Risk is the potential of experiencing a loss when a system does not operate as expected due to uncertainties. Its assessment requires the quantification of both the system failure potential and the multi-faceted failure consequences, which affect further systems. Modern industries (including the engineering and financial sectors) require increasingly large and complex models to quantify risks that are not confined to single disciplines but cross into possibly several other areas. Disasters such as hurricane Katrina, the Fukushima nuclear incident and the global financial crisis show how failures in technical and management systems cause consequences and further failures in technological, environmental, financial, and social systems, which are all inter-related. This requires a comprehensive multi-disciplinary understanding of all aspects of uncertainty and risk and measures for risk management, reduction, control and mitigation as well as skills in applying the necessary mathematical, modelling and computational tools for risk oriented decision-making. This complexity has to be considered in very early planning stages, for example, for the realisation of green energy or nuclear power concepts and systems, where benefits and risks have to be considered from various angles. The involved parties include engineering and energy companies, banks, insurance and re-insurance companies, state and local governments, environmental agencies, the society both locally and globally, construction companies, service and maintenance industries, emergency services, etc. The CDT is focussed on training a new generation of highly-skilled graduates in this particular area of engineering, mathematics and the environmental sciences based at the Liverpool Institute for Risk and Uncertainty. New challenges will be addressed using emerging probabilistic technologies together with generalised uncertainty models, simulation techniques, algorithms and large-scale computing power. Skills required will be centred in the application of mathematics in areas of engineering, economics, financial mathematics, and psychology/social science, to reflect the complexity and inter-relationship of real world systems. The CDT addresses these needs with multi-disciplinary training and skills development on a common mathematical platform with associated computational tools tailored to user requirements. The centre reflects this concept with three major components: (1) Development and enhancement of mathematical and computational skills; (2) Customisation and implementation of models, tools and techniques according to user requirements; and (3) Industrial and overseas university placements to ensure industrial and academic impact of the research. This will develop graduates with solid mathematical skills applied on a systems level, who can translate numerical results into languages of engineering and other disciplines to influence end-users including policy makers. Existing technologies for the quantification and management of uncertainties and risks have yet to achieve their significant potential benefit for industry. Industrial implementation is presently held back because of a lack of multidisciplinary training and application. The Centre addresses this problem directly to realise a significant step forward, producing a culture change in quantification and management of risk and uncertainty technically as well as educationally through the cohort approach to PGR training.

Since the 2004 Energy Act, nuclear fission has rapidly grown, and continues to grow, in significance in the UK's Energy and Net Zero Strategies. Government's Nuclear Industrial Strategy states clearly that the nuclear sector is integral to increasing productivity, driving growth across the country and meeting our Net Zero target. Nuclear is, and will continue to be, a vital part of our energy mix, providing low carbon power now and into the future, and the safe and efficient decommissioning of our nuclear legacy is an area of world-leading expertise. In order for this to be possible we need to underpin the skill base. The primary aim of SATURN is to provide high quality research training in the science and engineering underpinning nuclear fission technology, focussed on three broad themes: Current Nuclear Programmes. Decommissioning and cleanup; spent fuel and nuclear materials management; geological disposal; current operating reactors (AGRs, Sizewell B, propulsion); new build reactors (Hinkley C, Sizewell C, possibly Wylfa Newydd; Future Nuclear Energy: Advanced nuclear reactors (light water reactors, including PWR3, gas cooled reactors, liquid metal cooled reactors, other concepts); advanced fuel cycles; fusion (remote handling, tritium); Nuclear Energy in a Wider Context: Economics and finance; societal issues; management; regulation; technology transfer (e.g. robotics, sensors); manufacturing; interaction of infrastructure and environment; systems engineering. It has become clear that skills are very likely to limit the UK's nuclear capacity, with over half of the civil nuclear workforce and 70% of Subject Matter Experts due to retire by 2025. High level R&D skills are therefore on the critical path for all the UK's nuclear ambitions and, because of the 10-15 year lead time needed to address this shortage, urgent action is needed now. SATURN is a collaborative CDT involving the Universities of Manchester, Lancaster, Leeds, Liverpool, Sheffield and Strathclyde, which aims to develop the next generation of nuclear research leaders and deliver underpinning (Technology Readiness Level (TRL) 1-3), long term science and engineering to meet the national priorities identified in Government's Nuclear Industrial Vision. SATURN also provides a pathway for mid technology level research (TRL 4-6) to be carried out by allowing projects to be based partly or entirely in an industrial setting. The consortium partners have been instrumental in a series of highly successful CDTs, Nuclear FiRST (2009-2013), NGN (Next Generation Nuclear, 2013-2018) and GREEN (Growing skills for Reliable, Economic Energy from Nuclear, 2018-2023). In collaboration with an expanded group of key nuclear industry partners SATURN will create a step-change in PhD training to deliver a high-quality PhD programme tailored to student needs; high profile, high impact outreach; and adventurous doctoral research which underpins real industry challenges.

Global warming, environmental change/degradation and human activities have led to an unprecedented threat to the world's biodiversity. How to quantify and estimate biodiversity change - how biodiversity is changing over time - has become one of the most pressing issues in biology, ecology, evolution, environmental science, bioinformatics, and related research fields. Robust and meaningful diversity measures that possess good mathematical/statistical properties and support biological reasoning about diversity are required. To date, most of the effort has been directed towards quantifying taxonomic diversity - i.e. species relative abundance and composition. However, it is now recognized that biodiversity has multiple dimensions and that it is essential to consider phylogenetic and functional diversity as well. Fortunately, remarkable progress in our understanding of phylogenies and the extensive collection of species traits opens the door to innovative approaches to the measurement and assessment of biodiversity change. At the same time, this is a complex challenge; collaboration among ecologists and mathematicians/statisticians is essential to tackle it. This project will bring together world experts in the assessment of biodiversity, in a new collaboration. Its goal is to develop an integrated mathematical and statistical framework to quantify and estimate changes in taxonomic, phylogenetic and functional diversity, focusing on the BioTIME database. The focus of the work will be ecological assemblages, and how they change through time. Project partners are Sandra Diaz (Argentina), a world leader in quantifying functional diversity, and Anne Chao (leading the MOST component of the work) who is globally renowned for her statistical contributions to the quantification of biodiversity. They will collaborate with the UK (St Andrews) team (Anne Magurran and Maria Dornelas) who have pioneered the quantification of biodiversity change in taxonomic diversity. The new methodology will permit rigorous analysis of diversity changes for alpha, beta and gamma diversities based on all three dimensions of biodiversity (taxonomic, functional, phylogenetic). Access to the BioTIME database (biotime.st-andrews.ac.uk), currently the world's largest repository of assemblage time series, will provide a proof of concept of the methodology. We will also develop appropriate user-friendly, self-interpreting software, complete with online versions, and maintain a website featuring all software and statistical tools developed in this project. By offering a number of short visiting fellowships to postdocs, who will have an opportunity to work on key components of the analyses, we will increase the global reach of the collaboration. A workshop will provide a further opportunity to disseminate findings and secure the future of the collaboration. The project will thus forge a strong partnership between researchers who have not had the opportunity to work together in the past, while providing innovative solutions to an urgent ecological challenge.

Exploiting the laws of quantum mechanics for the benefit of society in the so-called "second quantum revolution" is one of the greatest challenges of 21st-century physics. With such capability, we would be able to make quantum technologies that allow secure communication, quantum computers that outperform supercomputers, and quantum simulators of complex physical problems inaccessible to solve with current computing technologies. In order for this to happen, we need to efficiently produce particles, control their states, detect them and make them interact strongly with each other. Photons, quantum particles of light, are one of the most promising building blocks of future quantum technologies. We can easily detect and control their states and we can efficiently produce them individually. However, making them interact strongly to build a large quantum network is a notoriously difficult task because photons do not interact at low energies. To make them interact indirectly, we can hybridise them with other particles that do strongly interact and form new particles called 'polaritons'. In this project, we aim to hybridise photons with Rydberg excitons. Rydberg excitons are highly excited electron-hole pairs that can span macroscopic dimensions. Because of their macroscopic dimensions they strongly repel each other. The semiconductor device that we have chosen for hybridisation is a 2-dimensional semiconductor microcavity formed by two highly reflective mirrors encompassing nanocrystals and thin films of cuprous oxide. Photons confined in the microcavity strongly couple to Rydberg excitons in cuprous oxide to form Rydberg polaritons. The Rydberg polaritons interaction strength will be orders of magnitude higher than the current microcavity polaritons. This breakthrough will allow us to explore quantum optics at the single-particle limit and form 2-dimensional networks of strongly correlated photons for future single-photon switches and quantum simulators.