Research PhD in Pure Mathematics: Geometry and Number Theory

CDT students taking this PhD Course will not select their supervisor until the end of year one and their project title andsummary will not be confirmed until they upgrade to PhD status at between 24 - 30 months into the course.

In an EPSRC-commissioned report by Deloitte, the impact of mathematical sciences research (MSR) was estimated as contributing 10% of UK jobs and 16% of UK gross value added (approximately £208 billion). The total GVA contribution in the UK in 2010 of MSR was £556 billion, or over 40% of total GVA. MSR underpins almost every aspect of the knowledge economy, and that economy requires ever more sophisticated theoretical ideas for continuing growth and competitiveness. The Deloitte report recognises also that the time-lag between curiosity-driven blue-skies research in MSR and technological innovation is often very long (many decades, typically) but when they do appear their impact can be enormous. The recent Bond Review, facilitated by EPSRC, makes a strong case for the impact of mathematics to the UK: 'Approximately 50% of the growth in productivity in the UK in recent decades has derived from the development and uptake of innovative processes and technologies. Innovation across the entire economy is a fundamental driver of living standards for the UK and mathematics is arguably the single most pervasive and powerful of all drivers of innovation in the world today.'

This CDT, which comprises a partnership between Imperial College London, King's College London and University College London, will deliver a high-level training programme in pure mathematics, integrating transferable skills activities as a central and challenging part of the programme. The students graduating from our CDT will thus have undergone a universal training which will equip them to respond to the widest possible range of future theoretical challenges, whether from environmental consultancy, hedge-fund management, intelligence agencies and software development, biotech companies, artificial intelligence (as highlighted recently by the PM) and visualisation of large data (as in priority area 30: Towards a Data-driven Future). Pure mathematics PhD graduates are therefore in high demand in a diverse range of sectors, as evidenced by our list of industrial partners, and, by taking up such roles in industry, they contribute directly to the competitiveness of the UK economy and quality of life.

Given the extremely high quality of our current students and their significant academic achievements thus far, we expect a significant proportion are likely to find employment in academia: of the 14 graduating in the summer, 9 already have confirmed postdoctoral positions. This indicates the success of the CDT in terms of recruitment, training and development of students into potential future research leaders, which will undoubtedly contribute directly to the future educational and academic needs of the UK over the coming decades. We also have several students who have either confirmed or are considering taking up positions in industry, with Credit Suisse, Goldman Sachs and Morgan Stanley as the potential or chosen employers. In this way, we also see the direct contribution of the LSGNT to the financial sector, in particular.

We have direct links to GCHQ, through the Heilbronn Institute for Mathematical Research (HIMR), which supports an LSGNT PhD studentship each year, involving summer internships at HIMR, and which views geometry and number theory as of critical importance to their work. Through this strong support and fruitful interaction with HIMR, the LSGNT gives an invaluable contribution to national security and, more widely, to applied research.

The LSGNT students, as they graduate, represent future industrial partners who understand the value of pure mathematics, and with whom the CDT has a direct connection. The LSGNT can utilize this link, allowing a growing and potentially powerful dialogue to develop between pure mathematics and industry, with mutual benefits for both, which is strongly aligned to the recommendations of the Bond Review.