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 that can receive foreign payments.
Read about the different MIORPA projects for the 2026 programme below:
| Project Title | Project Description | Mentor | |
|---|---|---|---|
| 1. | Holographic Krylov Complexity from gravity | In this project, we will investigate Krylov complexity by studying geodesics (straight lines) in a curved background. The project will utilise tools in differential geometry and general relativity to study this problem. This approach provides geometric insight into quantum chaos, information spreading, and the deep relationship between spacetime geometry and quantum dynamics, and is ideal for students interested in theoretical high-energy physics. | 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. | Producing useful states for continuous-variable quantum computers
| Most research on quantum computing focuses on devices built from qubits, i.e., quantum bits, which can simultaneously represent different combinations of “yes” and “no” answers. While powerful, this approach still uses binary values, similar to how digital computers process information as sequences of 1s and 0s. An alternative approach is to instead build devices that work with continuous ranges of values, like how analogue systems can represent any value within a range rather than just discrete steps. However, while these devices may even be more computationally powerful than qubit-based quantum computers, it remains challenging to find ways to utilise them to their full potential. A major hurdle is the construction of high-quality quantum states that are mathematically proven to unlock a computational advantage over classical systems. While there are various techniques — known as conversion protocols — to produce such states, they are scattered widely through the literature. The student’s goal would be to produce a literature review of these techniques and to compile them into a single unified framework. Depending on the student's progress and interests, the project could be extended to investigate whether machine learning techniques could be used to construct new conversion protocols that would make it easier to produce experimentally useful quantum states. | Cameron Calcluth
University of Oxford |
| 4. | Quantum algebras and their representations | Quantum algebras are objects of fundamental importance in modern mathematics, with powerful applications spanning combinatorics, geometry, topology and physics. Studying their structure and representation theory is a highly active and rapidly developing area of research. Nevertheless, many 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 algebras, helping them build a solid understanding of the foundational concepts. Students can first work up to the core algebraic definitions, before progressing to the representation theory. Depending on their interests, students may then explore connections to combinatorics via crystal bases, or to other areas of algebra via Schur-Weyl dualities. The project seeks to provide valuable research experience, both through engagement with a current research topic and by developing research ideas and tackling problems. Prerequisites: students should have taken algebra courses focusing on group theory or ring theory. Some familiarity with (the basic notions of) algebras, Lie algebras, or representations is highly desirable. | Duncan Laurie
University of Edinburgh |
| 5. | It’s not you, it’s the math: your friends are (probably) more important than you | Have you ever suspected that your friends are more popular and better connected than you? Surprisingly, this intuition is often correct. This social phenomenon, known as the friendship paradox, was noted and formalized in 1991 by sociologist Scott L. Feld. In its classical form, the paradox states that, on average, your friends have more friends than you do. Remarkably, this property holds for all undirected networks and more generally for a wide range of definitions of "importance" (one of which is, as said, the number of friends). In this project, you will investigate generalized versions of the friendship paradox in real-world networks. First, you will focus on the theoretical foundations of friendship inequalities, drawing on key concepts from linear algebra and graph theory While the average-case behavior is mathematically well understood, much less is known about how the paradox manifests at the level of individual nodes, especially in complex or highly unbalanced networks. For this reason, through data analysis of real networks, you will quantify and characterize these inequalities for single nodes, paying particular attention to the role of hubs and degree heterogeneity Finally, you may explore how such inequalities behave in randomly generated graphs and how they scale with network size, connecting the project to central questions in random graph theory. Overall, this project combines theoretical mathematics, data analysis, and programming (Python or MATLAB) in an interdisciplinary setting. | Francesco Hrobat
University of Oxford |
| 6. | Tracking and Predicting Urban Sprawl | Urban sprawl is a major driver of greenhouse gas emissions, habitat fragmentation, and long term degradation of ecosystem services. Despite its environmental and social consequences, systematic and comparable measures of urban sprawl are limited in many regions, particularly in rapidly urbanising areas of the Global South. The aim of this project is to construct a scalable framework for measuring and forecasting urban sprawl using historic Landsat satellite imagery. The student will process multispectral satellite data to compute the Built up Index and related indicators of land cover change. These measures will be combined with demographic data to construct an urban sprawl index based on the ratio of land consumption to population growth and on weighted urban proliferation metrics. The project will begin with a review of remote sensing methods for land use classification and existing definitions of urban sprawl indices. The student will then develop a reproducible data pipeline for extracting, cleaning, and analysing satellite imagery using tools such as Google Earth Engine or Python based geospatial libraries. Time series analysis and statistical or machine learning methods will be used to model and forecast trends in urban expansion for selected cities across sub Saharan Africa and beyond. Students will gain skills in geospatial data analysis, remote sensing, environmental modelling, and reproducible research workflows. The primary outputs will be a harmonised dataset of urban sprawl rasters and indices, together with projected trends for major cities. Results will be prepared for dissemination through an open access journal or preprint platform. | Jessica Rapson
University of Oxford |
| 7. | Pattern Formation in Tea | When a cup of tea cools, patterns can appear on its surface. Thin films form, break, and reorganise into cellular or filament-like structures. Although familiar and easy to observe, the mechanisms behind these structures are not yet fully understood. This project will investigate the mathematical processes responsible for pattern formation on the surface of tea. We will formulate and analyse mathematical models that describe the coupled eBects of fluid motion, heat transfer, and surface tension. These models are typically based on continuum descriptions such as the Navier–Stokes equations, supplemented by appropriate boundary conditions at the free surface. Through studying these, the student will learngeneral techniques that can be applied to other impactful scenarios. The project will focus on identifying the key time scales over which patterns emerge and evolve, and the characteristic length scales that determine their size and spacing. The student should have some knowledge in numerical methods and software, and some exposure to fluid dynamics. | Jesus Ait Idir Lahuerta
University of Oxford |
| 8 | Computer-Assisted Study of Invariants and Structural Properties of Finite Groups | Modern computational algebra systems such as GAP allow large datasets of finite groups to be explored experimentally. This project investigates to what extent basic numerical invariants encode structural properties of finite groups, and how computational and data-driven methods can be used to analyse this relationship. The student will generate data using the GAP Small Groups Library, computing invariants such as group order, center size, number of conjugacy classes, subgroup counts, and related quantities. Many of these reflect properties such as nilpotency, solvability, or derived length, but the extent to which they determine them remains only partially understood. A central component will be to analyse how well structural properties can be predicted from these invariants. Machine learning methods will be used to identify informative and redundant invariants, and to extract simple relationships suggested by the data. Possible directions include: Studying how invariants such as the number of conjugacy classes relate to nilpotency or solvability. Investigating empirical relationships between commuting probability, center size, and other invariants. Exploring which structural properties are determined, or well approximated, by distributions of element orders. Depending on the student’s interests and progress, data-driven methods may also be used to suggest new relationships, to be tested computationally and, where possible, explained through group-theoretic arguments. The project is particularly suitable for students interested in the interface between algebra and data-driven methods. No prior experience with GAP or machine learning is required, though helpful. | Paula Heim
University of Oxford |
| 9 | Lunar tides of a basal magma ocean | Earth and other planets had (or have) an ocean of molten rock beneath their solid mantle and above their liquid core. There is a sharp interface between the liquid-iron core and the immiscible liquid-silicate magma ocean. This interface is like the boundary between the atmosphere and the water ocean: it is susceptible to tides. In this project, we’ll work on mathematical models of the response of the magma ocean to lunar tides. This may use shallow-water theory in Cartesian coordinates, or it may consider tides in cylindrical or spherical coordinates. In any case, the aim will be to solve fluid dynamical problems analytically. | Richard Katz
University of Oxford |
| 10 | Where did we come from, where do we go? Inference of parameters of branching process models | Branching processes are used as a model of a variety of phenomena in biology, epidemiology and physics, among others. The behaviour of these models depends heavily on “hidden” parameters that cannot be readily observed; to make predictions on the long term behaviour of the system, we might wish to estimate these quantities from data. Unfortunately, in many such settings, data is only available for very recent history (eg. genetic data can only be sampled today, while the time scale of evolution is millions of years). This makes estimation into the past challenging. A variety of estimators have been proposed already in the literature; as a first step the student will become familiar with some of this recent literature, at which point the project may follow a variety of directions depending on the students interest: we might conduct numerical experiments to test new approaches or obtain theoretical guarantees on the robustness of some algorithms that are used. | Ruairi Garrett & Žarko Bulić
University of Oxford |
| 11 | Towards new models aware of diverse cultures, values and beliefs in NLP | The need to design models aware of multiple beliefs, values and cultures arises because of the relevance of AI models in society. Indeed, not all countries and societies have equal access to technologies and their development, and if on the one hand, stereotypes about nationalities and cultures are learnt by models because of training data, on the other hand, their opinions and perspectives are not considered by AI models [1,2].
The aim of this project is to explore methods (e.g., retrieval-augmented strategies, fine-tuning) to enhance the knowledge of models towards specific cultures, values and beliefs to detect highly subjective phenomena such as hate speech detection, emotion, misinformation and irony. [1] Dignum (2022) Responsible Artificial Intelligence - From Principles to Practice: A Keynote at TheWebConf 2022. | Simona Frenda
Heriot-Watt University, Edinburgh |
| 12 | New supergravity solutions | In this project we will construct new supergravity solutions which encode the near-horizon region of a black hole. The project will begin by learning some differential geometry, with a focus on how to make metrics well defined using toric geometry methods. We will then construct explicit analytic solutions in type IIB supergravity which are of the form AdS3 x M(7) and analyse in detail the geometry of M(7). The project will expose the student to differential geometry, solving differential equations in Mathematica and toric geometry. | Tabea Sieper & Chris Couzens
University of Oxford |