Abstract

Persistence homology is a tool originally developed in topological data analysis. Nowadays, it has also found many successfully applications in symplectic topology. In the first part of the talk, we introduce the concepts of persistence modules and barcodes. In the second part, we will focus on Floer theory in this context. Many flavors of Floer homology come with a natural filtration that gives rise to a persistence structure. We will see how spectral invariants can be interpreted in this language. Further, we explain some stability properties of the resulting Floer barcode under perturbations of the data. If time permits, we will present some of the difficulties arising from the usage of coefficients in Novikov fields.