Our strategy for this research area aims to nurture not only intradisciplinary but also relevant interdisciplinary links by considering how best to invest in people and skills. It recognises the key underpinning role that algebraic research plays across the mathematical sciences, as well as the UK's world-leading position in the area.
We aim by the end of the Delivery Plan period, to have:
- Supported development of a research and training portfolio that sustains the UK's current position, building on key strengths (e.g. representation theory, group theory and non-commutative algebra) and nurturing new, leading research topics that aim to further connect algebra to other areas within mathematical sciences and beyond. We will achieve this by supporting novel research via standard-mode grants and continued support for researchers across all career stages, to maintain a balance of new researchers and research leaders
- Encouraged and supported establishment of new directions and synergies with other research areas within the mathematical sciences and other disciplines, such as Information and Communication Technologies (ICT) through the Theoretical Computer Science area
- Worked with the community to identify the most appropriate routes to maximise the impact of ongoing algebraic research and highlight it to the wider scientific community.
The UK has major strengths in many aspects of algebraic research (see strategic focus section). The 2014 Research Excellence Framework (REF) exercise emphasised that algebraic research is well-connected and geographically diverse within the UK, with support from a number of learned society and EPSRC network grants. (Evidence sources 1-5)
Algebra is a fundamental, underpinning research area that continues to have significant overlaps with subjects within the mathematical sciences and other research disciplines. Intradisciplinary overlaps continue to emerge, emphasised by significant crossover in research topics with, for instance, combinatorics, geometry, topology, mathematical analysis, mathematical physics and number theory; links have also been highlighted to other disciplines such as ICT. Through theoretical computer science and topics such as linear algebra and algebraic statistics, links have emerged that will make key contributions to data science. It is important, then, to continue to encourage links to centres such as the Alan Turing Institute. (Evidence sources 1-8)
Despite the UK's pedigree in algebraic research, it continues to operate below capacity. Recent years have seen a cycle of some researchers retiring while others are attracted to this stimulating research landscape. A key concern, common to all areas of the mathematical sciences, is to ensure adequate PhD training to facilitate emergence of a new generation of leading academics. Many Centres for Doctoral Training (CDTs) touch on algebraic research and are training PhD students in aspects of this field. It is also vitally important to go on supporting early-career researchers, and we aim to achieve this through support for fellowships. (Evidence sources 2-5, 8)
This area plays a key role underpinning all Outcomes on a longer timescale and is required to achieve many Ambitions, in particular:
C1: Enable a competitive, data-driven economy
C3: Deliver intelligent technologies and systems
C5: Design for an inclusive, innovative and confident digital society
Linear algebra and algebraic statistics currently play a key role in algorithm and data science research.
H2: Improve prevention and public health
H3: Optimise diagnosis and treatment
Analysis of large datasets has the potential to be better understood through algebraic research (e.g. through persistent homology).
R3: Develop better solutions to acute threats: cyber, defence, financial and health
By underpinning a variety of topics within theoretical computer science and algorithmic research, algebraic research can have an impact here. For instance, cyber-security, encryption and secure communication have a basis in fundamental algebraic research.
The influence of mathematics on the Productive Nation has also been widely established. (Evidence source 9)
- Research Excellence Framework (REF) exercise, (2014).
- REF 2014, Impact Case Studies, (2014).
- EPSRC, Pure Mathematics Evidence and Engagement Workshop Report, (2016).
- EPSRC Mathematical Sciences Regional Workshops 2016.
- EPSRC, Algebra Community Overview Document, (2016).
- Council for the Mathematical Sciences (CMS), Mathematical Sciences Driving the UK Economy Forward.
- European Research Council.
- CMS, The Mathematical Sciences People Pipeline, (2015).
- Deloitte, Measuring the Economic Benefits of Mathematical Science Research in the UK, (2012).