This Centre for Doctoral training in Industrially Focused Mathematical Modelling will train the next generation of applied mathematicians to fill critical roles in industry and academia. Complex industrial problems can often be addressed, understood, and mitigated by applying modern quantitative methods. To effectively and efficiently apply these techniques requires talented mathematicians with well-practised problem-solving skills. They need to have a very strong grasp of the mathematical approaches that might need to be brought to bear, have a breadth of understanding of how to convert complex practical problems into relevant abstract mathematical forms, have knowledge and skills to solve the resulting mathematical problems efficiently and accurately, and have a wide experience of how to communicate and interact in a multidisciplinary environment. This CDT has been designed by academics in close collaboration with industrialists from many different sectors. Our 35 current CDT industrial partners cover the sectors of: consumer products (Sharp), defence (Selex, Thales), communications (BT, Vodafone), energy (Amec, BP, Camlin, Culham, DuPont, GE Energy, Infineum, Schlumberger x2, VerdErg), filtration (Pall Corp), finance (HSBC, Lloyds TSB), food and beverage (Nestle, Mondelez), healthcare (e-therapeutics, Lein Applied Diagnostics, Oxford Instruments, Siemens, Solitonik), manufacturing (Elkem, Saint Gobain), retail (dunnhumby), and software (Amazon, cd-adapco, IBM, NAG, NVIDIA), along with two consultancy companies (PA Consulting, Tessella) and we are in active discussion with other companies to grow our partner base. Our partners have five key roles: (i) they help guide and steer the centre by participating in an Industrial Engagement Committee, (ii) they deliver a substantial elements of the training and provide a broad exposure for the cohorts, (iii) they provide current challenges for our students to tackle for their doctoral research, iv) they give a very wide experience and perspective of possible applications and sectors thereby making the students highly flexible and extremely attractive to employers, and v) they provide significant funding for the CDT activities. Each cohort will learn how to apply appropriate mathematical techniques to a wide range of industrial problems in a highly interactive environment. In year one, the students will be trained in mathematical skills spanning continuum and discrete modelling, and scientific computing, closely integrated with practical applications and problem solving. The experience of addressing industrial problems and understanding their context will be further enhanced by periods where our partners will deliver a broad range of relevant material. Students will undertake two industrially focused mini-projects, one from an academic perspective and the other immersed in a partner organisation. Each student will then embark on their doctoral research project which will allow them to hone their skills and techniques while tackling a practical industrial challenge. The resulting doctoral students will be highly sought after; by industry for their flexible and quantitative abilities that will help them gain a competitive edge, and by universities to allow cutting-edge mathematical research to be motivated by practical problems and be readily exploitable.

We are in a biodiversity crisis. A million species of plants and animals are threatened with global extinction, and wildlife populations across much of the planet have been dramatically reduced, perhaps by as much as a half in recent decades. This is of profound concern because biodiversity underpins human existence. Biodiversity provides the foundation of our economies, livelihoods, food security, health and quality of life. Increasing numbers of people, organisations and governments recognise the need to reverse the perilous state of our ecological inheritance. However, while there is unprecedented willingness to act, what we do not know is what will work most effectively to renew biodiversity and ensure continued delivery of its benefits. The Renewing biodiversity through a people-in-nature approach (RENEW) programme will develop solutions to the renewal of biodiversity. We will work, with a sense of urgency, to reshape understanding and action on biodiversity renewal across scales, creating knowledge at the cutting edge of global debates and policy development, and influencing national institutions, communities and individuals. We know that understanding of, and action on, renewal must take a step change and we will focus on the agency of people in nature, both as part of the problem and as the solution. We focus on a set of challenges: how popular support for biodiversity renewal can be harnessed; how populations that are disengaged, disadvantaged, or disconnected from nature can benefit from inclusion in solutions development; how renewal activities can be designed and delivered by diverse sets of land-managers and interest groups; and how biodiversity renewal can most effectively be embedded in finance and business activities (as has occurred with carbon accounting and climate change). This sits alongside the scientific and technical development necessary to underpin solutions options. Biodiversity renewal is a complex and whole system problem. The solutions require the creation of a new kind of inclusive and diverse research community, one that transcends traditional boundaries between the disciplines needed to tackle the environmental crises of the Anthropocene. Solutions also need to address the inequalities and lack of diversity found in current renewal practices. RENEW has therefore prioritised partnership building, to allow us to combine research with experiment, learning, sharing, outreach and impact, across relevant organisations and wider communities. Our approach means that practical impact is guaranteed. With the National Trust as co-owners of RENEW, we will have significant reach through their membership, outreach programs and public voice. Alongside other key partners in RENEW, our links are responsible for or have influence over much of the UK landscape in which biodiversity renewal activities need to occur. We will use the many landscape-scale nature activities currently underway (or planned in the near future) to develop learning, as if they were 'real time' experiments. The UK is one of the most biodiversity depleted countries in the world. Our ways of working in RENEW, the knowledge we develop, and the solutions we propose, will be of international importance. The lessons we learn will enable future biodiversity researchers and practitioners around the world to do better science, and deliver fairer outcomes.

NEASQC is devoted to the emergence of practical applications of quantum computing in its NISQ era, and to the construction of a strong community. NEASQC is use-case centric and organized around 10 real use cases (UC). These UC have been defined by the industrial members and validated by the academic members as NISQ compatible. Each use case will be investigated with a rigorous methodology by an integrated team made of at least one industrial and one academic: 1-Algorithm research and design 2-Development of a prototype software 3-Qualification of the prototype with real data on real or simulated NISQ device 4-Benchmark against state-of-the-art techniques. NEASQC is coordinated by Bull, the Atos subsidiary in charge of Quantum Computing, developer of the QLM/myQLM quantum programming platform. Bull will act as the integrator of NEASQC software deliverables and will guarantee their industrial quality. An important objective of our project is to build an active European community of applied QC. As such, much attention is paid to dissemination, with a significant number of actions toward a large number of end-user communities. The project will welcome associate end users all along. NEASQC will build quantum computing open source libraries out of the use case developments. These libraries will be delivered to the European QT community all along the project, through the project portal. A ready-to-install quantum programming environment (QPE) will be built and made available for free to the community, starting from year 2. NEASQC will work with the flagship funded hardware projects to ensure the QPE is compatible with their platforms. In particular, our libraries will be optimized for each platform. NEASQC does believe in HW/SW co-design, and will define a series of use-case specific benchmarks, to help guide the hardware effort toward the highest efficiency on applications

The UKRI Centre for Doctoral Training in "Application of Artificial Intelligence to the study of Environmental Risks" will develop a new generation of innovation leaders to tackle the challenges faced by societies across the globe living in the face of environmental risk, by developing new methods that exploit the potential of Artificial Intelligence (AI) approaches to the proper analysis of complex and diverse environmental data. It is made of multiple departments within Cambridge University, alongside the British Antarctic Survey and a wide range of partners in industry and policy. AI offers huge potential to transform our ability to understand, monitor and predict environmental risks, providing direct societal benefit as well as potential commercial opportunities. Delivering the UN 2030 Sustainable Development Agenda and COP 21 Paris Agreement present enormous and urgent challenges. Population and economic growth drive increased demands on a planet with finite resources; the planet's biodiversity is suffering increasing pressures. Simultaneously, humanity's vulnerabilities to geohazards are increasing, due to fragilities inherent in urbanisation in the face of risks such as floods, earthquake, and volcanic eruptions. Reliance on sophisticated technical infrastructures is a further exposure. Understanding, monitoring and predicting environmental risks is crucial to addressing these challenges. The CDT will provide the global knowledge leadership needed, by building partnership with leaders in industry, commerce, policy and academia in visionary, creative and cross-disciplinary teaching and research. Vast and growing datasets are now available that document our changing environment and associated risks. The application of AI techniques to these datasets has the potential to revolutionise our ability to build resilience to environmental hazards and manage environmental change. Harnessing the power of AI in this regard will support two of the four Grand Challenges identified in the UK's Industrial Strategy, namely, to put the UK at the forefront of the AI and data revolution and to maximise the advantages for UK industry from the global shift to clean growth. The students in the CDT will be trained in a broad range of aspects of the application of AI to environmental risk in a multi- disciplinary and enthusing research setting, to become world-leaders in the arena. They will undertake media training activities, public engagement, and training in the delivery of policy advice as well as the development of entrepreneurial skills and an understanding of the approach of business to sustainability. Discussion of the broader societal, legal and ethical dimensions will be integral to this training. In this way the CDT will seed a new domain of AI application in the UK that will become a champion for the subject globally.

Observed, Strategic, sustained action is now needed to avoid further negative consequences of climate change and to build a greener, cleaner and fairer future. According to the Intergovernmental Panel on Climate Change the rise in global temperature is largely driven by total carbon dioxide emissions over time. In order to avoid further global warming, international Governments agreed to work towards a balance between emissions and greenhouse gas removal (GGR), known 'net zero', in the Paris Agreement. In June 2019 the UK committed to reaching net zero emissions by 2050, making it the first G7 country to legislate such a target. Transitioning to net zero means that we will have to remove as many emissions as we produce. Much of the focus of climate action to date has been on reducing emissions, for example through renewable power and electric vehicles. However, pathways to net zero require not just cutting fossil fuel emissions but also turning the land into a net carbon sink and scaling up new technologies to remove and store greenhouse gases. This will require new legislation to pave the way for investment in new infrastructure and businesses expected to be worth billions of pounds a year within 30 years. This challenge has far-reaching implications for technology, business models, social practices and policy. GGR has been much less studied, developed and incentivised than actions to cut emissions. The proposed CO2RE Hub brings together leading UK academics with a wide range of expertise to co-ordinate a suite of GGR demonstration projects to accelerate progress in this area. In particular the Hub will study how we can (1) reduce technology costs so that GGR becomes economically viable; (2) ensure industry adopts the concept of net zero in a way that will maintain and create jobs; (3) put in place sensible policy incentives; (4) make sure there is social license for GGR (unlike fracking or nuclear); (5) set up regulatory oversight of environmental sustainability and risks of GGR; (6) understand what is required to achieve GGR at large scale and (7) guarantee there are the skills and knowledge required for all this to happen. Building on extensive existing links to stakeholders in business, Government and NGOs, the Hub will work extensively with everyone involved in regulating and delivering GGR to ensure our research provides solutions to strategic priorities. We will also encourage the teams working on demonstrator technologies to think responsibly about the risks, benefits and public perceptions of their work and consider the full environmental, social and economic implications of implementation from the outset. CO2RE will seek to bring the GGR community in the UK as a whole closer together, functioning as a gateway to UK inter-disciplinary research expertise on GGR. We will inform, and stay informed, about the latest developments nationally and internationally, and reach out to engage the wider public. In doing so we will be able to respond to a rapidly evolving landscape recognising that technical and social change are not separate, but happen together. To accelerate and achieve meaningful change, we will be guided by consultation with key decision-makers and the general public, and set up a £1m flexible fund to respond to priorities that emerge with the help of the wider UK academic community. Ultimately we will help the UK and the world understand how GGR can be scaled up responsibly as part of climate action to meet the ambition of net zero.