone: 0234 / 32 23343
room: 1.1 (Wasserstr.)
Faculty of Mathematics
Ruhr-University Bochum
Impressum Institution of DFG, MI University of Cologne and FM Ruhr-University Bochum