Nodal count via topological persistence

It is possible to measure oscillations of a function by means of the theory of persistence modules and barcodes. I will explain how Sobolev norms can control such measurements. Applications include generalizations of Courant's nodal domain theorem and Bezout's theorem. The talk is based on a joint work with Jordan Payette, Iosif Polterovich, Leonid Polterovich, Egor Shelukhin, and Vukašin Stojisavljević. No prior knowledge of spectral geometry and topological persistence will be assumed.