Mathematics: Fully Funded Swansea PhD Scholarship: Solving Polynomial Systems

  • Phd
  • Full cost of UK tuition fees and an annual stipend
  • 20 April 2022

Funding provider: Swansea University's Faculty of Science and Engineering

Subject areas: Applied Algebra and Geometry

Project start date:

  • 1 July 2022 (Enrolment open from mid-June)


  • Principal supervisor- Dr Nelly Villamizar (Senior Lecturer, Department of Mathematics)
  • Second supervisor- Professor Chenggui Yuan (Department of Mathematics)

Aligned programme of study: PhD in Mathematics

Mode of study: Full-time

Project description:

Different control design problems in power electronics, robotic locomotion, and agent-based models can be cast in terms of polynomial systems. That is, a set of algebraic equations representing the different design and system constraints for which we need to find suitable real solutions. In order to enable the implementation of optimal control policies, such polynomial systems need to be solved in real time, in a data-driven framework where the system itself is updated from real-time measurements.

This project focuses on algebraic and geometric aspects of polynomial systems and the study of effective solution methods with an outlook to applications in feedback control design.

The overarching goal of this project is to explore novel solution methods for polynomial systems by combining elements from applied algebraic geometry and symbolic computation, including tools from elimination theory, Groebner bases, resultants, and Sturm sequences, with efficient iterative methods in optimization.

By analysing the structure of polynomial systems arising in feedback control problems (such as pole placement, model predictive control, and switching control), we will develop an applied algebraic geometry methodology for the computation of control laws in real time.


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 UK and EU based students only. EU Students must be eligible to receive the EU Transitional Bursary Scheme.


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This scholarship covers the full cost of UK tuition fees and an annual stipend of £15,609.

Additional research expenses will also be available.


Please visit our website for more information.

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