Homology theories in topological data analysis

Lead Research Organisation: University of Southampton
Department Name: School of Mathematics

Abstract

At the centre of modern topological data analysis one finds persistent homology, which provides some of the essential computable invariants that have found use in a wide variety of contexts. This project will focus first of all on developing formal properties of persistent homology, starting with the excision property. The aim here is to complete the list of already known formal properties of persistent homology to make it similar to other known homology theories. A second aim of the project is to develop a new form of twisted de Rham-type homology theory for simplicial complexes. This will extend the work of Brodzki, Mukherjee and Gao from the case of graphs to the general case. This will provide a very useful generalisation of the algebraic and geometric structure that is at the centre of synchronisation problems. The project will also investigate appropriate practical applications of these ideas.

Publications

10 25 50
publication icon
Palser Megan (2019) An Excision Theorem for Persistent Homology in arXiv e-prints

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509747/1 01/10/2016 30/09/2021
1948907 Studentship EP/N509747/1 28/09/2017 30/09/2020 Megan Palser
 
Description Talk at Early Career Topology Conference, Sheffield 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Postgraduate students
Results and Impact Talk at an Early Careers conference, aimed at undergraduate and postgraduate students and post doctoral researchers in Topology in the UK. The talk was titled `Discrete Hodge Theory for Ranking Problems'. The talk prompted discussions with other young researchers in similar fields and was subsequently invited to give a talk at a potential follow-up conference in 2020.
Year(s) Of Engagement Activity 2019
URL http://alg-top.group.shef.ac.uk/ectr.html