Fully-Funded EPSRC International PhD Positionsin Mathematics

  • Phd
  • UK tuition fees + ¬£15,245 p.a. stipend
  • 1 August 2021
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This scholarship is funded by the Engineering and Physical Sciences Research Council (EPSRC).
Start date: October 2021 or January 2022
Project Supervisor: Dr Arno Pauly
Project description:
Algorithmic questions pertaining to linear algebra are predominately studied by either taking the underlying field to be discrete (e.g. the rationals) or by forgoing a rigorous model of computation and instead focussing on the development of concrete numerical algorithms. Computable analysis provides a convenient framework to simultaneously consider non-discrete fields (e.g. real or complex numbers) and a rigorous model of computation (ultimately founded on Turing machines). However, only few initial investigations have been undertaken so far, and the field is wide open for research by an ambitious PhD student.
Many interesting computational problems in linear algebra will not be computable in general (this holds e.g. for solving systems of linear equations, finding the rank of a matrix or computing the orthogonal complement of a subspace in infinite dimensions). In these cases, it is very interesting to determine how non-computable the problem is, using the framework of Weihrauch degrees. Such results let us draw conclusions to what extent additional input information or a relaxed notion of algorithm can resolve the non-computability.


Candidates must have a First, Upper Second Class Honours or a Master’s degree with Merit, in a relevant discipline.
For candidates whose first language is not English, we require IELTS 6.5 (with 6.0 in each component) or equivalent. Please visit our website for a list of acceptable English language tests. We prefer candidates to have already met the English Language requirements at the point of application, although this is not a requirement.
This scholarship is open to candidates of any nationality.
NB: If you are holding a non-UK degree, please see Swansea University degree comparisons to find out if you meet the eligibility. 


Do you wish to become an international student next year?
Demonstrate your English skills with IELTS.


This four-year fully funded scholarship covers UK tuition fees and an annual stipend of £15,245.
Research Training Support Grant of £1,000 per annum is also provided. 
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