The space of maps between classifying spaces

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.

The theory of p-local groups developed by C. Broto, R. Levi and B. Oliver encapsulates the p-local homotopy theory of classifying spaces of finite and compact Lie groups in a categorical setup that takes account of exactly the properties that are essential to the p-local homotopy type. It allows furthermore the creation of exotic homotopy types that enjoy the same homotopy theoretic properties as p-completed classifying spaces of genuine groups. One major achievement of the theory is a categorical description of spaces of self homotopy equivalences of classifying spaces of p-local groups. However, to date, more general mapping spaces are very poorly understood. The aim of this project is to address this and related questions. Potential candidates for this studentship should have strong background in basic algebraic topology, group theory and category theory.

Informal enquiries can be made by contacting Prof R Levi (r.levi@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. Potential candidates for this studentship should also have strong background in basic algebraic topology, group theory and category theory.

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.

References

1. C. Broto, R. Levi, B. Oliver, Homotopy equivalences of p-completed classifying spaces of finite groups; Invent. Math. 152 (2003) 611–664
2. C. Broto, R. Levi, B. Oliver, The homotopy theory of fusion systems; J. Amer. Math. Soc. 16 (2003), 779–856