Research in Algebra

There is a large and active algebra research group at Glasgow, one of the largest algebra groups in the UK in fact. Its members are Professor Ken Brown, Professor Peter Kropholler, Dr Alec Mason, Dr. Volodymyr Mazorchuk, Emeritus Professor Douglas Munn, Professor Steve PrideProfessor Patrick Smith and Dr Catharina Stroppel.

Over the last 25 years, worldwide research trends in algebra have increasingly emphasised the subject's connections with, and applications to, other areas of mathematics and science. As examples one can cite geometry, topology, Lie theory, theoretical computing science and integrable systems. This development is very apparent in the research in algebra carried on at Glasgow. Algebra research here splits into two main themes - group theory and ring and modules and representation theory.  In addition, research is carried out in semigroup theory. There is a very strong (and continuing) tradition of post-graduate research in algebra at Glasgow. Details of recent and current Ph.D. students in algebra can be found by clicking here.

Group Theory

Research in group theory at the University of Glasgow is currently centred in three fields: Professor Peter Kropholler carries out research on cohomology of groups; Dr Alec Mason on the modular group and related groups; and Professor Steve Pride on geometric and combinatorial group theory. These research areas have extensive connections with other research fields, both within mathematics and beyond. For example, research on cohomology of groups includes the study of group actions on cell complexes, leading to applications to important modern conjectures in K-theory, to the study of Poincare duality groups, having close connections with 3-manifold theory, and to complete cohomology, which has links with both homotopy theory and with abstract algebra. Research on the modular group is closely linked to number theory and to hyperbolic geometry, while geometric and combinatorial group theory developed in tandem with topology and still has strong links with that subject,  but has also increasingly developed connections with theoretical computing science.

Rings and Modules and Representation Theory

Research in rings and modules and representation theory at the University of Glasgow is currently centred in two fields - Professor Patrick Smith carries out research in module theory; and Professor Ken Brown, Dr. V. Mazorchuk and Dr Catharina Stroppel work on noncommutative noetherian rings and representation theory of Lie algebras and connections to geometry.

A great deal of the work here is focussed on connections with other research fields, particularly Lie theory, quantum groups, knot theory, category theory and algebraic geometry.   This leads to interactions with many other areas, including algebraic geometry, algebraic topology, representations of groups, and mathematical physics.

The entire algebra group at Glasgow meets together at the Departmental Algebra Seminar , held weekly during term time (usually on Wednesdays at 4 p.m.). As well as the members of the algebra group (including students and visitors) the seminar is often attended by members of other research groups in the department - those having a high level of interaction with algebra are the algebraic topology, category theory, geometry, integrable systems and number theory groups. We also run a number of working seminars and postgraduate courses .

The Edinburgh Mathematical Society and the London Mathematical Society provide support for Scottish Algebra Day , an annual meeting of algebraists (and others) in Scotland. The London Mathematical Society also support the meetings of the North British Quantum Groups Collective which usually meets four times a year, once at each of its centres Edinburgh, Glasgow, Lancaster and York. In addition, we have strong links with Australia, Belgium, Brazil, Denmark, France, Germany, India, Israel, Poland, Romania, Spain, Taiwan, the U.S.A. and Vietnam. Recently the group has been supported by the Engineering and Physical Sciences Research council, the European Union and NATO.