Seabed sediment represents a significant sink for carbon (C) and represents a major natural asset. Bottom-trawl fishing provides a quarter of global seafood but is also the most extensive anthropogenic physical disturbance to sediment C stocks with recent evidence suggesting that seabed disturbance could result in significant greenhouse gas release from the seabed and to the atmosphere. There are major uncertainties in our understanding of the effect of disturbance on seabed C stores and air/sea CO2 fluxes (in both magnitude and direction). Consequently, the impact of seabed disturbances on C are largely unquantified and currently unregulated. This project will determine how the disturbance associated with bottom trawling modifies C storage, cycling and air/sea CO2 fluxes. For the first time, the impact of trawling on sediment-water and air-sea CO2 exchange will be assessed holistically, providing essential guidance on seabed activity management policies that mitigate climate impacts and help achieve net-zero. The project will answer all four questions defined in the Highlight Topic call: How do fishing gear, trawling frequency and the sedimentary environment affect the potential for marine sediments to act as a net source of CO2? How does C resuspended due to trawling modulate seawater chemistry and what is the fate of the resuspended C? How do horizontal and vertical mixing, water column production and respiration affect the potential for trawl-driven biogeochemical change to result in impacts on air-sea exchanges? Will management interventions result in the reduction of C loss and CO2 emissions and recovery of seabed sediment C stocks? The project comprises of 4 integrated work packages (WPs) that directly address these 4 questions. WP1 will characterise sediment pore waters and quantify the stocks of POC and PIC in the sediment and will identify how trawl gears affect the fluxes of C under different environmental settings. WP2 will characterise changes in the water column and suspended C and sediment and establish its fate in the water column after trawl disturbance. WP3 will quantify the exchange of sub-surface trawl plumes with the surface mixed layer and resultant seawater CO2 and air/sea fluxes. WP1-3 will generate novel insights about the mechanisms through which disturbance affects C fluxes and transformations. A focussed campaign of ship-based experiments will be used to inform and improve model assessments. We selected four representative sites that allow understanding of processes in contrasting environmental settings. The 3 integrated WPs will inform and improve models, which will be used to upscale and extend the spatial and temporal assessment of trawling impacts. These spatial assessments will feed into WP4, which will evaluate and identify the most effective seabed C stock management measures in collaboration with stakeholders from policy, fishing industry, eNGOs and green finance. This research will link processes, impact and mitigation of CO2 emissions due to seabed disturbance. The outcomes of the research will inform environmental solutions by avoiding emissions from seabed sediments while maintaining food production, which sits at the centre of the NERC, UKRI, DEFRA and UK strategies for clean growth and achieving net-zero. This project will make a step change in our understanding of how trawling impacts C dynamics in shelf seas and will diminish the risk of under-valuing natural climate regulation by facilitating cost-benefit analysis and risk assessments.

This CDT will create a cohesive, internationally-leading, cross-domain training and research community fusing algebraic, geometric and quantum methods across Algebra, Geometry and Topology, Mathematical Physics, and their Interfaces. The scientific aim of our CDT is no less than to develop new foundations unifying all three disciplines, and in the process to bolster and future-proof UK capability in mathematics. The breadth of mathematical mastery necessary to achieve these aims, on which our training programme is based, is of the highest international standard, and training students in this area requires both the deep focus and the wide scope which only the resources of a CDT can enable. Our three scientific areas Algebra, Geometry and Quantum Fields are established, flagship, internationally-leading areas of UK mathematical strength. Algebra: quite simply *the* language, and controlling structure, of symbolic computation and symmetry. Geometry: the mathematically rigorous foundations of our human spatial and visual intuition. Quantum Fields: the mathematical incarnation of our quantum physical reality. A hallmark feature of 21st century mathematics is the dramatically increased synergy and inter-dependence between these three fundamental disciplines. Whereas in centuries past mathematics and physics interacted primarily through analysis and calculus, the advent of quantum mechanics posits a fundamentally different, fundamentally algebraic, set of laws for the universe. Geometry enters irrevocably when we pose quantum mechanical laws in the presence of fields, such as the electro-magnetic and gravitational fields, which permeate throughout time and space. A surprising and thrilling discovery of 21st century mathematics has been that the mathematically rigorous study of quantum fields yields some of the most powerful predictive theories within algebra and geometry, even to questions with no a priori physical formulation. These fundamental scientific developments have had a vast and direct impact on our modern world, and on a remarkably short timescale. Algebra, geometry and quantum fields are the driving force behind key developments such as internet search, quantum computation, machine learning, and both classical and quantum cryptography. Society and industry need the students we will train. Our graduates' skills are both fundamentally transferable and widely applicable across many external partnerships and stakeholders. The Deloitte report, commissioned by EPSRC, attributed 2.8M jobs and £200BN of the UK economy to mathematical sciences research, highlighting R&D, computing/tech, public administration, defence, aerospace and pharmaceuticals as economic sectors requiring graduates with advanced mathematical training. Sustainable energy consulting has since emerged as a further industry requiring ever-advanced mathematical sophistication. Crucially a physical and mathematical powerhouse needs to be a diverse powerhouse, yet the traditional structure of training in these areas has inhibited diversity of entrants, both to career academia and to industry. Building on our track record, and equipped with the resources and flexibility only a CDT can provide, we will create a diverse and confident cohort, equipped with the mathematical skillsets needed for our tech-led future to flourish, and able to influence a wide range of people, sectors and institutions.

The Centre for Doctoral Training MAC-MIGS will provide advanced training in the formulation, analysis, and implementation of state-of-the-art mathematical and computational models. The vision for the training offered is that effective modern modelling must integrate data with laws framed in explicit, rigorous mathematical terms. The CDT will offer 76 PhD students an intensive 4-year training and research programme that equips them with the skills needed to tackle the challenges of data-intensive modelling. The new generation of successful modelling experts will be able to develop and analyse mathematical models, translate them into efficient computer codes that make best use of available data, interpret the results, and communicate throughout the process with users in industry, commerce and government. Mathematical and computational models are at the heart of 21st-century technology: they underpin science, medicine and, increasingly, social sciences, and impact many sectors of the economy including high-value manufacturing, healthcare, energy, physical infrastructure and national planning. When combined with the enormous computing power and volume of data now available, these models provide unmatched predictive tools which capture systematically the experimental and observational evidence available. Because they are based on sound deductive principles, they are also the only effective tool in many problems where data is either sparse or, as is often the case, acquired in conditions that differ from the relevant real-world scenarios. Developing and exploiting these models requires a broad range of skills - from abstract mathematics to computing and data science - combined with expertise in application areas. MAC-MIGS will equip its students with these skills through a broad programme that cuts across disciplinary boundaries to include mathematical analysis - pure, applied, numerical and stochastic - data-science and statistics techniques and the domain-specific advanced knowledge necessary for cutting-edge applications. MAC-MIGS students will join the broader Maxwell Institute Graduate School in its brand-new base located in central Edinburgh. They will benefit from (i) dedicated academic training in subjects that include mathematical analysis, computational mathematics, multi-scale modelling, model reduction, Bayesian inference, uncertainty quantification, inverse problems and data assimilation, and machine learning; (ii) extensive experience of collaborative and interdisciplinary work through projects, modelling camps, industrial sandpits and internships; (iii) outstanding early-career training, with a strong focus on entrepreneurship; and (iv) a dynamic and forward-looking community of mathematicians and scientists, sharing strong values of collaboration, respect, and social and scientific responsibility. The students will integrate a vibrant research environment, closely interacting with some 80 MAC-MIGS academics comprised of mathematicians from the universities of Edinburgh and Heriot-Watt as well as computer scientists, engineers, physicists and chemists providing their own disciplinary expertise. Students will benefit from MAC-MIGS's diverse network of more than 30 industrial and agency partners spanning a broad spectrum of application areas: energy, engineering design, finance, computer technology, healthcare and the environment. These partners will provide internships, development programmes and research projects, and help maximise the impact of our students' work. Our network of academic partners representing ten leading institutions in the US and Europe, will further provide opportunities for collaborations and research visits.

The Scottish Doctoral Training Centre in Condensed Matter Physics, known as the CM-DTC, is an EPSRC-funded Centre for Doctoral Training (CDT) addressing the broad field of Condensed Matter Physics (CMP). CMP is a core discipline that underpins many other areas of science, and is one of the Priority Areas for this CDT call. Renewal funding for the CM-DTC will allow five more annual cohorts of PhD students to be recruited, trained and released onto the market. They will be highly educated professionals with a knowledge of the field, in depth and in breadth, that will equip them for future leadership in a variety of academic and industrial careers. Condensed Matter Physics research impacts on many other fields of science including engineering, biophysics, photonics, chemistry, and materials science. It is a significant engine for innovation and drives new technologies. Recent examples include the use of liquid crystals for displays including flat-screen and 3D television, and the use of solid-state or polymeric LEDs for power-saving high-illumination lighting systems. Future examples may involve harnessing the potential of graphene (the world's thinnest and strongest sheet-like material), or the creation of exotic low-temperature materials whose properties may enable the design of radically new types of (quantum) computer with which to solve some of the hardest problems of mathematics. The UK's continued ability to deliver transformative technologies of this character requires highly trained CMP researchers such as those the Centre will produce. The proposed training approach is built on a strong framework of taught lecture courses, with core components and a wide choice of electives. This spans the first two years so that PhD research begins alongside the coursework from the outset. It is complemented by hands-on training in areas such as computer-intensive physics and instrument building (including workshop skills and 3D printing). Some lecture courses are delivered in residential schools but most are videoconferenced live, using the well-established infrastructure of SUPA (the Scottish Universities Physics Alliance). Students meet face to face frequently, often for more than one day, at cohort-building events that emphasise teamwork in science, outreach, transferable skills and careers training. National demand for our graduates is demonstrated by the large number of companies and organisations who have chosen to be formally affiliated with our CDT as Industrial Associates. The range of sectors spanned by these Associates is notable. Some, such as e2v and Oxford Instruments, are scientific consultancies and manufacturers of scientific equipment, whom one would expect to be among our core stakeholders. Less obviously, the list also represents scientific publishers, software houses, companies small and large from the energy sector, large multinationals such as Solvay-Rhodia and Siemens, and finance and patent law firms. This demonstrates a key attraction of our graduates: their high levels of core skills, and a hands-on approach to problem solving. These impart a discipline-hopping ability which more focussed training for specific sectors can complement, but not replace. This breadth is prized by employers in a fast-changing environment where years of vocational training can sometimes be undermined very rapidly by unexpected innovation in an apparently unrelated sector. As the UK builds its technological future by funding new CDTs across a range of priority areas, it is vital to include some that focus on core discipline skills, specifically Condensed Matter Physics, rather than the interdisciplinary or semi-vocational training that features in many other CDTs. As well as complementing those important activities today, our highly trained PhD graduates will be equipped to lay the foundations for the research fields (and perhaps some of the industrial sectors) of tomorrow.

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