Mathematical physics

Developing new mathematics inspired by, or relevant to, physics. This research area has close connections to the Science and Technology Facilities Council’s (STFC's) Particle Physics Theory remit and our own physical sciences capability, as well as strong intradisciplinary connections within our Mathematical Sciences portfolio.

Over the last Delivery Plan, this research area reduced as a proportion of the EPSRC portfolio, in line with the previous proposed strategic focus. We now aim to maintain the current level of support as a proportion of the EPSRC portfolio, in the context of the specific strategic objectives summarised below.

By the end of the current Delivery Plan, we aim to have:

  • Supported and developed a portfolio of high-quality core research across the full breadth of sub-fields in Mathematical Physics
  • A portfolio in this research area which seeks to advance the strong intradisciplinary links to both pure and applied mathematics, to further developments in areas such as Network Science, Number Theory, Statistics and Applied Probability, and Quantum Information
  • Ensured that the research base has the appropriate people and skills to keep the UK at the forefront of advances in Mathematical Physics; this will include providing skills and training for the next generation of leaders in the field 
  • Encouraged novel interactions between Mathematical Physics and new research challenges of national importance relating to EPSRC's Outcomes. There are many opportunities to contribute towards these challenges through links to pure and applied mathematics and theoretical physics (e.g. quantum computing and superconductivity)
  • Maintained regular dialogue with STFC to ensure that research proposals at the interface between us are managed appropriately.
Highlights:

Traditionally, Mathematical Physics is one of the strongest fields of mathematics in the UK and continues to be recognised for its excellence through prizes, awarded Fellowships of the Royal Society (FRS) and European Research Council (ERC) awards. Its links to both pure and applied mathematics, as well as the obvious links to physics, mean it is highly intradisciplinary and interdisciplinary (Evidence source 1,2,3,4).

Mathematical Physics has a long history of stimulating important developments in other fields of the mathematical sciences (e.g. algebraic geometry and geometric analysis), making it key to the health of other disciplines. It draws on ideas from both pure and applied mathematics, while feeding back to them new techniques, examples and conjectures.

The UK continues to have world-class research programmes in several of the more mathematical areas of theoretical physics (e.g. general relativity, cosmology, string theory and quantum chaos). The Research Excellence Framework (REF) 2014 expert panel noted that “the large submission in mathematical/theoretical physics showed breadth and depth in areas where the UK has been strong for decades. For example, there were many world-leading outputs in quantum field theory (including string theory, integrable systems, high-energy particle physics and cosmology), and aspects of general relativity and statistical mechanics” (Evidence source 1,2,3,4).

Today, world-leading groups in Mathematical Physics are located both in many small institutions and in the larger, well-established centres. A distinctive feature in the UK is that Mathematical Physics groups are placed in mathematics departments rather than physics departments. This has emerged as a great strength, leading to more cross-fertilisation with pure mathematics than arises elsewhere (Evidence source 1,4).

In terms of the national importance of Mathematical Physics, in addition to the high-quality research this area has produced, it has contributed to progress towards understanding a variety of important phenomena such as quantum entanglement and superconductivity.

It is important to note the underpinning nature of this research area and its indirect contributions to advances in many areas of engineering and physical sciences (Evidence source 1,2,3,4,5,6,7).

Numbers of EPSRC-funded PhD students in this area have remained constant over the last Delivery Plan (against an overall growth in numbers) and junior appointments have remained robust. However, there is concern that previous levels of support for postdocs will not even be enough to regain losses due to recent and upcoming retirements (Evidence source 3,4).

This area can potentially contribute to several Outcomes in the medium to long term, especially with regard to the Connected and Resilient Nation. The following Ambitions are of particular note:

C1: Enable a competitive, data-driven economy

Work related to quantum computing and to superconductivity and such phenomena is directly relevant.   

C3: Deliver intelligent technologies and systems

Work related to quantum computing is directly relevant.

R2: Ensure a reliable infrastructure which underpins the UK economy

Work related to quantum computing and to superconductivity and such phenomena is directly relevant.

R4: Manage resources efficiently and sustainably

Work related to superconductivity and such phenomena is directly relevant.

Research area connections

This diagram shows the top 10 connections between Research Areas within the EPSRC research portfolio. The depth of the segment relates to value of grants and the width of the segment relates to the number of grants shared by those two Research Areas. Please click to see the related Research Area rationale.

Maintain

We aim to maintain this area as a proportion of the EPSRC portfolio.

Visualising our Portfolio (VoP)
Visualising our portfolio (VoP) is a tool for users to visually interact with the EPSRC portfolio and data relationships.

EPSRC support by research area in mathematical physics (GoW)
Search EPSRC's research and training grants.

Contact Details

In the following table, contact information relevant to the page. The first column is for visual reference only. Data is in the right column.

Name: Katharine Moore
Job title: Manager
Department: Mathematical Sciences
Organisation: EPSRC
Telephone: 01793 444246