Persistence modules in analysis and symplectic topology

Persistence modules and their associated barcodes have originated in data sciences, but have recently had new applications in pure mathematics: in symplectic topology and in the study of Laplace eigenfunctions in particular. I will present a couple of my favorite such applications, one of which is recent joint work with L. Buhovsky, J. Payette, I. Polterovich, L. Polterovich and V. Stojisavljevic.