Berlin-Hamburg-Seminar am 8.12.2023

Sonja Hohloch (Antwerp)   Lifting of Hamiltonian S¹-actions to integrable Hamiltonian systems

Completely integrable Hamiltonian systems are Hamiltonian systems with a maximal number of independent symmetries. Although this is a quite special property many interesting natural systems in physics are in fact integrable (spinning tops, coupled angular momenta...). Moreover, completely integrable Hamiltonian systems give rise to singular Lagrangian fibrations and are therefore also of natural interest from a symplectic-topological point of view.
In this talk, we explain how an effective Hamiltonian S¹-action on a compact, connected, symplectic 4-manifold can be extended to an integrable Hamiltonian system of which the singularities are 'as nice as possible'. This is based on a joint work with Joseph Palmer (UIUC), see https://arxiv.org/abs/2105.00523.

Igor Uljarevic (Belgrad)   Contact Floer homology

In this talk I will explain the construction of the contact Floer homology and discuss its main features. I will also explain how one can associate spectral invariants with a contact Hamiltonian via contact Floer homology. If time allows, I will touch on some older results obtained using the contact Floer homology. The talk is based on joint work with Danijel Djordjevic and Jun Zhang.