Algebra
Algebra is the study of abstract objects arising from across mathematics, unifying apparently distant areas.
Academic staff
 Yuri Bazlov
 Alexandre Borovik (Emeritus)
 Charles Eaton
 Florian Eisele
 Marianne Johnson
 Mark Kambites
 Alexander Premet (Emeritus)
 Mike Prest (Emeritus)
 Peter Rowley
 Peter Symonds
 Nora Szakacs
 Richard Webb
Dame Kathleen Ollersenshaw Trust Research Fellow

CarlFredrik Nyberg Brodda
Heilbronn Fellows
 Kieran Calvert
 Simon Crawford
 Aram Dermenjian
 Alex Evetts
 Adam Jones
 Veronica Kelsey
 Simon Peacock
 Georgia Schneider
Neumann Fellow
Postdoctoral Research Fellow
 Michael Livesey
Postdoctoral Research Assistant

Kostas Karagiannis
Algebra is the study of abstract structures which arise across all areas of mathematics. The same structure could be found, for example, in number theory, geometry, or topology, and used as a bridge between these subjects. Study of the structure as an abstract object in isolation also allows us to see properties which wouldn't be apparent in the original setting, and is a powerful mathematical tool. A main example of such a structure is a group, arising in the study of roots of polynomials in Galois theory, in topology as the fundamental group and in geometry in the form of symmetries, as well as in many other places in virtually every field of mathematics.
Algebra has long been strength in Manchester, with expertise across much of the subject. The deep connection algebra has with the rest of mathematics is represented in the group, and the weekly algebra seminar is a lively and wellattended event.
We are engaged in research projects relating to:
 Representations of Lie algebras
 Finite nonabelian simple groups
 Coxeter groups
 Profinite groups
 Fusion systems
 Modular representation theory of finite groups
 Picard groups of finite dimensional algebras
 Semigroups
 Geometric group theory
 Automata
 Hopf algebras and quantum groups
 Cohomology of groups
 Module categories
 Representations of algebras
 Groups of finite Morley rank
 Algebraic groups
 Algebraic geometry
 Invariant theory
 Black box groups