Interactions between higher categories and homological algebra

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 dives into the vibrant intersection of higher category theory—a rapidly evolving framework with applications from homotopy theory to mathematical physics and computer science—and the classical power of homological algebra, which probes topological spaces and algebraic structures through invariants like homology and cohomology.

Key directions include:

• Investigating homology theories for higher categories and their mathematical and computational applications.
• Reimagining the classical Dold-Kan correspondence using categorical structures beyond the traditional simplicial delta—opening new pathways beyond the landscape of chain complexes and simplicial objects.

This is a chance to contribute to foundational mathematics while engaging with cutting-edge ideas that resonate across disciplines. If you are excited by abstraction, structure, and synthesis, we would love to hear from you.

Informal enquiries can be made by contacting Dr S Paoli (simona.paoli@abdn.ac.uk).

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.

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.

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.