Differential calculus on modules over category algebras

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. 

This project is motivated by topological data analysis and is centred around the concept of a generalised persistence module. A persistence module is an algebraic structure that associates with a partially ordered set a vector spaces for each of the elements of the set and a homomorphism with each of the relations. These objects have been studied for almost two decades, but due to genuine difficulties in obtaining classification results, little progress has been reported, specifically when applications are on interest.

This project aims to address this problem. In a recent paper a theory of calculus for persistence modules was introduced. The theory aims to enable a study of persistence module  by local means, much like the way in which functions of several variables are studied by considering differential operators. This approach, which lends itseld nicely to computations, is expected to make significant contribution to the study of real world problems by means of generalised persistence modules.

The direction of the project will be dictated by the candidate’s expertise and strengths as well as by their appetite to develop new skills in adjacent disciplines. It may therefore develop into an interdisciplinary project. Candidates are required to have a first class degree in mathematics, with established knowledge of advanced linear algebra and ring theory. Knowledge in graph theory, algebraic and/or geometric topology and combinatorics is an advantage.

Informal enquiries are welcome. Please send a copy of your full undergraduate transcript (and/or Masters

Transcript and Masters dissertation, if applicable) to Prof. Ran Levi with a brief description of why you are

interested in this project and main strengths you will use to work on this project.

Essential Background:

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 Mathematics.

Application Procedure:

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

You should apply for Mathematics (PhD) to ensure your application is passed to the correct team for processing.

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

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.

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 pgrs-admissions@abdn.ac.uk