Around the uniqueness of Hofer's metric

A remarkable discovery in modern symplectic topology is that the group of

Hamiltonian diffeomorphisms carries a bi-invariant Finsler metric with non-degenerate

distance function, known as the Hofer metric. The question about the uniqueness of Hofer’s metric, originally posed by Yakov Eliashberg and Leonid Polterovich, inspired several interesting developments. I will discuss the early and recent attempts to address this question and related phenomena. Based on joint work with Yaron Ostrover, and recent joint work with Maksim Stokic.