Details of Grant 

EPSRC Reference:	EP/R010048/1
Title:	Fusion Systems and Localities
Principal Investigator:	Henke, Dr E E
Other Investigators:
Researcher Co-Investigators:
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:	Algebra & Geometry
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 06 Sep 2017 EPSRC Mathematical Sciences Prioritisation Panel September 2017 Announced
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 long-term 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 structure-preserving 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.
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Organisation Website:	http://www.abdn.ac.uk