Infinite Hofer diameter conjecture for Hamiltonian diffeomorphism groups

Establish that the Hamiltonian diffeomorphism group of every closed symplectic manifold has infinite diameter with respect to the Hofer metric.

Background

The paper identifies the infinite-diameter problem for the Hofer metric as a central conjecture in the geometry of Hamiltonian diffeomorphism groups. It is known for several classes of symplectic manifolds, but the general statement remains unresolved.

References

One central conjecture in the study of the geometry of $Ham(M,\omega)$ states that it has infinite diameter with respect to the Hofer metric, which is a bi-invariant Finsler type metric, see \Problem 20.

— Biran decomposition and relative symplectic cohomology  (2610.01334 - Jo et al., 1 Oct 2026) in Section 1, Introduction