Symplectic Geometry Seminar

The dynamics associated with mechanical Hamiltonian flows with smooth potentials that include sharp fronts may be modeled, at the singular limit, by Hamiltonian impact systems: a class of generalized billiards by which the dynamics in the domain’s...

In the study of Hamiltonian systems, integrable dynamics play a crucial role. Integrability, however, appears to be a delicate property that is not expected to persist under generic small perturbations. Understanding the essence of this fragility...

Results concerning rigidity of Lagrangian submanifolds lie at the heart of symplectic topology, and have been intensively studied since the 1990s. An example for this phenomenon is the concept of Lagrangian Barriers, a form of symplectic rigidity...

An old open question in symplectic geometry asks whether all normalised symplectic capacities coincide for convex domains in the standard symplectic vector space. I will show that this question has a positive answer for smooth convex domains which...

A compact invariant set of a flow is called locally maximal when it is the largest invariant set in some neighborhood. In this talk, based on joint work with Erman Cineli, Viktor Ginzburg, and Basak Gurel, I will present a "forced existence" result...

An old problem in classical mechanics is the existence of periodic flows within specific classes of Hamiltonian systems such as geodesic and magnetic flows, and central forces. In the last years, interest in this problem has been revitalized since...

Chaidez and Edtmair have recently found the first examples of dynamically convex domains in R4 that are not symplectomorphic to convex domains (called symplectically convex domains), answering a long-standing open question. In this talk we shall...

The C0 flux conjecture predicts that a symplectic diffeomorphism that can be C0

 approximated by a Hamiltonian diffeomorphism is itself Hamiltonian. We describe how the flux conjecture relates to new instances of the strong Arnol’d conjecture and...

It is well known that all contact 3-manifolds can be obtained from the standard contact structure on the 3-sphere by contact surgery on a Legendrian link. Hence, an interesting and much studied question asks what properties are preserved under...