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 Pride**, **Professor 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.