Mathematics: Fully Funded EPSRC PhD at Swansea: Approximating shapes with algebraic spline geometry

  • Phd
  • Full cost of tuition fees and an annual 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 Nelly Villamizar
Project description:
The overarching aim of the project is to explore tools from commutative algebra, algebraic geometry, and combinatorics to study approximation methods based on piecewise polynomial functions, also known as splines.
This project will focus on algebraic aspects of trivariate splines, particularly for tridimensional simplicial complexes, and 3-dimensional generalizations of quadrangular and T-meshes. For this, we will combine elements from homological algebra, fat points schemes, and syzygies, along with methods from rigidity theory and symbolic computation, including computational algebraic geometry and Groebner bases.
The ideal candidate for this project should have a background in algebra, and/or combinatorics & geometry, and throughout the project will complement their knowledge in the remaining areas, as well as developing an understanding of the different applications of spline methods.
This project can be oriented towards the applicant's interest on theoretical or computational aspects of the topic. Coding skills are desirable, but not essential.


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.


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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.


Please visit our website for more information.
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