Probabilistic modelling permeates all branches of engineering and science, either in a fundamental way, addressing randomness and uncertainty in physical and economic phenomena, or as a device for the design of stochastic algorithms for data analysis, systems design and optimisation. Probability also provides the theoretical framework which underpins the analysis and design of algorithms in Data Science and Artificial Intelligence. The "CDT in Mathematics of Random Systems" is a new partnership in excellence between the Oxford Mathematical Institute, the Oxford Dept of Statistics, the Dept of Mathematics at Imperial College and multiple industry partners from the healthcare, technology and financial services sectors, whose goal is to establish an internationally leading PhD training centre for probability and its applications in physics, finance, biology and Data Science, providing a national beacon for research and training in stochastic modelling and its applications, reinforcing the UK's position as an international leader in this area and meeting the needs of industry for experts with strong analytical, computing and modelling skills. We bring together two of the worlds' best and foremost research groups in the area of probabilistic modelling, stochastic analysis and their applications -Imperial College and Oxford- to deliver a consolidated training programme in probability, stochastic analysis, stochastic simulation and computational methods and their applications in physics, biology, finance, healthcare and Data Science. Doctoral research of students will focus on the mathematical modelling of complex physical, economic and biological systems where randomness plays a key role, covering mathematical foundations as well as specific applications in collaboration with industry partners. Joint projects with industrial partners across several sectors -technology, finance, healthcare- will be used to sharpen research questions, leverage EPSRC funding and transfer research results to industry. Our vision is to educate the next generation of PhDs with unparalleled, cross-disciplinary expertise, strong analytical and computing skills as well as in-depth understanding of applications, to meet the increasing demand for such experts within the Technology sector, the Financial Service sector, the Healthcare sector, Government and other Service sectors, in partnership with industry partners from these sectors who have committed to co-funding this initiative. ALIGNMENT with EPSRC PRIORITIES This proposal reaches across various areas of pure and applied mathematics and Data Science and addresses the EPSRC Priority areas of (15. Mathematical and Computational Modelling), (22. Pure Mathematics and its Interfaces) ; however, the domain it covers is cross-disciplinary and broader than any of these priority areas taken in isolation. Probabilistic methods and algorithms form the theoretical foundation for the burgeoning area of Data Science and AI, another EPSRC Priority area which we plan to address, in particular through industry partnerships with AI/technology/data science firms. IMPACT By training highly skilled experts equipped to build, analyse and deploy probabilistic models, the CDT in Mathematics of Random Systems will contribute to - sharpening the UK's research lead in this area and training a new generation of mathematical scientists who can tackle scientific challenges in the modelling of complex, simulation and control of complex random systems in science and industry, and explore the exciting new avenues in mathematical research many of which have been pioneered by researchers in our two partner institutions; - train the next generation of experts able to deploy sophisticated data driven models and algorithms in the technology, finance and healthcare sectors

Global climate change threatens our future. Urgent societal action is demanded. However, crucial uncertainties regarding the future climate still need to be addressed. Extreme climate events are wreaking enormous environmental, societal, and economic tolls and they are becoming increasingly common and intense. The huge number of uncertainties related to our future climate combine with the sensitivity of the Earth's climate system to create extremely demanding challenges. Extending our understanding for deriving effective solutions demands interdisciplinary collaboration to determine the dominant factors in climate change. Currently, there is a lack of highly qualified mathematicians with the necessary training and experience to address the diverse problems and urgent challenges posed by climate change using computational and data-driven research. Our Centre for Doctoral Training (CDT) will train new cohorts of PhD students and build a scientific community to address the grand mathematical challenges raised by the significant levels of uncertainty in our future climate. The mission of our CDT will be to prepare graduates with strong mathematics, physics and engineering backgrounds to apply their skills in mathematical modelling, scientific computing, statistics and machine learning to key climate-related problems in oceanic, atmospheric and engineering contexts. By bringing together leading experts from Imperial College London, the University of Reading and the University of Southampton along with a wide range of external partners, our CDT will be uniquely placed to equip future mathematicians with the tools required to address global climate uncertainties. Our CDT will achieve its goals by developing the mathematics and its applications that are required to understand, better predict and, ultimately, respond to impending changes in the Earth's climate and the associated risks. A particular emphasis will be the creation of a vibrant environment to integrate strong cross-disciplinary engagement and collaboration, both within and between cohorts and disciplines, in advancing the range of scientific techniques, fundamental theories, approaches and applications. This will include engaging with academics, government organisations, industry and the public. As a result, the development of outstanding skills in mathematics and science communication will be a priority. The collaborative and peer-to-peer interactions will help develop the complementary techniques and approaches that will underpin essential technical research and innovation and will be coupled with exciting opportunities to discover and advance fundamental mathematics to provide practical solutions in climate science and beyond. Our CDT will act as a seed for growing the capability and capacity to inform decisions and efforts related to climate change on a rapid timescale. The technical focus of our CDT will be enhanced by activities to appreciate the social, political and economic dimensions of societal response to climate change. Furthermore, sustained efforts to mitigate and adapt to climate change will be required during the coming decades. For this reason, along with building a professional community of graduates, the CDT will invest in imaginative outreach programmes involving school pupils and undergraduates, building on opportunities through the institutions partnering with the CDT, including the Grantham Institute for Climate Change and the Environment, the National Oceanography Centre, the National Centre for Earth Observations, the UK Meteorological Office, the European Centre for Medium-Range Weather Forecasts, and the Natural History Museum.