Area of investment and support

Mathematical analysis

Quantifying change, with a key role played by fundamental notions of continuity and approximation.

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

The scope and what we're doing

Mathematical analysis is concerned with quantifying change, with a key role played by fundamental notions of continuity and approximation. This research area includes, for example:

• Fourier and harmonic analysis
• operator theory
• ordinary and partial differential equations
• probability theory
• stochastic analysis
• applications of analysis.

Mathematical analysis has links with all other areas of pure and applied mathematics.

The UK is strong across all areas of mathematical analysis and we aim to maintain this world-leading position. This strategy recognises the research area’s many intradisciplinary links to all fields of mathematics and strong links to other disciplines, which will help it contribute strongly to the EPSRC outcomes. It also considers how best to support the people pipeline, given the major investment in relevant centres for doctoral training (CDTs).

Our aims

High quality research

We aim to maintain high-quality research across the breadth of mathematical analysis to sustain support for core areas and drive developments in key challenges.

Encourage novel interactions

We aim to encourage novel interactions between mathematical analysis and application areas, particularly research relating strongly to EPSRC outcomes. There are many opportunities to engage with research challenges related to EPSRC ambitions, as a result of this area’s underpinning nature and links to all areas of mathematics, for example:

• algebra
• geometry
• mathematical biology
• mathematical physics
• continuum mechanics
• non-linear systems
• numerical modelling
• statistics and applied probability
• data science.

Support for early career analysts

Another aim is to increase support for early career analysts and so build capacity across the breadth of the area, to respond to growing demand for broad mathematical analysis skills. This recognises the relatively large number of well trained analysts in the UK delivered by investment in three CDTs. We wish to maintain this momentum and build on the greater connectedness of analysis, both in the UK and internationally.

Why we're doing it

Traditionally strong in mathematical analysis, the UK is at the leading edge of research in:

• dynamical systems
• ergodic theory
• harmonic analysis
• partial differential equations (PDEs) and their applications
• operator algebras and operator theory
• stochastic analysis.

Mathematical analysis is of high importance to the mathematical sciences as a whole, linking many areas of pure mathematics to applied areas. For example, there are strong interactions with:

• algebra
• applied mathematics
• geometry
• materials science
• physics
• statistics and applied probability.

The UK has seen a blurring of boundaries as mathematical analysis finds new applications, and the area is expected to keep growing. World-leading groups are located across the UK at many big centres, as well as several smaller institutions.

The high quality of mathematical analysis in this country is demonstrated, for example, by a plethora of prizes and the ability to attract international leaders in the field to the UK. The Research Excellence Framework (REF) 2014 exercise noted, since the Research Assessment Exercise (RAE) 2008, an increase in quantity and quality of research in theoretical partial differential equations and stochastic analysis (some of which was world-leading at the highest level).

The connection of modern statistics to mathematics remains strong and is growing. For example, both theory and methodology of functional data analysis rely on ideas and results from mathematical analysis, as noted by the International Review of Mathematical Sciences (IRM) 2010 and by REF expert panel B. Mathematical analysis has potential to contribute strongly to developments in data science. Connections with developments in data science should be encouraged.

As of April 2016, over half the EPSRC portfolio in mathematical analysis was in training, largely in the form of three CDTs. These now generate relatively large numbers of well-trained analysts. It is important that the best analysts in the UK are supported at the next stage of their career.

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 Mathematical analysis.

Find previously funded projects on Grants on the Web.

Last updated: 22 December 2022