Topology & Equivariant Theories 
A1, A2, A3, A5, A6, A7

Dynamics & Variational Methods 
B1, B2, B3, B4, B5, B6, B7

Algebra, Combinatorics & Optimization 
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 nth 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 / 322 3345  room: NA 4/33  Faculty of Mathematics  RuhrUniversity Bochum 
  Prof. Barney Bramham (PI)  mail: barney.bramham at rub.de  phone: 0234 / 322 4179  room: NA 5/32  Faculty of Mathematics  RuhrUniversity Bochum 


