Science: Swansea University Research Excellence Scholarship: Geometry and Topology Form and Algebraic Point of View

Closing date: 22 January 2018

Key Information

Start date: 1 October 2018

Swansea University is proud to offer 15 fully-funded PhD scholarships for students commencing study in October 2018 or January 2019.

The scholarships will be awarded on the basis of student excellence across a portfolio of 34 potential projects.

Swansea University is a UK top 30 institution for research excellence (Research Excellence Framework 2014) and has been named Welsh University of the Year 2017 by the Times and Sunday Times Good University Guide.

Applications are invited for a fully funded PhD studentship in Mathematics.

The aim of the project is to explore deep connections between three main fields of mathematics: algebra, geometry and topology, which goes back to ancient times, but proves constantly extremely fruitful, and through modern extensions to noncommutative algebras brings geometric aspects e.g. to fundamental physical theories of the nature such as quantum mechanics, to computer design. The more specific aim of the project is the study of smoothness of algebraic structures and noncommutative geometric objects encoded by them from various points of view: differential, homological, topological and categorical, both by looking at particular examples and developing new methods and techniques. By contrasting these points of view, not only a deep understanding of noncommutative smoothness will be achieved, but also categorical foundations of noncommutative geometry will be developed. Possible examples and applications of the techniques mentioned above might include the methods of smoothing of algebras of splines, which play an important role in computational mathematics, such as the numerical approximation of partial differential equations (the finite element method), and the parametrization of shapes in geometric modelling and computer-aided geometric design. 

Supervisors/Academic Contacts: Professor Tomasz Brzezinski  and Dr Nelly Villamizar

The successful applicant will have access to our Postgraduate Research Student Training programmes.


Applicants should have (or expect to obtain) a first class honours degree (or equivalent) and/or a distinction at master's level in mathematics. 

Due to funding restrictions, this scholarship is available to UK/EU students only.


The scholarship covers the full cost of UK/EU tuition fees, plus an annual stipend of £14,553 (in line with the RCUK stipend amount) for 3 years. 

There will also be £1,000 per annum available for research expenses such as travel, accommodation, field trips and conference attendance.

How to Apply

To apply please complete and return the following documents to Dr Vivienne Jenkins ( using the quote reference COS4:

Student applications will be evaluated against the following criteria:

  • Literary and Academic attainments (60%)
  • Demonstrable esteem indicators i.e. ambassadorial skills, instincts and opportunities to demonstrate leadership, experience and interest in extracurricular and community activities (40%)

The deadline for applications is Monday 22 January 2018.

Informal enquiries before the deadline are welcome and should be directed to Professor Tomasz Brzezinski by email ( or telephone: +44 (0)1792 295460.