Mathematics

Title: Extending the Poincaré-Birkhoff Theorem to higher dimensions: issues and ideas

Abstract: The Poincaré-Birkhoff Theorem states that every area-preserving, orientation-preserving, twist-homeomorphism of the annulus admits at least two fixed point. In this talk I will give a review of the issues and ideas that arise in the attempts to generalize this result for higher dimensional Hamiltonian systems, in spite of its strong planar nature.
I will briefly illustrate the two main ways to think the theorem in higher dimensions: the "spherical" version, that exploits the T-Maslov index, and the "toric" version, corresponding to a periodicity condition in the Hamiltonian function.

This seminar is part of the AJS series of seminars.