We live in the "Era of Mathematics" (UKRI, 2018), in which mathematics research has deep and widespread impact. Medical imaging is enhanced using the theory of inverse problems. Predicting sewage contamination in waterways after storms requires solving complicated systems of hydrodynamic equations. Machine learning tools are revolutionising data-intensive computing and, handled with proper mathematical care, have vast potential benefits for science and society. These are examples of the ongoing explosion in mathematical innovation driving, and being driven by, the analysis and modelling of data running through every aspect of life. Cutting-edge research now sits at the interface of data science and mathematical modelling. Methods and fields such as compressed sensing, stochastic optimisation, neural networks, Bayesian hierarchical models - to name but a few - have become interwoven and contributed to the delivery of a new domain of research. We refer to this research interface as "statistical applied mathematics". Established in 2014, the Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa, samba.ac.uk) delivers leading research and training in this space. In the development of this bid, we have consulted widely with academic, industrial, and governmental partners, who consistently report a large and widening gap between demand and supply for highly skilled graduates. Our vision is to create a new generation of statistical applied mathematicians ready to lead high-impact, data-driven, mathematically-robust research in academia and industry. We will nurture a vibrant culture of cohort learning, enabling internationally-leading training in modern mathematical data science. A particularly important research focus will be the synthesis of data-driven methods with robust mathematical modelling frameworks. Tomorrow's industrial mathematicians and statisticians must understand when machine learning tools are (and are not) appropriate to use and be able to conduct the underpinning research to improve these tools by integrating scientific domain knowledge. This research challenge is informed by deep partnerships with a range of industry and government bodies. Our long-term partners such as BT, Syngenta, Novartis, the NHS, and the Environment Agency co-create our vision and our training. They are emphatic that we must address the urgent need for mathematical data science talent in this key strategic area for the UK economy. Many of our students will work directly on industry challenges during their PhD either in their core research or with internships. Our unique Integrative Think Tanks are the key mechanism for exploring new research ideas with industry. These are week-long events where SAMBa students, leading academics, and partners work together on industrial and societal problems. SAMBa graduates will be able to develop and apply new ideas and methods to harness the power of data to tackle challenges affecting society, the economy, and the environment. Our students will move into academia, providing sustainability to the UK's capacity in this field, as well as industry and government, providing impact through societal benefits and driving economic growth. Many alumni now hold permanent positions at leading UK universities and senior positions in a range of businesses. The CDT will be embedded within the University of Bath's Department of Mathematical Sciences, where 98% of the research is world leading or internationally excellent (REF2021). The CDT is supported by 58 academics in maths, with similar numbers of co-supervisors from industry and other departments. The centre will be co-delivered with 22 industry and government partners. A vital international perspective is provided by a worldwide network of 11 academic institutions sharing our scientific vision.

Recent years have seen increased global policy concern with the management and governance of fresh-water resources. From a humanitarian perspective, the United Nations aims to tackle 'global challenges' associated with water access. From the perspective of international law, a growing body of multilateral agreements aims to ensure countries have fair access to trans-border rivers. Against this policy background, the social sciences pay increasing attention to fresh water as a scarce global resource requiring careful management. Unlike other economically significant resources like coal and oil, water is regarded as supremely important as it is essential for the maintenance and reproduction of life on earth. This project aims to explore the politics of managing, and planning the management of, trans-border rivers on water resource frontiers. In such contexts the actions of 'upstream' riparian states affect those in 'downstream' ones, and so often have strategically, politically and economically significant consequences. In particular, we aim to understand how these politics of management work in contexts where multilateral legal agreements on trans-border river use are eschewed. These aims frame and support a range of objectives. We seek to understand contexts in which participation in multilateral agreements on equitable access to trans-border rivers are unappealing. We aim to understand how, in the absence of such agreements, the management of such rivers works - or does not work - in practice. And we propose examining the frictions caused by the intersection of different national laws in relation to trans-border rivers. The river Selenga, which runs from Mongolia into Russia's Lake Baikal, provides an exemplary case study. The Selenga is divided between two countries (Mongolia and Russia), and is the object of extensive Chinese economic and political interest. Unhindered by multilateral agreements, each country harbours different national interests in relation to the Selenga. Mongolia strives for energy security by planning hydroelectricity plants on the Selenga and its tributaries. Russia aims to preserve the unique ecology and cultural significance of Lake Baikal by protecting its water inflow from the Selenga. China seeks to fuel economic growth in its arid northwest and central agricultural provinces with water abstracted from the river. Legal studies thoroughly examine trans-border river disputes, and political science documents international relations in Inner Asian regions. But little is known about the day-to-day realities of managing the Selenga and their wider political, economic and cultural implications for this geopolitically sensitive region. Using the Selenga as an example, this project draws on the methods and theories of Social Anthropology to provide a critically important means for understanding trans-border river management. Anthropological approaches are inherently suitable for examining the social relations through which management plans and proposals are conceptualised, implemented and worked through in everyday life. Six field-sites spanning Mongolia, Russia and China have been selected for their importance in generating data to support project aims and objectives. Academic beneficiaries include UK and global scholars from disciplines including Social Anthropology, Law and International Relations. They will benefit from new perspectives on resource nationalism, sovereignty, and infrastructure generated by the project. Other beneficiaries include regional NGOs advocating for sustainable water resource management policies, policy units interested in trans-border river governance and the reach of international law, and residents of the Selenga river basin and other areas connected to its management.