What is… the Lagrangian Hofer norm?

Vortrag von Ibrahim Trifa

Datum: 16.09.25  Zeit: 16.30 - 18.30  Raum:

Given a Lagrangian inside a symplectic manifold, one can define a metric, called the Hofer distance, on the space of Hamiltonian isotopies of this Lagrangian. It is known to be bounded in the case of a circle inside the plane, while it is unbounded for a diameter inside the disc (Khanevsky, 2009), or the standard Lagrangian inside the Euclidean ball of even dimension (Seyfaddini, 2013). The question remains open in most cases, such as the equator inside the sphere or a circle inside the disc. In this talk, I will show the unboundedness of this distance for a disjoint union of circles inside the disc. This result relies on a theorem of Morabito, together with a standard argument of Khanevsky.