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.
Organisations
People |
ORCID iD |
Jacek Brodzki (Primary Supervisor) | |
Megan Palser (Student) |
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
EP/N509747/1 | 30/09/2016 | 29/09/2021 | |||
1948907 | Studentship | EP/N509747/1 | 30/09/2017 | 29/09/2020 | 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 |