Colloquium: Tuesday, May 3, 2 pm. Speaker: Frol Zapolsky (Haifa). Title: “Poisson bracket – rigidity and flexibility”.
I will give an overview of recent results regarding the behavior
of the Poisson bracket under perturbations of the functions relative to
different topologies. It turns out that it exhibits both rigidity and
flexibility. For instance, if the Poisson bracket of F, G is nonzero, then
it cannot be made to vanish by arbitrarily small C^0 perturbations of F, G,
due to a result of Cardin and Viterbo. However if the perturbations are
allowed in L^p topology for finite p, then certain flexibility appears, due
to recent results by K. Samvelyan. Finally I’ll discuss some fresh results
in dimension two, which are part of joint work in progress with K.
Samvelyan.
