Area of investment and support

Algebra

Algebra stems from the study of equations, their solutions and associated operations and symmetries, including group theory, representation theory and ring theory.

• Partners involved: Engineering and Physical Sciences Research Council (EPSRC)

The scope and what we're doing

Algebra stems from the study of equations, their solutions and associated operations and symmetries, including group theory, representation theory and ring theory.

We aim to:

• support development of a research and training portfolio that sustains the UK’s current position, building on key strengths (for example, 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
• support novel research through standard grants and continued support for researchers across all career stages, to maintain a balance of new researchers and research leaders
• encourage and support the establishment of new directions and synergies with other research areas within the mathematical sciences and other disciplines, such as information and communication technologies through the Theoretical computer science areas
• work 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.

Why we're doing it

The UK has major strengths in many aspects of algebraic research. 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.

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.

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.

View evidence sources used to inform our research strategies.

Past projects, outcomes and impact

Visualising our portfolio (VoP) is a tool for users to visually interact with the EPSRC portfolio and data relationships. Find out more about research area connections and funding for Algebra.

Find previously funded projects on Grants on the Web.

Last updated: 21 December 2022