MATHEMATICS: FULLY FUNDED PHD SCHOLARSHIPS IN TORIC GEOMETRY AND MULTIVARIATE SPLINES (RS759)

Organisation/Company: Swansea University

Department: Central Research

Field: Mathematics

Researcher Profile: First Stage Researcher (R1)

Positions: PhD Positions

Country: United Kingdom

Application Deadline: 24 Feb 2025 - 11:59 (Europe/London)

Type of Contract: Temporary

Job Status: Full-time

Offer Starting Date: 1 Oct 2025

Is the job funded through the EU Research Framework Programme? Not funded by a EU programme

Is the Job related to staff position within a Research Infrastructure? No

Offer Description

The aim of this PhD project is to explore the properties of splines through the lens of applied algebraic geometry, with a particular focus on their relationship to toric geometry. Splines are mathematical representations built upon simpler pieces (usually defined by low-degree polynomials) glued together to form smooth curves, surfaces, or higher-dimensional objects. They are fundamental tools for approximation and computational design, crucial in finite element methods, computer vision, and geometric deep learning.

Splines can be viewed as functions defined over polyhedral complexes. These complexes, in turn, define toric varieties in algebraic geometry, and it has been proved that the set of splines on a polyhedral complex can be seen as the equivariant cohomology ring of the associated toric variety. This project will focus on the equivariant cohomology subrings and representations corresponding to splines with continuous derivatives of order at least 1, with the aim of making significant progress toward a deeper understanding of these structures.

The ideal candidate for this project should have a background in algebra, combinatorics, and/or geometry, and will have the opportunity to complement their knowledge in the remaining areas throughout the project, as well as develop an understanding of the various applications of spline methods. Coding skills are desirable but not essential.

Informal scholarship enquiries from applicants to prospective supervisors – prior to the application deadline – are warmly encouraged.

Additional Information

Swansea University is pleased to offer fully-funded Swansea University Research Excellence Scholarships (SURES) for full-time doctoral students to its seventh cohort, commencing in October 2025.

Each SURES scholarship includes tuition fees and a stipend at UKRI rate (currently £19,237 for 2024/25) – reviewed annually at the UKRI standard rate and a £1,000 annual training allowance to support immersive training experiences, conference attendance, engagement with industry and international collaborative opportunities.

Each scholarship is offered for a maximum period of three years; SURES students are expected to submit their theses within this timescale.

Scholarship open to UK fee eligible students only, however applications can be considered from International students, if they wish to be considered for the SUIPRES Award to run alongside this Studentship.

Swansea University is pleased to offer the Swansea University International Postgraduate Research Excellence Scholarship (SUIPRES). This is a competitively awarded Scholarship open to overseas PhD and Professional Doctorate applicants eligible for the international rate of tuition fees who can demonstrate excellence in academic achievement.

The SUIPRES Scholarship covers the difference between the International and the Home tuition fee for the duration of the PhD/Professional Doctorate programme. Successful candidates will be charged fees aligned to the UK rate per year. The scholarship will be offset against your tuition fee liability.

All International applications will be considered for a SUIPRES Scholarship. You will be informed whether a SUIPRES Scholarship will be offered within your offer letter.

Eligibility criteria

• Candidates must have attained, or must be expected to attain, a first-class UK undergraduate degree (or equivalent international qualification), or an upper second-class UK undergraduate degree and a Distinction in a UK master’s degree (or international equivalent).
• Where applicants have multiple master’s degrees, a distinction must be held in the degree that is most relevant to the intended PhD study.
• If you are currently studying for a master’s level qualification with an expected award date that is later than 01/10/2025, you should hold a minimum of an upper-second-class (2:1) honours degree.
• You should be able to demonstrate a pass with a minimum grade average of at least 70% for your part-one master’s degree modules (the taught aspect of your master’s course rather than a research-focused dissertation) and submit your dissertation by no later than 30/09/2025.

Applicants must be able to begin their course of study in October 2025. As a cohort-based programme, deferral to an alternative enrolment window within the academic year or to another academic year is not permissible.

English Language requirements: If applicable – IELTS 6.5 overall (with a score of at least 6.5 in each individual component) or a equivalent that is recognised by Swansea University. Details on the Swansea University English Language entry policy can be found here.

Please note that both the degree and language-proficiency entry requirements for SURES are higher than the baseline standard for entry that is stipulated for most of the PhD programmes at Swansea University.

ATAS clearance is NOT required to be held as part of the scholarship application process; successful award winners (as appropriate) are provided with details as to how to apply for ATAS clearance in tandem with scholarship course offer.