Student research bursaries

Choose from the list of research projects for 2026 listed below and then submit an Expression of Interest to Dan Rust using the subject heading "STUDENT RESEARCH BURSARY APPLICATION" in capitals by 20 November 2026.

Your Expression of Interest should be no longer than 500 words and should contain:

• your name, Personal Identifier and preferred email address
• your choice of projects, in order of preference (at most two)
• a list of grades for all university modules taken at the Open University (a screenshot or pdf printout of your academic transcript is acceptable)
• a summary of how you meet the eligibility criteria above and why you are suitable for your project choice(s)
• a brief statement on how you will benefit from taking part in the scheme

Title: Structural elasticity of Liquid crystal elastomers

Supervisor: Dr. Cheng-Tai Lee

Summary:

Liquid crystal elastomers (LCEs) are polymeric networks of cross-linked rod-like particles. These networks can be found in biological gels, including actin networks, and in industrial smart materials that change shape in response to stimuli that reorient the particles. Although many macroscopic phenomenological models have been established to describe LCE elasticity, how the microscopic structure and topology of the underlying network influence its elastic response remains underexplored. These structural effects are particularly important in sparsely-connected networks with stiff cross-linkers as demonstrated in very recent LCE experiments. In this project, we will develop a mathematical model to investigate such effects analytically and, if time permits, numerically with the core computational code provided.

Prerequisite knowledge

Essential:

mathematical methods (such as calculus and linear algebra)

Desirable:

Some familiarity with computer programming, e.g. C++ or Python, and basic knowledge of elasticity theory

Availability:

Remote July to September

Title: The mathematics and the history in the Cambridge Higher Local Examinations.

Supervisor: Elinor Flavell

Summary:

In 1869, the first woman's college at Cambridge University, Girton College, was founded with the aim to show that women were just as capable as men in higher education. Girton College did this by getting their students to take the same exams as the men in the same time frame despite women generally having a much poorer schooling background than men. The same year, however, saw another option for women wanting to gain a qualification from Cambridge University. Intended for women wanting to teach, this was the Cambridge Higher Local Examinations. Both options expanded women's access to higher education, but both options were created with different motivations behind them. In this project we will focus on the historical context and mathematical content of the Cambridge Higher Local Examinations to help us understand the options that were available in women's higher education in the late nineteenth century.

To investigate the historical context, the intern will explore who was taking the Cambridge Higher Local Examinations, how were students taught, and the differences with other mathematical qualifications available to women in the late nineteenth century. The project will also study the mathematical content found in the exam papers. For example, the intern could choose to focus on the geometric material found within the papers allowing them to gain experience with conic sections, Euclid and deductive geometry. They will compare the Cambridge Higher Local Examinations with other mathematical examinations found at Cambridge with the aim to gain a broader picture of the standard of mathematical practice for women in the late nineteenth century.

Prerequisite knowledge

Essential:

Enthusiasm for learning about mathematics outside of the curriculum, Good written communication, Good time management, Interest in the history of mathematics, Interest in geometry

Desirable:

Experience in analysing or summarising texts (historical or contemporary)

Availability:

Remote July and August with a 2 week break in the middle (to be negotiated with the successful candidate)

Title: Assessing facial reconstruction models using AI

Supervisor: Dr. Kaustubh Adhikari

Summary:

Our appearance is a major component of our social and personal identity. Human appearance is multi-faceted, with many different aspects such as skin colour, facial shape, body height, and so on. Researchers in the area of genetics are using various methods to understand the architecture (including but not limited to the biological basis) of several aspects of our appearance.

AI and machine learning-based techniques are popular approaches to predict people's faces given their genetic information. However, a person's face is not fully predictable from DNA alone, since DNA is only partially responsible for a person's appearance, and lifestyle habits (choice of hair style, for example), environment, and accidents play an essential role in the final human appearance.

The student will work as part of a research team to evaluate the face reconstruction model's performance and understand its limits and strengths, using statistical analysis. The immediate goal is to produce a research output, but the broader goal is to have a better understanding of the latest research and delicate issues around this area. It will be a useful experience for someone planning to do further study in applied statistics, AI and machine learning, or biomedical fields.

Prerequisite knowledge

Essential:

Basic understanding of probability and statistics

Prior knowledge of AI models is not necessary

Desirable:

Some familiarity with data analysis or programming tools (R / Python / MS Excel etc.) would be helpful, but is not essential

Some basic knowledge of biology or genetics (high school level) would be helpful to grasp the context of the problem easily, but is not essential

Availability:

Remote, in-person, or hybrid July to September

Title: Hydrodynamic optimization of nearly spherical microswimmers: Balancing shape and propulsion

Supervisor: Dr. Abdallah Daddi-Moussa-Ider

Summary:

Active microswimmers—whether biological cells or synthetic constructs—harness internal or external energy sources to achieve self-propulsion within viscous fluids. In low-Reynolds-number hydrodynamics, the problem naturally bifurcates into an inner mechanics problem, describing the force generation mechanism, and an outer hydrodynamics problem, governing fluid-structure interactions and far-field flow disturbances. Identifying optimal propulsion strategies is fundamental to understanding microbial locomotion and designing efficient synthetic swimmers. While perfectly spherical squirmers minimize viscous dissipation through neutral swimming, morphological deviations from sphericity can prompt swimmers to adopt pusher or puller propulsion modes. In this work, we apply a recently established variational framework that accounts for both internal energy losses and external hydrodynamic dissipation to determine the flow field of an optimal, nearly spherical microswimmer. Utilizing an asymptotic expansion in shape perturbation, we determine how boundary geometry governs the selection of pusher, puller, or neutral swimming dynamics, and identify the leading-order Legendre shape modes that dictate these strategy transitions.

Prerequisite knowledge

Essential:

Calculus, fluid mechanics, differential equations

Desirable:

Basic knowledge of computer algebra systems like Mathematica or Maple, as well as LaTeX, is helpful

Availability:

Remote June to September

Title: Exploring networks in general position

Supervisor: Dr. James Tuite

Summary:

Imagine a collection of robots stationed at the nodes of a network. The robots communicate by sending signals along shortest paths, and we want to ensure that their signals are not blocked by other robots. How many robots can the network accommodate while satisfying this requirement? This question leads to the study of the general position and mutual visibility problems in graph theory.

Researchers have also investigated mobile versions of these problems, in which the robots must explore the entire network while maintaining the required visibility properties. In this project, we will investigate variations of these mobile problems. For example, existing models allow only one robot to move at each step; we will explore what happens when multiple robots can move simultaneously, or when every robot is required to move. Depending on the student's interests, we can also explore related questions, such as finding bounds in terms of other network parameters, determining the mobile general position number of particular families of graphs, or quantifying how long it takes the robots to visit every vertex.

The project will give the student the opportunity to experience real mathematical research, including finding good questions, attacking problems, writing papers, presenting results, being stuck, making mistakes, going down blind alleys and sometimes finding our way out again.

Prerequisite knowledge

Essential:

Experience constructing proofs

Desirable:

Programming with Python, C, GAP, knowledge of group theory or number theory

Availability:

Remote July to September with a two-week gap in the middle (negotiable with the successful student)

Student research bursaries coordinator

Dan Rust