Abstract: From the topological fact that the circle is the representing space for the functor $X \to H1(X,\mathbb Z)$ follows that by computing degree 1 cohomology and picking cocycle representatives corresponds to computing equivalence classes of continuous maps $X\to S1$. In a research project with Vin de Silva and Dmitriy Morozov, we use this in a data analysis context to produce intrinsic coordinate functions with values on the circle.

We shall discuss the derivation of circle-valued coordinates for point clouds using persistent cohomology to distinguish useful coordinate functions from functions appearing from noise in the data set, and discuss applications to the analysis of periodic signals and periodic dynamical systems.