Berlin-Hamburg-Seminar am 13.11.2017
Patrick Massot (Orsay) Invariant norms on contact transformation groups
Inspired by the Hofer and Viterbo distances on groups of Hamiltonian diffeomorphisms, several recent works define and study invariant distances on groups of contact transformations. In some cases, contact and symplectic rigidity results allow to prove that such a distance is unbounded, hence sees a significant part of the group. But understanding when this happens is not obvious. For instance this happens for the standard contact structures on projective spaces but not for their two-fold covers, the standard spheres.
In joint work in progress with Sylvain Courte, we shed new lights on this puzzle by uncovering links with Giroux's theory of open book decompositions and Murphy's theory of loose Legendrian embeddings.
Jean Gutt (Köln) Knotted embeddings
I will discuss a joint result with Mike Usher, showing that many toric domains X in the 4-dimensional euclidean space admit symplectic embeddings f into dilates of themselves which are knotted in the strong sense that there is no symplectomorphism of the target that takes f(X) to X.