Unlinked fixed points of Hamiltonian diffeomorphisms and a dynamical construction of spectral invariants

Princeton/IAS Symplectic Geometry Seminar
Topic:Unlinked fixed points of Hamiltonian diffeomorphisms and a dynamical construction of spectral invariants
Speaker:Sobhan Seyfaddini
Affiliation:Massachusetts Institute of Technology
Date:Friday, April 17
Time/Room:1:30pm - 2:30pm/S-101
Video Link:http://video.ias.edu/puias/2015/0417-SobhanSeyfaddini

Hamiltonian spectral invariants have had many interesting and important applications in symplectic geometry. Inspired by Le Calvez's theory of transverse foliations for dynamical systems of surfaces, we introduce a new dynamical invariant, denoted by $N$, for Hamiltonians on surfaces (except the sphere). We prove that, on the set of autonomous Hamiltonians, this invariant coincides with the classical spectral invariant. This is joint work with Vincent Humilière and Frédéric Le Roux.