MIORPA
MIORPA (Mathematical Institute’s Online Research Projects with Africa) is a virtual mentorship platform that supports pre-PhD students who are based in sub-Saharan Africa. MIORPA builds on the success of Mfano Africa, which was started by Geoffrey Mboya in 2020.
During the eight-week programme (July - September), you will undertake an online research project meeting regularly with a mentor 1:1 remotely, attend training skills and information sessions, and have the opportunity to develop your research skills. Interested applicants should apply to work on a specific research project and, if successful, will be paired with a mentor based on shared research interests. Please note, we may add more projects to the list of available research projects, up until one week before the deadline.
Students will be expected to meet online with their mentor regularly, to work on the research project suggested by the mentor, and to produce a report and presentation at the end of the programme. The MIORPA programme also includes skills training sessions for students considering further study, for example in preparation for a PhD programme. Please note that the MIORPA programme does not itself lead directly to graduate study at Oxford.
Applicants should
- be ordinarily based in a sub-Saharan African country
- have completed a mathematical sciences BA or BSc degree;
- not yet be enrolled in a PhD programme;
- demonstrate academic excellence and give evidence of striving to improve;
- be motivated for further study.
A £300 (GBP) stipend will be available to students to support any associated costs for internet data, printing and stationery, etc. In order to receive the stipend, students will need to have set up a bank account.
Read about the different MIORPA projects for the 2025 programme below:
| Project Title | Project Description | Mentor | |
|---|---|---|---|
| 1. | Where is my brane? | Branes are extended dynamical objects in string theory. A large number of branes backreact on the geometry through gravity and can form black holes. An alternative use of branes is to probe geometries. By placing a single brane within your geometry, you can study how the forces of the background field influence the ‘probe brane’ and from this better understand the geometry. This is the higher dimensional version of test particles in classical mechanics and general relativity.
In this project we will study how to include certain probe branes in various string backgrounds. We are interested in branes which preserve supersymmetry which imposes constraints on where these branes can be located known as calibration conditions. The project will begin with recovering these calibration conditions in known setups before obtaining new results for different background theories including black hole geometries. During the project the student will familiarize themselves with various concepts in string theory and supersymmetry, whilst also learning some Mathematica for some of the computations. | Alice Luscher & Chris Couzens University of Oxford |
| 2. | Classifying rational conformal field theories/vertex operator algebras using modular linear differential equations | Two-dimensional Conformal Field Theories (2D CFTs) play a central role in both Physics and Mathematics. In physics, they describe critical phenomena in condensed matter systems and govern phase transitions. The worldsheet theory in String Theory is also a 2D CFT. A special class known as Rational Conformal Field Theories (RCFTs) is of particular interest due to their finite spectrum of operators. In the mathematical literature, these are referred to as Vertex Operator Algebras (VOAs) and find applications in Representation Theory, Affine Lie Algebras, Modular Tensor Categories (MTCs), and the Theory of Lattices. A classification of RCFTs would, therefore, be of significant value to both communities. This project focuses on classifying RCFTs of low rank using number-theoretic tools such as modular forms, automorphic forms, Rademacher series, and the theory of Modular Linear Differential Equations (MLDEs). The method, known as the Mathur-Mukhi-Sen (MMS) approach, begins by postulating a general holomorphic MLDE of a fixed order. Solutions whose series expansions have non-negative integer coefficients are selected as admissible characters. These are then used to construct modular-invariant partition functions. One then employs techniques from affine Lie algebras and MTCs to determine whether these correspond to genuine RCFTs. The MMS approach has successfully identified novel RCFTs and revealed new structures within VOAs. While prior knowledge of Lie groups, Lie algebras, modular forms, SAGE-math and Mathematica is helpful, it is not essential, as these can be learned during the course of the project. | Arpit Das University of Edinburgh |
| 3. | Phase separation in bio-materials
| Biomolecular condensates are dynamic, liquid-like compartments within cells composed of macromolecules such as proteins and RNAs. Recent experimental findings indicate that these structures form through liquid-liquid phase separation (LLPS), akin to the way oil droplets spontaneously emerge in water. This project aims to investigate the thermodynamical and electro-chemical aspects of protein liquid-liquid phase separation (LLPS). The first goal would be to familiarize yourself with the phase field theory developed in and the Maxwell construction approach to compute phase separated equilibria. The project might follow different directions depending on the student's interests.
| Andreas Muench University of Oxford |
| 4. | Time-delayed switching in heterogeneous populations | Understanding how populations coordinate behaviour across spatial and temporal scales remains a central challenge in mathematical biology. Many systems exhibit heterogeneity—either through intrinsic phenotypic variation or via quorum sensing, where gene expression is triggered only after reaching a critical local density. For example, run-and-tumble motility vs. sessile phases in bacteria, or different cell types in the tumour microenvironment. These transitions are often governed by biochemical or regulatory networks that exhibit time delays. This project will develop and analyse mathematical models that incorporate time delays into systems describing heterogeneous populations. The goal is to assess how delay mechanisms impact population-level behaviour—such as front propagation, aggregation, or bistability. Numerical simulations and asymptotic analysis could be used to study emergent dynamics. This project may suit a student interested in nonlinear dynamics, delay differential equations, and biologically motivated modelling. It offers a strong foundation in theory, computation, and biological interpretation, with potential relevance to microbiology, infection spread, or synthetic biology applications. | Rebecca Crossley University of Oxford |
| 5. | Tidal turbulence in Earth’s core — numerical modelling with spectral methods | Today, Earth’s magnetic field is generated by thermochemical convection in its metallic outer core. The turbulence associated with this convection creates a geodynamo, which produces the magnetic field. Early in Earth history convection was not active, but the magnetic field was of a similar strength to today. How was the turbulence generated to power the early-Earth geodynamo? One hypothesis is that lunar tides within the core generated the turbulence. This project will test that hypothesis by modelling the tidal flow and measuring its capacity to produce turbulence. The models will be numerical, using the spectral method via the Dedalus code, and based on the incompressible Navier-Stokes equations at high (but finite) Reynolds number. The project student should have some training in numerical modelling and software, and exposure to fluid dynamics. | Richard Katz & Patrick Farrell University of Oxford |
| 6. | Quantum algebras and their representations | Since their inception, quantum groups and quantum algebras have become objects of fundamental importance within mathematics. Studying their structure and representation theory is an incredibly active and dynamic area of modern research. Nevertheless, in many cases, these quantum algebras remain rather mysterious, and so there are always exciting new directions to explore! The aim of this project is to introduce students to the theory of quantum groups, helping them build an understanding of the foundations of the area. They can first work up to the initial algebraic definitions, then approach the representation theory of quantum algebras, as well as explore the connections to combinatorics via crystal bases. Once they are familiar with some of the basic ideas, they can start to think about hands-on questions and try to tackle research problems. The hope is that students gain valuable research experience, both through learning up on this ‘hot research topic’ and by spending time coming up with ideas to approach new problems. Prospective students should have taken algebra courses focusing on group theory or ring theory. Moreover, some experience with (the definition of) an algebra, a Lie algebra, or a representation is desirable. | Duncan Laurie University of Edinburgh |
| 7. | Exploiting clustering with vine copulas to examine the Scottish Multiple Deprivation Index 2020 (SIMD-2020) | The Scottish Index of Multiple Deprivation (SIMD) is widely used as a measure of deprivation, covering the composite domain index by seven domains; income, employment, education, health, access to services, crime, and housing. This real-life data set can be examined via clustering with vine copulas to understand the complex multivariate relationship between the seven domains. From that point of view, widely known clustering methods offer a set of techniques to identify groups of areas with similar patterns of deprivation and vine copulas can be beneficial to cover the complex dependence patterns between the specific domains. The clustering methods, such as K-means, offer a way to find groups of geographic areas that face similar challenges. Besides, vine copulas are flexible modelling tools in the multivariate statistics field. Beyond the traditional vines, there are certain vine copula-based approaches that allow the identification of casual relationships between variables, such as the copula-directed acyclic graphs (copula DAGs). The joint application of these methods can play a role in understanding the joint behaviour of deprivation domain indicators and their causal relationship. In this project, we will exploit the clustering methods and vine copula approaches to discover the grouped structures of the SIMD 2020 domain indicators. With the clustering techniques, the patterns of deprivation among local regions in Scotland will be explored. By integrating multiple deprivation domains into a flexible copula framework, the approach captures non-linear and asymmetric dependencies. The copula DAG method enables the differentiation between direct and indirect effects between the domain indicators.
| Ozan Evkaya University of Edinburgh |
| 8 | Mathematical modelling of schistosomiasis transmission dynamics | This research project focuses on the modelling of infectious disease dynamics, with a specific application to schistosomiasis, a water-borne parasitic disease. Schistosomiasis is transmitted through contact with water contaminated by the larvae of parasitic flatworms called schistosomes released through the urine or faeces of infected individuals. The parasites can penetrate the skin and infect the body, leading to schistosomiasis. The aim is to adapt existing compartmental models to better understand the transmission dynamics within populations considering mixing patterns and mobility. The project will begin with a concise review of existing compartmental models for schistosomiasis and other infectious diseases, providing a foundational understanding of the methodologies employed. Building upon this knowledge, the project will adapt and refine existing models, integrating relevant parameters gathered from literature and available data sources. The methods employed will predominantly revolve around systems of ordinary differential equations, encompassing deterministic and/or stochastic approaches. Students will gain valuable skills in literature review, infectious disease modelling, and coding with an in-depth look at applied mathematics for real-world global health problems. Desirable skills for prospective students include a keen interest in infectious disease transmission and some proficiency in programming languages such as Julia, Python, or R. | Melissa Iacovidou University of Oxford |