REF 2021

As a specialised department, our aim has always been to be among the top in our areas. These results show that we achieved that.

Professor Jan van den Heuvel, Head of Department


We are extremely proud that the quality of our research has been recognised by the assessors in the 2021 Research Excellence Framework (REF 2021).

Our research was submitted jointly with the Department of Statistics to the Mathematical Sciences Unit of REF 2021. All aspects of our research were rated ‘world-leading’ (4*) or ‘internationally excellent’ (3*). In particular, more than half of our publications received the top 4* grade.

Researchers from the two departments also submitted four impact case studies to the Mathematical Sciences Unit of Assessment. 63% of this impact received the top 4* grade.

Overall, these outstanding results saw our submission to REF 2021 ranked joint 9th in the UK for Mathematical Sciences (based on Times Higher rankings). We are one of only seven submissions to Mathematical Sciences (out of 54) whose research outputs, impact and environment were all rated internationally excellent or above.

Impact Case Studies


The Research Excellence Framework (REF) is the system by which the UK’s higher education funding bodies assess the quality of research in publicly funded UK higher education institutions (HEIs).  REF 2021 comprised three elements:  

  • academic outputs, comprising a portfolio based on the FTE of REF-eligible staff submitted;
  • research impact, submitted as a number of impact case studies (ICSs) in proportion to the total FTE of REF-eligible staff submitted;  
  • research environment, comprising the total number of research degrees awarded between 2014 and 2020, total research income received over the same time period, and an environment statement detailing how the submitting unit(s) supported research and impact over the period. 

Outputs, impact and environment were weighted 60:25:15 respectively.  All three elements were graded on a scale from 0 (unclassified) to 4* (world leading) and the results were published as quality profiles showing the percentage of outputs, impact and environment considered to meet each of the starred levels.  Submissions were invited to 34  Units of Assessment (UoAs); LSE made 15 submissions to 13 UoAs across the SHAPE subjects.  

For REF 2021, HEIs were required to submit research outputs by all eligible members of staff.  Each submitted member of staff could submit between one and five outputs, with the total number of outputs per UoA calculated as total FTE of staff multiplied by 2.5.   

Staff were eligible for REF 2021 where they were on a teaching-and-research or research-only contract of at least 0.2 FTE on 31 July 2020 and had a substantive connection to the submitting HEI.  Research-only staff also had to be classified as independent researchers.  HEIs were also required to identify which eligible staff had significant responsibility for research.  LSE submitted 100% of its staff meeting these definitions, but other HEIs had eligible staff who did not have significant responsibility for research and hence had a submission rate of less than 100%. 

Here is a full glossary of REF terminology.