Research in Algebra

The Algebra group plays a major role in the School's research activities. We run a weekly Algebra seminar and also organize occasional seminars of a more specialised nature. There are many interactions with other research areas in the school, notably with topology, geometry and combinatorics and mathematical logic.

Research Interests

Research interests of the algebraists at the University of Manchester include: Lie theory; group theory; group geometries; graph theory; homological algebra; homotopy theory; combinatorics; black box groups; model theory; invariant theory; structure and representation theory of algebraic groups and related Lie algebras; semigroup theory; computational algebra; cohomology, modular and ordinary representation theory of finite groups; modular group algebras of finite p-groups; the unit group of the Steenrod algebra; representations of quivers and algebras; group actions on rings, topological spaces and free Lie algebras.

Members of staff interests

Dr Yuri Bazlov:

Hopf algebras and quantum groups, applications to representation theory, combinatorics and integrable systems.

Professor Alexandre Borovik:

Group Theory: structural properties and finite subgroups of simple algebraic groups; black box groups and non-deterministic methods; Combinatorics: discrete geometries and configurations arising from homogeneous spaces, Model Theory: groups of finite Morley rank

Professor Roger Bryant (Emeritus):

Groups acting on free Lie algebras; automorphisms of relatively free groups.

Dr Charles Eaton:

Ordinary and modular representation theory of finite groups.

Dr Jelena Grbic:

Toric topology; loop spaces decompositions and representations of groups; connections between homotopy groups of spheres and braids; homotopy theory; p-local finite groups

Dr. Mark Kambites:

Combinatorial and geometric group theory, semigroup theory, formal languages and automata, computational complexity, parallel processing, cryptography, and interactions between the above.

Professor Alexander Premet:

Lie Theory: classifications of finite dimensional simple Lie algebras, enveloping algebras, primitive ideas, finite W-algebras; Modular Representation Theory of Reductive Lie Algebras; Invariant Theory of Algebraic Groups.

Professor Mike Prest

The Ziegler spectrum of an associative ring, representations of algebras and quivers; structure and complexity of categories of modules and other additive categories.

Professor Peter Rowley

Finite Simple Groups, Amalgams of groups and completions of amalgams, Group Geometries, Point-Line Collinearity Graphs of Sporadic Simple Groups, Coxeter Groups, Commuting Graphs and Cages.

Professor Toby Stafford

Non-commutative algebra, non-commutative algebraic geometry, rings of differential operators

Professor Ralph Stohr

Lie Algebras: Group actions on free Lie algebras. Group Theory: Homological methods in Group Theory, Combinatorial Group Theory, Equations over groups.

Professor Peter Symonds

Representation theory and cohomology of groups, homological algebra, profinite groups, group actions on rings, group actions on topological spaces, homotopy theory, and invariant theory.

Contact details

NAME		Title	EMAIL @manchester.ac.uk	PHONE	LOCATION
Bazlov	Yuri	Dr.	Yuri.Bazlov	0161 27 55816	2.220
Borovik	Alexandre	Prof.	Alexandre.Borovik	0161 30 63645	2.125
Bryant	Roger	Prof. (Emeritus)	Roger.Bryant	0161 30 63642	1.115
Eaton	Charles	Dr (Royal Society Research Fellow)	Charles.Eaton	0161 30 63697	2.135
Grbic	Jelena	Dr	Jelena.Grbic	0161 27 55849	2.114
Kambites	Mark	Dr	Mark.Kambites	0161 30 63211	2.144
Premet	Alexander A	Prof.	A.Premet	0161 27 55854	1.131
Prest	Mike	Prof.	MPrest	0161 27 55875	1.120
Rowley	Peter	Prof.	Peter.Rowley	0161 30 63648	2.131
Stafford	Toby	Prof.	Toby.Stafford	0161 27 55828	2.116
Stöhr	Ralph	Prof.	Ralph.Stohr	0161 30 63647	2.140
Symonds	Peter	Prof.	Peter.Symonds	0161 30 63675	2.209