Interleaving for sheaves and quantitative problems in symplectic geometry

The interleaving distance is a canonical pseudo-distance for persistence modules and plays an essential role in topological data analysis. After the pioneering work by Curry, Kashiwara and Schapira introduced the interleaving distance on the category of sheaves and studied its stability property. In this talk, I will explain that we can use this distance for sheaves to get a lower bound of the Hamiltonian displacement energy in a cotangent bundle through its stability with respect to Hamiltonian deformations. I would also like to explain our recent result on the completeness of the distance and its application to C^0-symplectic geometry. Joint work with Tomohiro Asano.