Mathematics) Fully-funded Engineering and Physical Sciences Research Council (EPSRC) PhD Scholarship 2021/22

Title: Approximating shapes with algebraic spline geometry

Project Supervisor: Dr Nelly Villamizar

Closing date for applications: The deadline for full consideration of applications is 1 August 2021. Applications received after 1 August 2021 and before the positions are filled will be accepted but may not receive a full consideration

Start date: 1 October 2021 or 1 January 2022

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. Informal enquiries before the deadline for formal applications are welcome by emailing

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


International students are eligible to apply for this studentship.

How to apply:

Candidates must complete and submit the following documentation by the stated deadline.

To apply for this studentship, please download the Postgraduate Research Scholarship Application Form and Equality, Diversity and Inclusion Form and return them to the College of Science with the following:

  • Academic References – all scholarship applications require two supporting references to be submitted. Please ensure that your chosen referees are aware of the funding deadline, as their references form a vital part of the evaluation process. Please either include these with your scholarship application or ask your referees to send them directly to
  • Academic Transcripts and Degree Certificates – academic transcripts and degree certificates must be submitted along with the scholarship application by the funding deadline. We will be using these to verify your academic qualifications.
  • A recent CV
  • Candidates should use the ‘Supplementary Personal Statement’ section of the application form to explain why the award they are applying for particularly matches their skills and experience and how they would choose to develop the project.

Please email the documents to and put EPSRC DTP 21 ALGEBRAIC SPLINE GEOMETRY SCHOLARSHIP 2021-2022 in the email subject header.