EPSRC Reference: 
EP/R010048/1 
Title: 
Fusion Systems and Localities 
Principal Investigator: 
Henke, Dr E E 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematical Sciences 
Organisation: 
University of Aberdeen 
Scheme: 
First Grant  Revised 2009 
Starts: 
01 November 2017 
Ends: 
30 September 2019 
Value (£): 
100,913

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
The abstract algebraic concept of a group is central in contemporary mathematics, since it allows us to handle objects of a diverse mathematical origin in a uniform way. Groups arise for example from symmetries of other mathematical or geometrical objects. On the other hand, a given group leads again to new algebraic, topological and geometric structures. In particular, to every group one associates a topological space, called the classifying space. This leads to many different ways of studying groups. However, it is a common feature of different approaches that they focus on properties related to a fixed prime p.
Saturated fusion systems provide a new algebraic framework which allows us to discover more and more connections between the different approaches related to a prime. There are however still many open questions remaining. For the prime 2, it is an important longterm goal to classify the simplest building blocks of saturated fusion systems. In this project, we will overcome some major conceptual difficulties arising on the way to such a classification result for fusion systems. This will feed into a simplified proof of the classification of finite simple groups, which is an important theorem classifying the simplest building blocks of finite groups. The new algebraic theory we develop will also allow us to study structurepreserving maps between classifying spaces of groups "at a prime p". We expect that this will open new ways for research in homotopy theory and representation theory.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
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Summary 

Date Materialised 


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Project URL: 

Further Information: 

Organisation Website: 
http://www.abdn.ac.uk 