"PhD Studentship in Operator Algebras – C*-algebras, Groups, and Topological Dynamics"

Award summary

100% fees covered, and a minimum tax-free annual living allowance of £20,780 (2025/26 UKRI rate). Additional project costs will also be provided.

Overview

Operator algebras is an active area of research with deep connections to other areas of mathematics such as topology, representation theory, and topological dynamics. One of the most important classes of operator algebras are C*-algebras, which are operator-norm closed subalgebras of the bounded linear operators on a complex Hilbert space that are closed under taking adjoints.

This project will focus on C*-algebras arising from considerations in topological dynamics, algebra, or group theory. The research problem will be co-created with the student to align with their background and interests. Example topics include:

• Groupoid models for C*-algebras;
• Cartan subalgebras of C*-algebras;
• Semigroup C*-algebras;
• Ring C*-algebras;
• C*-algebras from algebraic actions.

The project will combine techniques from functional analysis, topology, and algebra, so background in these areas–in particular functional analysis–is desirable.

Number of awards:

1

Start date:

1st October 2026

Award duration:

4 years

Sponsor:

EPSRC

Supervisors:

Dr Chris Bruce

Eligibility criteria

We are adopting a contextual admissions process. This means we will consider other key competencies and experience alongside your academic qualifications. An example can be found here.

A minimum 2:1 Honours degree or international equivalent in a subject relevant to the proposed PhD project is our standard entry, however we place value on prior experience, enthusiasm for research, and the ability to think and work independently. Excellent Analytical skills and strong verbal and written communication skills are also essential requirements. A Masters qualification may not be required if you have a minimum 2:1 degree or can evidence alternative experience in a work or research-based project. If you have alternative qualifications or experience, please contact us to discuss flexibilities and request an exemption.

Applicants whose first language is not English require an IELTS score of 6.5 overall with a minimum of 5.5 in all sub-skills. International applicants may require an ATAS (Academic Technology Approval Scheme) clearance certificate prior to obtaining their visa and to study on this programme.

How to apply

Please read and complete this document as your Personal statement, and upload this with your application. Applications which do not include this document will not be considered. Further details can be found here.

You must apply through the University’s Apply to Newcastle Portal

Once registered select ‘Create a Postgraduate Application’.

Use ‘Course Search’ to identify your programme of study:

• Search for the ‘Course Title’ using the programme code: 8080F
• Research area: Pure Mathematics
• Select ‘PhD Mathematics (full time)’ as the programme of study

You will then need to provide the following information in the ‘Further Details’ section:

• A ‘Personal Statement’ (this is a mandatory field) – Use this template.
• The studentship code DLA2616 in the ‘Studentship/Partnership Reference’ field.
• When prompted for how you are providing your research proposal - select ‘Write Proposal’. You should then type in the title of the research project from this advert. You do not need to upload a research proposal.

You must submit one application per studentship; you cannot apply for multiple studentships on one application.

Contact details

Chris.Bruce@newcastle.ac.uk. You can contact: doctoral.awards@ncl.ac.uk for independent advice on your application.