Funding providers: Engineering and Physical Sciences Research Council (EPSRC) DTP and Swansea University's Faculty of Science and Engineering
Subject areas: Mathematics
Project start date:
- 1 October 2023 (Enrolment open from mid-September)
Project supervisors:
- Professor Tomasz Brzeziński
Aligned programme of study: PhD in Mathematics
Mode of study: Full-time
Project description:
In arithmetic one usually considers binary operations (addition, multiplication, subtraction, etc.). These then extend to geometry and physics (addition of vectors, multiplication of operators). In all cases this requires to specify one particular element (zero vector, observer, fixed gauge). Liberation from this constraint is provided by affine structures (affine spaces, bundles with affine fibres) in which no particular point or gauge is selected upfront. However in affine situation there might not be a natural binary operation, one needs to consider a ternary one (roughly a combination of addition and subtraction). On algebraic level this requires replacing rings by more general structures known as trusses. The aim of the project is to study abstract properties of trusses and their applications to geometry and physics.
The project may be tailored to the candidate’s personal interests (algebra, geometry, mathematical physics) and their specific academic background.
Eligibility
Candidates must normally hold an undergraduate degree at 2.1 level or master’s degree with a minimum overall grade at ‘Merit’ (or Non-UK equivalent as defined by Swansea University).
English Language requirements: If applicable – IELTS 6.0 overall (with at least 5.5 in each individual component) or Swansea recognised equivalent.
Due to funding restrictions, this scholarship is open to applicants eligible to pay tuition fees at the UK rate only, as defined by UKCISA regulations.
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