A major tool in symplectic topology to study Lagrangian submanifolds are Lagrangian Floer homology groups. A richer algebraic invariant can be obtained using filtered Lagrangian Floer theory. The resulting object is a persistence module, giving rise to a barcode, whose bar lengths are invariants for pairs of Lagrangians. It is well-known that these numbers are lower bounds of the Lagrangian Hofer distance between the two Lagrangians.

In this talk we will discuss a reverse inequality: We will show an upper bound of the Lagrangian Hofer distance between equators in the cylinder in terms of a weighted sum of the lengths of the finite bars and the spectral distance.