Abstract:
The Poisson brackets of smooth functions, {F, G}, measure the conservation of F along Hamiltonian trajectories of G. The $C^0$-semicontinuity of the Poisson brackets was proven in 2010 by Entov and Polterovich, a surprising fact considering they involve the first derivatives of F, and G. In this talk I will discuss this $C^0$-robustness phenomenon and show how certain variational problems involving the supremum norm of the Poisson brackets give rise to dynamically flavored invariants. Given time, I will comment on a numeric experiment to calculate one such invariant.
