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.

In this proposal we seek to establish a Centre for Doctoral Training in Mathematical Analysis and its Applications. The main purpose of the centre is to train upwards of 60 new PhD students in this area over several years, and in doing so address the proven skills need for highly-trained researchers in this area. The centre will be founded on rigorous mathematical analysis and its applications, with a strong focus on nonlinear partial differential equations, under three broad themes: theoretical, stochastic and numerical. Its scope includes harmonic analysis, mathematical analysis of large-scale discrete structures, applied analysis, dynamical systems, stochastic analysis, financial mathematics, applied probability and computational mathematics. There will be a special emphasis on the connections and interactions between these areas, and their applications, and active collaboration with industry -- in the formulation of student projects, in mentoring PhD students, in developing work placements for the students, and more broadly in two-way knowledge exchange -- will be a key feature of this CDT. The need for mathematicians trained in this centre is manifest in real-world phenomena where cutting-edge differential and/or stochastic models are needed, for example in oil extraction, in power grid renewable energy strategies, in finance processes, in ecological impacts of climate change, and in procceses inside the brain. We shall provide a flow of such PhDs with multiple skill sets and the ability to deal with the sophisticated challenges arising in mathematical modelling: they will be able to both analyse and implement and will be in a position to mount rapid and agile responses to current and future challenges. MIGSAA training will be constructed on two main pillars: outstanding academic provision and early-stage career development. These are underpinned by development of a strong sense of cohort. As a fully integrated joint 4 year PhD programme, it will offer much more than the standard UK Mathematics PhD model. Initial academic training will build upon the firm foundation provided by SMSTC, and will feature a strong taught and assessed component. Students will also complete two assessed projects during their first year. It is intended that the two projects will span the areas of MIGSAA, and will provide a firm basis for choosing the topic for the main PhD dissertation towards the end of Year 1. The main PhD project, which will be challenging and substantial, will lead to original research findings at the cutting edge of mathematical endeavour. A tranche of specially designed, more advanced courses will be available for students in Year 2 and beyond so that students will continue to consolidate the available knowledge and expertise as they continue on their main research project. Students will be further supported by a carefully-planned programme of complementary research activities. There will be a strong focus on early-stage career development in its broadest sense. This will include training in public engagement, effective collaboration, understanding the impact agenda and responsible innovation, leadership, outreach, media training, engagement with industry and networking. Central to our vision for MIGSAA is the sense of cohort which it will foster. Beginning with the annual induction event, the cohort environment already offered by participation in SMSTC will be significantly enhanced by provision of contiguous office accommodation and dedicated common spaces, with Year 1 students collocated at ICMS in central Edinburgh. For the later years cohort activities include: physical attendance at higher level courses, research seminars and generic skills courses; active working groups encouraging peer-to-peer learning; annual residential symposia.

In a consortium led by Heriot-Watt with St Andrews, Glasgow, Strathclyde and Dundee, this proposal is for an EPSRC CDT in Applied Photonics and responds to the Integrative Technologies priority area, but also impacts on the Measurement and Sensing, Photonic Materials and Innovative Production Processes priorities. Technologies integrating photonics and electronics pervade products and services in any modern economy, enabling vital activities in manufacturing, security, telecommunications, healthcare, retail, entertainment and transport. The success of UK companies in this technology space is threatened by a lack of doctoral-level researchers with a grasp of photonic- / electronic-engineering design, fabrication and systems integration, coupled with high-level business, management and communication skills. By ensuring a supply of these individuals, our CDT will deliver broad-ranging impacts on the UK industrial knowledge base, driving the high-growth export-led sectors of the UK economy whose photonics-enabled products and services have far-reaching impacts on society, from consumer technology and mobile computing devices to healthcare and security. Building on the success of our current IDC in Optics and Photonics Technologies, the proposed CDT will again be configured as an IDC but will enhance our existing programme to meet industry's need for engineers able to integrate photonic and electronic devices, circuits and systems to deliver high value products and processes. Our proposal was developed in partnership with industry, whose letters of support show a commitment to sponsoring 71-74 EngD and 14-17 PhD projects -- 40% more than the minimum required -- demonstrating exceptional industrial engagement. Major stakeholders include Fraunhofer UK, NPL, Renishaw, Thales, BAE Systems, Gooch and Housego and Selex ES, who are joined by a number of SMEs. The CDT follows a model in which (annually) EPSRC funds 7 EngD students, with 3 more supported by industrial / university contributions. In a progressive strategy supported by our industrial partners, we will, where appropriate, align university-funded PhD projects to the programme to leverage greater industry engagement with PhD research in the consortium. The focus of the CDT corresponds to areas of research excellence in the consortium, which comprises 89 academic supervisors, whose papers since 2008 total 584 in all optics journals , with 111 in Science / Nature / PRL, and whose active EPSRC PI photonics funding is £40.9M. All academics are experienced supervisors, having each supervised on average >6 doctoral students, with many previously acting as IDC supervisors. The strategic commitment by the participating universities is evidenced by their recruitment since 2008 of 29 new academic staff in relevant areas (including 9 professors). An 8-month frontloaded residential phase in St Andrews and Glasgow will ensure the cohort strongly gels together, and will equip students with the technical knowledge and skills they need before they begin their industrial research project. Business modules (x3) will bring each cohort back to Heriot-Watt for 1-week periods, and weekend skills workshops will be used to regularly reunite the cohort, further consolidating it to create opportunities for peer-to-peer interactions. Taught courses will total 120 credits, and will be supplemented by new Computational Methods, Systems Integration and Research Skills workshops delivered by our industry partners, as well as public-engagement training led by Glasgow Science Centre. Another innovation is an International Advisory Board, comprising leading academics / industrialists , who will benchmark and advise on our performance. The requested EPSRC support of £4.5M is complemented by £2.8M of industrial / academic cash, covering the cost of 3 students in each cohort of 10. In-kind industrial / academic contributions are worth a further £5.4M, providing exceptional value.

Metals have a finite supply, thus metal scarcity and supply security have become worldwide issues. We have to ensure that we do not drain important resources by prioritizing the desires of the present over the needs of the future. To solve such a global challenge we need to move to a circular, more sustainable economy where we use the resources we have more wisely. One of the founding principles of a circular economy is that waste is an unused feedstock; that organic and inorganic components can be engineered to fit within a materials cycle, by the design, engineering and re-purposing of waste streams. In this fellowship I propose to design and engineer bacteria to repurpose our waste streams for us. I plan to use the new tools and techniques provided by advances in biology to engineer a microbe with the ability to upcycle critical metal ions from waste streams into high value nanoparticles. Certain bacteria have the ability to reduce metal cations and form precipitates of zero-valence, pure metals, as part of their survival mechanism to defend against toxic levels of metal cations. I will adopt the modular approach used in Synthetic Biology alongside iterative design, build and test cycles in order to enhance, manipulate and standardise the biomanufacture of these nanosize precipitates as high value products. With training in life cycle assessment, I will determine the financial benefits for business of adopting biological waste treatment methods with high value resource recovery and I will provide biogenic material to other researchers (academic and industrial) free of charge to encourage user pull for the technology.

The vision for Edinburgh's Centre for Mammalian Synthetic Biology (SynthSys-Mammalian) is to pioneer the development of the underpinning tools and technologies needed to implement engineering principles and realise the full potential of synthetic biology in mammalian systems. We have an ambitious plan to build in-house expertise in cell engineering tool generation, whole-cell modelling, computer-assisted design and construction of DNA and high-throughput phenotyping to enable synthetic biology in mammalian systems for multiple applications. In this way we will not only advance basic understanding of mammalian biology but also generate tools and technologies for near-term commercial exploitation in areas such as the pharmaceutical and drug testing industries, biosensing cell lines sensing disease biomarkers for diagnositics, novel therapeutics, production of protein based drugs e.g. antibodies and also programming stem cell development and differentiation for regenerative medicine applications. In parallel we will develop and implement new understanding of the social and economic impact of this far-reaching technology to ensure its benefits to society.