240126 Lukas Nakamura

In this talk, I give an overview over several results concerning certain pseudo-metrics on the space of Legendrian submanifolds of a contact manifold. After reviewing the necessary background, I give a proof of an upper bound on the distance between two loose Legendrians with respect to the Shelukhin-Chekanov-Hofer pseudo-metric and show that this pseudo-metric is not always non-degenerate. If time permits, I will also touch on relations between the existence of positive loops of Legendrians and properties of the pseudo-metrics on the space of Legendrians.