Abstract: An action selector associates to every Hamiltonian function the action of one of
its periodic orbits, in a continuous way. The mere existence of an action
selector has many consequences in symplectic dynamics and geometry (like
Gromov’s non-squeezing theorem and the existence of closed orbits on energy
surfaces of contact type). The first selectors were constructed for the standard
symplectic vector space ℝ2n by Viterbo and Hofer-Zehnder, and then for
(essentially) all symplectic manifolds by means of Floer homology (Schwarz, Oh,
Usher). I will describe a more elementary construction of an action selector for
manifolds (M,ω) with [ω]|π2(M) = 0, that uses only Gromov compactness.
This is joint work with Alberto Abbondandolo et Carsten Haug.