Category: List of Bases 2011 Throughout the year  RESEARCH IN MATHEMATICS 

Title:

On the Bounded Isometry Conjecture

Start Time:

14:30

Location:

ICTP (Leonardo da Vinci Building Luigi Stasi Seminar Room)

Speaker(s):

Dr. Andrés Pedroza (University of Colima, Mexico)

Description:

Abstract:
F. Lalonde and L. Polterovich study the isometries of the group of Hamiltonian diffeomorphisms with respect to the Hofer metric. They defined a symplectic diffeomorphism ψ to be bounded, if the Hofer norm of [ψ, h] remains bounded as h varies on Ham(M, ω). The set of bounded symplectic diffeomorphisms, BI0 (M), of (M, ω) is a group that contains all Hamiltonian diffeomorphisms.
They conjectured that these two groups are equal, Ham(M, ω) = BI0 (M, ω) for every closed symplectic manifold. They prove this conjecture in the case when the symplectic manifold is a product of closed surfaces of positive genus. In this talk we give an outline of a new class of manifolds for which bounded isometry conjecture holds.