Eva Miranda, From electrons of the He atom to singular noncompact symplectic and contact topology
Channel: Scrambled Maths
Date: 08/09/2021

Full title: Eva Miranda, From the electrons of the Helium atom to (singular) non-compact Symplectic and contact Topology

Abstract:
In this talk we take as starting point the article by Urs Frauenfelder "Helium and Hamiltonian delay equation" arXiv:2002.00598 where a particular case of the 3-body problem is discussed. In the Helium atom two electrons which are mutually repulsing are attracted by a positive nucleus. The problem is highly non-integrable and the system shows chaotic features. However, it is possible to compute a periodic orbit in this set-up using variational techniques. Even though this variational approach works, as the energy surfaces are not compact it is not possible to view this result in terms of classical Floer theory. This example will be used as an excuse to make an excursion through new challenges in the current Symplectic and contact Topology scenario to extend Floer's techniques further. This includes the study of tentacular Hamiltonians (Federica Pasquotto-Jagna Wiśniewska), convex symplectic manifolds (Misha Gromov-Urs Frauenfelder-Felix Schlenk) and the case of Hamiltonian/Reeb on non-compact manifolds which can be compactified as a singular geometric structure (b-symplectic structures). This last scheme appears naturally in several problems in celestial mechanics such as the restricted three-body problem where the existence of singular periodic orbits is related to the existence of escape orbits. We will discuss open problems and new avenues in the theory.

Slides: https://unishare.nl/index.php/s/bwwFE3bnDHjbRsp

Recording of the workshop "Learning from Insulators: New Trends in the Study of Conductivity of Metals". For additional material and information, please consult the workshop page https://www.lorentzcenter.nl/learning-from-insulators-new-trends-in-the-study-of-conductivity-of-metals.html