# Meeting Details

Title: The spectral invariants and homological area of Hamiltonian diffeomorphisms with applications to Ham(M,\omega). Symplectic Topology Seminar Peter Spaeth, PSU > >> On any closed symplectic manifold we construct a > >> path-connected > >> neighborhood of the identity within the Hamiltonian > >> diffeomorphism group > >> with the property that each Hamiltonian > >> diffeomorphism in this > >> neighborhood > >> admits a Hofer and spectral length minimizing path > >> to the identity. > >> This > >> neighborhood is open in the $C^1-$topology. The > >> construction depends > >> on a > >> continuation argument in the spirit of the work of > >> Y. Chekanov and a > >> chain > >> level result in the Floer theory of Lagrangian > >> intersections. This > >> generalizes results of Lalonde and McDuff, McDuff > >> and Y.-G. Oh. > >> > >> While the proof is somewhat technical, effort will > >> be made to present > >> the > >> argument from scratch. Of independent interest, > >> Y.-G. Oh's spectral > >> metric, > >> which is a Floer theoretical refinement of the Hofer > >> metric and Oh's > >> homological area of will be presented in detail. > >> > >> Several open questions will also be addressed. > >>