• D.Phil. in Mathematics, University of Oxford, 2008
• M.Sci. in Mathematical Sciences, University of Birmingham, 2004

Dr Craven received an M.Sci. from Birmingham in 2004, then moved to Oxford, where he was first awarded a D.Phil. from St John’s College in 2008, and then moved to Christ Church as a Junior Research Fellow for the next three years.

He was appointed as a Birmingham Fellow in November of 2011.

Research Themes

• Modular representation theory: particularly Broué’s conjecture and representations of finite simple groups
• Fusion systems
• The Unit Conjecture for group rings
• Profinite and polycyclic groups
• Representation theory of symmetric groups and associated combinatorics 

Research Activity

The main areas of Dr Craven's research activity are representation theory of finite groups and fusion systems.

In finite group representation theory, Professor Raphael Rouquier of Oxford and Dr Craven have embarked on an ambitious project to prove, or at least make substantial progress on, Broué’s abelian defect group conjecture, particular for principal blocks of finite groups of Lie type. In recent work they have laid the foundations of a systematic attack on the geometric form of Broué’s conjecture, using the new concept of perverse equivalences.

In fusion systems, Dr Craven focuses on the algebraic side, attempting to construct an internal theory of fusion systems, that neither translates bolidy results from local finite group theory nor relies heavily on topological intuition, the two currently most successful methods of approaching the subject. This approach manifests itself in his recent theorem proving the equivalence of the two definitions of a simple fusion system.