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Homotopy representations of p-local groups

   Department of Mathematics

This project is no longer listed on and may not be available.

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  Prof R Levi  Applications accepted all year round  Self-Funded PhD Students Only

About the Project

The theory of p-local groups was introduced and developed by Broto-Levi-Oliver. These are algebraic objects that encode and generalise topological aspects that can be associated to a discrete group from a p-local point of view. In particular, it enables the construction of objects and functions between them and offers insight into the p-local structures that dominate the topological properties. An ordinary representation of a discrete group is a homomorphism from the group to a linear group. Representations therefore induce maps between the so called classifying spaces of the groups in question. However, there are maps between classifying spaces that are not resulting from any homomorphism. These exotic maps are referred to as “homotopy representations”. In this project we propose a study of “homotopy representations”, using the tools of p-local group theory and techniques of algebraic topology.

Selection will be made on the basis of academic merit. The successful candidate should have, or expect to obtain, a strong 1st Class degree in pure mathematics from a UK university, or international equivalent. Knowledge of topology, group theory, abstract algebra essential. Algebraic topology, homological algebra and category theory desirable.

Formal applications can be completed online:

• Apply for Degree of Doctor of Philosophy in Mathematics

• State name of the lead supervisor as the Name of Proposed Supervisor

• State ‘Self-funded’ as Intended Source of Funding

• State the exact project title on the application form

When applying please ensure all required documents are attached:

• All degree certificates and transcripts (Undergraduate AND Postgraduate MSc-officially translated into English where necessary)

• Detailed CV, Personal Statement/Motivation Letter and Intended source of funding

Informal inquiries can be made to R Levi ([Email Address Removed]) with a copy of your curriculum vitae and a brief description of why you are interested in this project, along with full undergraduate transcript (and Masters transcript, if applicable). All general enquiries should be directed to the Postgraduate Research School ([Email Address Removed])

Funding Notes

This PhD project has no funding attached and is therefore available to students (UK/International) who are able to seek their own funding or sponsorship. Supervisors will not be able to respond to requests to source funding. Details of the cost of study can be found by visiting
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