Student research bursaries

Choose from the list of research projects for 2025 listed below and then submit an Expression of Interest to Dan Rust using the subject heading "STUDENT RESEARCH BURSARY APPLICATION" in capitals by 2 December 2024.

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 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: Theory and computation of cellular and bacterial dynamics

Supervisor: Dr. Sam Cameron

Summary:

Biologically active systems, such as bacterial colonies, biofilms, and cells in living organisms, are driven far-from-equilibrium due to internal driving forces/stresses, which are generated by each constituent particle. For example, cells inside tissues convert chemical energy into mechanical motion or cellular division, and bacteria in a fluid use appendages such as flagella to explore their surroundings based on availability of nutrients or other stimuli. Consequently, standard methods used to describe dead matter cannot be applied to determine the collective behaviour of living systems. Biologically active fluids cannot be described by the Navier-Stokes equation without some modifications, and particle-based simulation methods must be modified if one is considering cell division and death. In this project, we will develop minimal models of living systems and predict their macroscopic and hydrodynamic behaviour using computational and analytical methods.

Prerequisite knowledge

Essential:

Familiarity with Newtonian and/or Fluid Mechanics (ODEs or PDEs), Python (or another programming language)

Desirable:

Stochastic calculus, statistical mechanics

Availability:

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

Title: A Queer History of Mathematics

Supervisor: Dr. Andrew Potter & Dr. Brigitte Stenhouse

Summary:

Researching the history of mathematics offers an exciting opportunity to delve into the rich human stories of mathematicians and their work, but some stories are easier to find than others. In particular, the experiences of LGBTQ+ mathematicians (Lesbian, Gay, Bisexual, Trans, Queer, and other minoritised sexual and gender identities) can be difficult to research, because of historic oppression and underrepresentation that still reverberate into the present day.

This project offers an opportunity to investigate how LGBTQ+ identities and experiences have shaped the history of mathematics. The successful bursary holder will research histories of queer mathematicians, look at their mathematical works and explore how they may have been influenced by the social and political contexts of their time, and navigate some of the challenges that are posed by undertaking queer historical research in mathematics. The project aims not only to give the successful bursary holder a taste of historical research, but to contribute to the School of Mathematics & Statistics’ efforts to amplify marginalised voices and create a more inclusive mathematical community.

Prerequisite knowledge

Essential:

Interest in the history of mathematics; interest in, and sensitivity to, the lived experiences of LGBTQ+ people; ability to clearly summarise texts and write comprehensibly for a broad, general audience; enthusiasm for reading and exploring online archives.

Desirable:

Experience of prior study in history at A-Level / AS-Level (England, Wales, Northern Ireland), Higher (Scotland), or at an equivalent level or above; experience of living, working or studying within/alongside LGBTQ+ community/ies.

Availability:

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

Title: A topic in aperiodic order (mathematical quasicrystals)

Supervisor: Dr. Andrew Mitchell

Summary:

The discovery of quasicrystals—naturally occurring crystalline structures that possess long-range order but lack translational symmetry—came as a surprise to materials scientists and was awarded the 2011 Nobel Prize in Chemistry. While the mathematics of classical, periodic crystals is well-understood, there remains much that we still don't know about quasicrystals. This has stimulated a wealth of research in the field of aperiodic order, the study of mathematical quasicrystals. Some of the most well-known examples of mathematical quasicrystals include the Penrose tiling and the recently discovered hat family of tilings, which resolved a long-standing open question about whether there exists a single shape (monotile) that tiles the plane non-periodically.

This project provides the opportunity to pursue an avenue of research in aperiodic order. Particular topics could include (but are not limited to) competition between order and disorder, diffraction spectra, and complexity of aperiodic tilings. There is also the possibility to investigate applications of aperiodic order in other disciplines, such as in metamaterials design.

Prerequisite knowledge

Essential:

Linear algebra, real analysis

Desirable:

Probability, combinatorics/discrete maths, metric spaces, fractal geometry, dynamical systems

Availability:

July to September

Title: Controlled motion of microswimmers in anisotropic fluid layers

Supervisor: Dr. Abdallah Daddi-Moussa-Ider & Dr. Elsen Tjhung

Summary:

To advance the development of a theory for the motion of self-propelled objects in thin structured films and membranes, we will examine a self-driven circular disk, known as a squirmer, in a two-dimensional, uniaxially anisotropic fluid layer. A squirmer is a theoretical model used to describe a self-propelled particle, typically representing a microorganism or synthetic microswimmer, that moves by generating surface flows rather than through external forces or body deformation. It is often modelled in 2D as a disk-like object with a prescribed tangential velocity at its surface, which mimics the propulsion mechanism of organisms like ciliates or bacteria. The squirmer model captures the fluid dynamics around the active swimmer, allowing for analysis of its movement and interactions with the surrounding medium, such as in viscous or anisotropic fluids.

In this project, we assume overdamped dynamics, fluid incompressibility, and a globally aligned axis of anisotropy. The motion of the active disk within the layer is influenced by additional linear friction with the environment, such as a supporting substrate. We will investigate the self-induced flows in the fluid as well as the swimming behaviour when the squirmer swims either parallel or perpendicular to the direction of anisotropy. The analytical theory we develop will be compared with finite element simulations provided by our collaborator.

Recent experiments have explored the orientational and transport behavior of self-driven bacteria and colloidal particles in nematic liquid crystals. Therefore, we will explore the potential of using the anisotropy of the host fluid, possibly switchable, to guide individual microswimmers and active particles along predetermined paths, enabling controlled active transport.

Prerequisite knowledge

Essential:

Calculus, differential equations

Desirable:

Basic knowledge of fluid mechanics and computer algebra systems like Mathematica or Maple, as well as proficiency in LaTeX, is beneficial.

Availability:

July to September

Title: Complexity of Life: From Evolutionary Biology to Astrobiology

Supervisor: Ivan Sudakow

Summary:

In this project, we aim to unravel the complex dynamics of biological systems both on Earth and in the broader search for extraterrestrial life. By leveraging advanced mathematical and computational tools, such as statistical mechanics, dynamical systems, and machine learning algorithms, we delve into critical biological phenomena including mass extinctions, algorithmic evolution, and the structure of food webs. These tools help us model and predict how life evolves, adapts, and interacts within ecosystems, as well as how it might behave in different planetary environments. A significant aspect of the project is the search for biosignatures—indicators of life in the universe—through the analysis of complex data patterns. By drawing connections between evolutionary biology and astrobiology, the project aims to enhance our understanding of the resilience and adaptability of life, whether in recovering from catastrophic events or in potentially inhabiting extraterrestrial environments.

Prerequisite knowledge

Essential:

Differential equations, statistics and probabilities, and programming.

Desirable:

Dynamical systems, computational mathematics, and stochastic processes.

Availability:

July and August

Title: Euler’s real exponential sequence

Supervisor: Dr. Vasiliki Evdoridou

Summary:

In 1777 Euler studied the sequence a,a^a,a^{a^a},...

and showed that for a>0 it is covergent if and only if

e^-e ≤ a ≤ e^1/e

This is a real iteration sequence and problems like this have motivated a lot of work in iteration theory (both for real and complex numbers). Moreover, such sequences, known as exponential sequences, have applications in various areas like machine learning, physics, finance etc. The importance of this problem is also reflected in the fact that many mathematicians after Euler have looked at it and provided their own proofs for the convergence interval of the sequence.

The aim of this project is to study and compare some of the known proofs. In this process, the successful candidate will explore the idea of a fixed point and its properties. At the end, the successful candidate will produce a document in which they will present in detail a proof of the result in a way that it is accessible to undergraduate students.

Essential knowledge:

The candidate should be confident with formulating mathematical proofs and should be familiar with fundamental real analysis.

Desirable knowledge:

Interest in dynamical systems.

Availability:

July to September.

Title: Exploring the architecture of our appearance 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. Unfortunately, some aspects of our appearance have also been the subject of societal misunderstandings, including discrimination and racism.

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. For example, many genes have been identified that explain the huge variability observed between ethnicities and also within any group of people.

Underlying all this are mammoth efforts in generating data and analysing it with various statistical techniques. In particular, AI (artificial intelligence) and machine learning models have been popular approaches. But understanding and interpreting the underlying architecture of complex AI models is challenging.

The student will be working as part of a research team to work with a dataset to investigate a specific aspect of the diversity of our appearance and its representation through AI models. 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, and to support the student in their own journey in academic research and public engagement. It will be a useful experience for someone planning to do further study in applied statistics, AI and machine learning, or biomedical fields.

Essential knowledge:

Basic understanding of probability and statistics. Some familiarity with programming (Python / R etc.) or data analysis software (such as MS Excel) would be helpful. Prior knowledge of AI models is not necessary.

Desirable knowledge:

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:

July to September.

Title: No three in line in networks

Supervisor: Dr. James Tuite

Summary:

This project concerns the general position problem in graph theory and its relatives. The problem originated in a puzzle by Henry Dudeney, who asked for the largest number of pawns that can be fitted on a chessboard without three pawns in a line. We can generalise this to graph theory by searching for subsets of vertices such that no three vertices lie on a common shortest path. The problem has applications in robotic navigation and has links to important areas in combinatorics.

This project will explore variations of the general position problem. For example, the problem could be explored in other structures, such as hypergraphs or directed graphs, or for other types of paths apart from geodesics (e.g. longest paths or induced paths). Other directions the research could take are investigating a dynamic version of the problem, general position games, algorithms for general position sets, etc. The successful candidate would have the opportunity to collaborate on these problems with researchers at institutions in the UK, Spain, Slovenia and Italy.

Essential knowledge:

The student should be familiar with producing mathematical proofs.

Desirable knowledge:

Prior knowledge in areas such as combinatorics, group theory, number theory etc. is an advantage. Knowledge of programming is also welcome, but not essential.

Availability:

July to September.

Student research bursaries coordinator

Dan Rust