Spectral invariants, the energy-capacity inequality, and the non-squeezing theorem

Geometry Topology Seminar
Monday, September 22, 2008 - 4:00pm for 1 hour (actually 50 minutes)
Room 322, Boyd Graduate Studies UGA
Michael Usher – Department of Mathematics, University of Georgia
John Etnyre
Based on work of Schwarz and Oh, information coming from a filtration in Hamiltonian Floer homology can be used to construct "spectral invariants" for paths of Hamiltonian diffeomorphisms of symplectic manifolds. I will show how these invariants can be used to provide a unified approach to proving various old and new results in symplectic topology, including the non-degeneracy of the Hofer metric and some of its variants; a sharp version of an inequality between the Hofer-Zehnder capacity and the displacement energy; and a generalization of Gromov's non-squeezing theorem.