Date of Award

1-1-2018

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (ii, xi, 69 pages) : illustrations (some color)

Dissertation/Thesis Chair

Justin M Curry

Committee Members

Elizabeth Munch, Marco Varisco, Boris Goldfarb

Keywords

Topological dynamics, Topology, Mathematical analysis, Algebra, Homological, Functor theory, Categories (Mathematics)

Subject Categories

Physical Sciences and Mathematics

Abstract

The interleaving distance was originally defined in the field of Topological Data Analysis (TDA) by Chazal et al. as a metric on the class of persistence modules parametrized over the real line. Bubenik et al. subsequently extended the definition to categories of functors on a poset, the objects in these categories being regarded as `generalized persistence modules' (GPM). These metrics typically depend on the choice of a `flow' (superlinear family of translations) on the poset. The purpose of this thesis is to develop a more general framework for the notion of interleaving distance using the theory of `monoidal actions on categories'. First we define dynamical categories, equivariant functors and discuss how to view some of the common constructions of TDA in this light. Next, we define categories with a

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