EPSRC logo

Details of Grant 

EPSRC Reference: EP/V036017/1
Title: Cohomology and Actions of Groups
Principal Investigator: Symonds, Professor P
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematics
Organisation: University of Manchester, The
Scheme: Standard Research
Starts: 15 October 2021 Ends: 14 October 2024 Value (£): 415,741
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
23 Feb 2021 EPSRC Mathematical Sciences Prioritisation Panel February 2021 Announced
Summary on Grant Application Form
A very classical thing to study, going back to the Ancient Greeks, is the symmetries of an object. In the abstract these are known as groups; they can be very complicated and difficult to understand. There are many ways of investigating these abstract groups of symmetries and trying to impose some order on them; one of these is to associate to the group a new algebraic invariant, of which cohomology is a prime example.

However, these new invariants can be very difficult to understand, or even to calculate, partly because they are infinite. By using a quantity called the regularity it is possible to show that these infinite objects are controlled by a specific finite part of themselves and they then become much easier to deal with.

This project aims to make these techniques available for much larger classes of groups than before and, in so doing, obtain much more detailed information about the structure of these groups and their cohomology.
Key Findings
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Potential use in non-academic contexts
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Impacts
Description This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Summary
Date Materialised
Sectors submitted by the Researcher
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Project URL:  
Further Information:  
Organisation Website: http://www.man.ac.uk