CENTRE VISION Our vision for the new CDT in Financial Computing and Analytics is to as a national 'beacon' linking PhD & Masters' students, industry and academia in financial computing and analytics. We and our Industry partners are also central to the forthcoming investments in Big Data from EPSRC and ESRC (e.g. Business Datasafe). Its principal objective is to educate the next generation of elite PhDs with unparalleled, cross-disciplinary expertise in applied computing, analytics and financial mathematics, as well as in-depth sector understanding, to meet an increasing demand for their skills within the Financial Service Industry, Government, Retail and other Service sectors. Our existing DTC in Financial Computing is unique (there is no other research & training activity like it in the world) and by placing our PhD students in financial institutions and regulators it has had a major impact on the UK financial sector, as indicated by the Financial Times article (School for QUANTS) and our Letters of Support. The CDT is a new partnership between UCL, LSE and ICL, all providing MRes courses and PhD supervision. NATIONAL IMPORTANCE & GROWING NEED FOR CROSS-DISCIPLINARY SKILLS London is the world's leading international financial centre and the UK financial services industry is the key sector for the UK economy, contributed £124bn to the UK economy, generating a trade surplus of £36bn in 2010 and employing 1 million people. London is also the location for our financial regulators and world-class Retailers. Our Financial and other Service industries are therefore crucial to the UK's, and especially London's, continuing social and economic prosperity. Although we receive over 600 enquiries/applications per annum, and growing, recent reports by McKinsey and Accenture highlight the major and growing skills shortage of (postgrad) IT/data scientists in the USA 22,000 and the UK 4,000. EPSRC PRIORITIES AND RESEARCH The proposed CDT is aligned to EPSRC priorities across a number of Themes, in particular: Data to Knowledge (an ICT Theme priority), Industrially Focussed Mathematical Modelling (Mathematical Sciences) and New Digital Ventures (Digital Economy). The crucially important IT research challenges in just one area, namely the application of software engineering, AI and verification/correctness to algorithms for automated trading, illustrates the enormous research opportunities. IMPACT The current DTC in Financial Computing is acknowledged by the Department of Business Innovation & Skills as having had a major impact on our financial industry partners and on our academic partners. This will continue with the new CDT, impacting Regulators, government, Retailers and analytics companies. * STUDENTS - In 2011 the Centre funded more female PhD students than males, and in 2012 the Centre started 40 new PhD students if we count DTC funded students, students funded by other sources, such as retail and analytics companies, and industry-based part-time students. * ACADEMIA - UCL, LSE and Imperial College have all appointed new faculty in applied financial computing and business analytics; and UCL and ICL have started new Masters programmes. * INDUSTRY - many of the Banks now have established formal PhD programmes, in part due to the current DTC, and proved lecturers to the partners for industry-oriented programmes. * REGULATORS AND GOVERNMENT- we have placed PhD students in the BoE/FSA/PRA/FCA and the Cabinet Office, and as discussed in the Case for Support, we have held individual meetings and workshops with the Regulators (BoE, PRA, FCA) and with new (Retailer) partners (Tesco, BUPA, Unilever) to discuss how we can support them. * SOCIETAL - we encourage and support our PhD students in launching their own start-up, and we provide Masters and Undergraduate students to London-based start-ups, especially in the area called New Finance (e.g. P2P lending, crowdfunding).

Geometry and number theory are core disciplines within pure mathematics, with many repercussions across science and society. They are subjects that have attracted some of the best minds in mathematics since the time of the Ancient Greeks and continue to exert a natural fascination on professional and amateur mathematicians alike. Throughout the history of mathematics, both topics have often inspired major mathematical developments which have had enormous impact beyond their original applications. The fascination of number theory is exemplified by the story of Fermat's last theorem, the statement of which was written down in 1637 and which is simple enough to be understood by anyone familiar with high school mathematics. It took more than 350 years of hard work and significant developments across mathematics before Wiles's celebrated proof was finally published in 1995. Wiles's proof, for which he was awarded the prestigious Abel Prize in 2016, involves a mixture of ideas from number theory and geometry, and the interplay between these topics is one of the most active areas of research in pure mathematics today. For example, the work of Ngo on the Langland's program (for which he was awarded the Fields Medal in 2010, the highest honour in mathematics) and Scholze on arithmetic algebraic geometry (for which he was offered a New Horizons in Mathematics Breakthrough Prize in 2016, and is expected to be awarded the Field Medals this year), show the significant impact of geometric ideas on number theory. In the other direction, number theory has been used to prove conjectures in geometry, including a path proposed by Kontsevich (Fields Medal 1998, Breakthrough Prize 2015) and Soibelman to help solve one of the major open problems in geometry, the SYZ conjecture, which lies at the interface of geometry and theoretical physics. These and other connections between geometry and number theory continue to lead to some of the most exciting research developments in mathematics. This CDT will be run by a partnership of researchers at Imperial College London, King's College London, and University College London, which together form the largest and one of the strongest UK centres for geometry and number theory. By training mathematicians to PhD level in geometry and number theory, and by ensuring that more general skills (for example, computing, communication, teamwork, leadership) are embedded as a demanding and enjoyable part of our programme, this CDT will deliver the next generation of highly trained researchers able to contribute not only to the UK's future educational needs but also to those of the financial and other high-tech industries. Our graduates will contribute directly to national security (GCHQ is, for example, a user of high-end pure mathematics) but also more indirectly as employees in industries which value the creative and novel approach that mathematicians typically bring to problem solving.

Lancaster University, together with a formidable consortium of industrial and third-sector partners, proposes a Centre for Doctoral Training (CDT) aimed at cultivating international research leaders in Statistics and Operational Research (STOR) through a programme in which real-world challenge is the catalyst for cutting-edge methodological advancement. Our partners face a challenging reality: the demand for highly-trained STOR data specialists consistently exceeds the available supply. This situation is exacerbated by the ever-growing significance of data in both the economy and society. Our proposal directly addresses this pressing demand, focussing on the priority area "meeting a user-need". The newly envisioned Centre builds upon the strengths and knowledge derived from an existing, internationally recognised EPSRC CDT. Expanding upon this foundation and with the input of an enlarged partner network, including blue-chip companies, SMEs, and third-sector organisations, we propose a Centre poised to recruit and train 70 students across five cohorts. This program will harness industrial and charitable challenges as inspirational springboards for conducting the highest calibre research. The new programme will innovate by * Developing a new MRes programme co-designed and delivered with our partners; * Including a comprehensive training programme on advanced, reproducible programming for STOR, co-ordinated by the Centre's dedicated, industry-funded, Research Software Engineer; * Embedding industrial and third-sector collaboration throughout the student experience; * Hosting seeded research clusters: vibrant, cross-cohort, cross-sector retreats to explore and develop early-stage challenges emerging from the shared interests of STOR-i and its partners; * Developing an ambitious doctoral exchange programme with highly regarded international university partners, comprising student exchanges, co-supervision and shared training activities. Our partners play an integral role in the Centre's plans, with 80% of doctoral projects adopting a CASE-like approach, receiving co-funding and co-supervision from industrial partners. All other students will engage in industrial research internships. Additionally, partners will lead problem-solving events, data immersion experiences, and contribute to Continuing Professional Development (CPD) activities such as leadership talks, fireside chats, and advanced programming training. The partnership is deeply committed to ensuring the broader impact of STOR-i as a national resource. To this end, the Centre will establish a suite of funded activities open to all UK STOR doctoral students. These include an annual STOR summer school with an emphasis on leadership skills, advanced programming, and a data dive focused on charitable endeavours. Additionally, students will have access to masterclasses and research visits. STOR-i will deliver a wide range of benefits and scientific outcomes to the end-user community, underpinned by three fundamental pillars: 1. People: Our CDT will inject 70 highly talented, diverse PhD graduates into the field, armed with the technical, interpersonal, and leadership skills essential for flourishing careers in STOR across a range of sectors. These graduates will serve as catalysts for innovation, driving cutting-edge research, and enhancing the UK's economic competitiveness. 2. Knowledge: The CDT will generate a wealth of cutting-edge research, disseminated in top STOR journals, and presented at major international conferences. This research will tackle substantial real-world challenges, yielding fresh insights and breakthroughs in STOR. 3. Impact: Our CDT will make a tangible difference in society and the economy by producing (i) case studies and (ii) a repository of documented and reproducible software, available to the public. This will facilitate widespread adoption of our research, leading to meaningful societal and economic impact.