Embeddings of free groups into asymptotic cones of Hamiltonian   diffeomorphisms
  Given a symplectic surface $(\Sigma, \omega)$ of genus $g \ge 4$, we show that the free group with two generators embeds into every asymptotic cone of $(\mathrm{Ham}(\Sigma, \omega), d_\mathrm{H})$, where $d_\mathrm{H}$ is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds. 
Daniel Alvarez-Gavela, Victoria Kaminker, Asaf Kislev, Konstantin   Kliakhandler, Andrei Pavlichenko, Lorenzo Rigolli, Danie...
math.SG math.DS