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Probability occupies a unique region of the scientific landscape, where pure mathematics can be applied to answer questions across many different sciences and industries, from the spread of disease and the evolution of the earliest life forms, through financial markets, to telecommunications, artificial intelligence and nuclear power.

Population genetics

Genetic traits are passed from parents to offspring, or from one cell to another, with random mutations that can lead to advantageous, deleterious, or neutral effects. Probability is used to predict how frequently particular alleles (different versions of a gene) will appear in future generations.

We use probabilistic models to study inheritance patterns, genetic variation, and evolution within populations. For example, probability can help estimate the likelihood that an individual will inherit a genetic disorder; predict how natural selection may change the frequency of genes over time; or how quickly cancer might return after treatment.

Radiation transport

Probability is also crucial in the study of radiation, with applications to health care, nuclear power and space exploration. For example, a nuclear reactor involves unimaginable numbers of particles interacting in unpredictable ways, which can be modelled by a system of branching particles.

Members of ProbLaB have been collaborating with the nuclear power industry over the last decade, using modern mathematical methods from probability theory, advanced Monte Carlo methods and inverse problems to develop novel approaches to the theory and application of radiation transport. This has culminated in the MaThRad project, an EPSRC programme grant across the Universities of Bath, Cambridge and Warwick, the NHS and the National Physical Laboratory.

These are just two prominent examples of ProbLaB's contributions, harnessing our mathematical breakthroughs to answer important scientific questions. Through our SAMBa Centre for Doctoral Training and the Institute for Mathematical Innovation, we collaborate with government and industry on numerous other projects, including how to assign data efficiently in modern 5G networks, managing player workloads to improve availability for the England cricket teams, improving AI models, and understanding the impact of water recycling centres and storm overflows on bacteria in rivers.

Members of ProbLaB with research in these areas include:

• has been integral to many collaborations with industry through his role as Director of SAMBa, and in particular has been involved in the MaThRad project and worked in mathematical finance.
• has worked with BT on self-organisation of wireless communication networks.
• has been heavily involved in SAMBa's interactions with industry, and also works on biological applications of probability.
• has many works at the forefront of mathematical population genetics, at the interface of probability and partial differential equations. In 2024 she was awarded the Erlang Prize for Applied Probability.
• has worked extensively on mathematical coverage processes and random geometric graphs, including a collaboration with BT on wireless network design.
• studies several models inspired by population genetics, for example studying how competing genetic types colonise space when expanding into a vacant region.
• is interested in how large scale order can be created out of the random interactions of individual particles or organisms, including lane formation in busy areas like train stations, and how epidemics and information spread through networks.