Quantitative Legendrian geometry

I will discuss some quantitative aspects for Legendrians in a (more or less) general contact manifold. These include lower bounds on the number of Reeb chords between a Legendrian and its contact Hamiltonian image, the non-degeneracy of the Chekanov/Hofer/Shelukhin Legendrian metric, and some 3-dimensional non-squeezing results. The main tool is the barcode of a relative Rabinowitz Floer theory. This is joint work with Georgios Dimitroglou Rizell.