Algebra
The members of staff working in this area are Prof A.D. King, Dr Y. Bazlov, Dr G.C. Smith, Dr X-P. Su and Dr G. Traustason.
Bath hosts the Group Pub Forum community pages.
In 2009 the conference Groups St Andrews visited Bath again after a gap of 12 years. This 4-yearly conference is the largest regular international meeting of group theorists in the world.
Group Theory
The focus of research in group theory at Bath has been on infinite discrete groups, and this will continue at least in the short to medium term.
Traustason's research interests include Engel groups and other generalized nilpotent groups, Engel Lie algebras and problems of Burnside type. In particular he has been involved in developing a structure theory for 4-Engel groups, making a significant contribution to the local nilpotence theorem for 4-Engel groups. Other recent work includes groups with all subgroups subnormal of bounded defect and a characterisation of group varieties of which the class of locally nilpotent (nilpotent-by-finite) groups form a subvariety, a property shared by the Burnside varieties. Smith is currently interested in the cycle structure of infinite permutation groups, and associated closure operations.
Representation Theory and Homological Algebra
The main focus of research in homological algebra is on applications to deformation theory and moduli problems for representations of algebras, which may be related to similar problems for sheaves on varieties through equivalences of derived categories, such as the Beilinson equivalence for projective spaces and the McKay correspondence. The role of derived categories in moduli problems and other areas of geometry is one of the exciting developments of recent years, which is closely followed at Bath. This leads on to the study of A-infinity structures, a tool from topology, whose importance in geometry and theoretical physics is beginning to be more widely appreciated.
