3 papers
math.AT2026
An Algebraic Introduction to Persistence
Ulrich Bauer, Thomas Brüstle, Luis Scoccola
We introduce persistence with an emphasis on its algebraic foundations, using the representation theory of posets. Linear representations of posets arise in several areas of mathem…
math.RT2026
A metrically complete and Krull--Schmidt space of multiparameter persistence modules
Ulrich Bauer, Cameron Gusel, Luis Scoccola
We show that the observable category of q-tame multiparameter persistence modules satisfies good metric and algebraic properties: it forms a complete metric space with respect to t…
math.DS2024
Cycling Signatures: Identifying Cycling Motions in Time Series using Algebraic Topology
Ulrich Bauer, David Hien, Oliver Junge +1
Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system…