Algebraic topology and graphs

About the Project

These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.

Graphs are among the most basic combinatorial objects studied in mathematics, consisting simply of a collection of objects and connections among them. They arise in a huge variety of contexts including computing, linguistics, biology, physics, chemistry, and of course mathematics itself.

Algebraic topology is the study of spaces using algebraic invariants to ‘measure’ and understand the spaces. Prominent examples of such invariants are homology and homotopy groups. As well as being a rich and highly developed part of pure mathematics, algebraic topology reaches further still thanks to the recent development of applied algebraic topology.

The last decade or so has seen the development of the algebraic topology of graphs, with the introduction of the new theories of magnitude homology and path homology, which can be regarded as algebraic ways to measure properties of graphs. This has been followed, in only the last few years, by the realisation that magnitude homology and path homology are in fact just two facets of a single overarching theory. This now gives us an entire spectrum of ways to measure properties of graphs, and researchers are working hard to understand this new theory and its implications.

The aim of this project is to develop new theory and applications of the algebraic topology of graphs. Possible directions include using the new techniques to study curvature properties of graphs, spectral theory of graphs, or random graphs; the underlying homotopy theory and homological algebra; or the connections to, and implications for, applied algebraic topology.

Informal enquiries are welcome. Please send a copy of your full undergraduate transcript (and Masters Transcript and Masters dissertation, if applicable) to Dr Hepworth-Young (r.hepworth-young@abdn.ac.uk) with a brief description of why you are interested in this project.

Decisions will be based on academic merit. The successful applicant should have, or expect to obtain, a UK Honours Degree at 2.1 (or equivalent) in Pure Mathematics. Knowledge of algebra and topology. Some knowledge of algebraic topology will be useful, but is not essential.

We encourage applications from all backgrounds and communities, and are committed to having a diverse, inclusive team.

Application Procedure:

Formal applications can be completed online: https://www.abdn.ac.uk/pgap/login.php.

You should apply for Degree of Doctor of Philosophy in Mathematics to ensure your application is passed to the correct team for processing.

Please clearly note the name of the lead supervisor and project titleon the application form. If you do not include these details, it may not be considered for the project.

Your application must include: A personal statement, an up-to-date copy of your academic CV, and clear copies of your educational certificates and transcripts and 3 academic references.

Please note: you do not need to provide a research proposal with this application.

If you require any additional assistance in submitting your application or have any queries about the application process, please don't hesitate to contact us at researchadmissions@abdn.ac.uk

Funding Notes

This is a self-funding project open to students worldwide. Our typical start dates for this programme are February or October.

Fees for this programme can be found here Finance and Funding | Study Here | The University of Aberdeen.