Area of investment and support

Geometry and topology

The study of shape and form, including algebraic geometry, algebraic topology, geometric topology and geometric group theory, differential geometry and geometric analysis.

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

The scope and what we're doing

Geometry and topology is the study of shape and form, including algebraic geometry, algebraic topology, geometric topology and geometric group theory, differential geometry and geometric analysis.

The UK continues to be a world leader in geometry and topology.

We aim to develop this research area by:

• supporting strong leadership within the community of researchers working in geometry and topology to ensure that existing excellence is preserved in the longer term and that the UK continues to have specialist capabilities to lead the global research landscape
• continuing to strengthen links to other areas of the mathematical sciences as a key priority, due to the broad nature of research within the mathematical sciences
• supporting research focused on overarching government priorities including, but not limited to, data science and robotics and autonomous systems – geometric and topological research has the potential to play a transformative role in data analytics (through topological data analysis, for instance)
• continuing to support the development of emerging research topics and building on areas of current UK strength to produce transformative research
• monitoring and supporting the training and development of researchers at all career stages to ensure an adequate balance of new researchers and research leaders
• working with the research community to identify the most appropriate routes to maximise and highlight the impact of ongoing research from this area.

Why we're doing it

The broad base of research within this field allows it to influence and impact other areas of the mathematical sciences and beyond. Multiple international prizes awarded to UK-based researchers and invitations to speak at the International Congress of Mathematicians have continually highlighted this.

This is a key fundamental research area, interconnected with nearly all subject areas within the Mathematical Sciences theme: for example with algebra, number theory, mathematical physics and mathematical analysis.

Geometric and topological research also plays an underpinning role in the advances of data science (for example, topological data analysis) and in robotics and autonomous systems (for example, through algebraic and differential topology, focusing on the configuration of spaces which are key to robotic mechanisms), with both of these topics identified as strategic priorities by government.

The current status of research in geometry and topology in the UK has led to the UK retaining and attracting world-leading researchers, causing significant growth in areas such as algebraic geometry, geometric analysis and differential geometry.

In contrast, research in algebraic topology may be on the decline, in line with the global decrease in activity in this area. This may be due to a re-classification of the subject topic, however, and monitoring of capacity in this area should continue.

As with all sub-areas of the mathematical sciences, the academic career path from PhD to established career is a concern. EPSRC supports a centre for doctoral training (CDT) with direct relevance to geometry and topology which aims to produce future world-leading academic researchers.

A concern for the community is support for early-career researchers and this should continue to be monitored and, where necessary, strengthened to support the UK’s leading position in this area.

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 Geometry and Topology.

Find previously funded projects on Grants on the Web.

Last updated: 21 December 2022