Persistent homology (PH) is a method used in topological data analysis (TDA) to study
qualitative features of data that persist across multiple scales. It is robust to perturbations of …

Comments• page viii, bottom of page: the following names should be added to the
acknowledgements:-Peter Landweber had an invaluable contribution to these notes. First …

Our intention, at the beginning, was to write a short paper resolving some technical issues in
the theory of topological persistence. Specifically, we wished to present a clean easy-to-use …

This thesis develops the theory of sheaves and cosheaves with an eye towards applications
in science and engineering. To provide a theory that is computable, we focus on a …

In 2009, Chazal et al. introduced ϵ ϵ-interleavings of persistence modules. ϵ ϵ-
interleavings induce a pseudometric d_ I d I on (isomorphism classes of) persistence …

The goal of this work is to extend the standard persistent homology pipeline for exploratory
data analysis to the 2-D persistence setting, in a practical, computationally efficient way. To …

The stability of persistence diagrams is among the most important results in applied and
computational topology. Most results in the literature phrase stability in terms of the …

We redevelop persistent homology (topological persistence) from a categorical point of view.
The main objects of study are (R,≦)-indexed diagrams in some target category. A set of …

We generalize the persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer to the
setting of constructible persistence modules valued in a symmetric monoidal category. We …

The Reeb graph is a construction which originated in Morse theory to study a real-valued
function defined on a topological space. More recently, it has been used in various …