School of Mathematical Sciences

Algebra and Number Theory Group

The Algebra and Number Theory Group at Queen Mary has a long and distinguished history, going back to such names as Kurt Hirsch, Karl Gruenberg and Ian G. Macdonald. 


Having made its reputation primarily in group theory, the group now covers a range of areas in number theory, representation theory, algebraic combinatorics, algebraic geometry, logic, homological/categorical algebra, and computational methods.

Research interests

Group theory

  • Structure of finite groups
  • Growth functions on finitely-generated groups and their combinatorics and number-theoretic properties
  • Computational group theory and group-theoretical databases

Representation theory

  • Representations of finite groups
  • Representations of p-adic groups
  • Representations of symmetric groups and Hecke algebras

Number theory

  • K-theory of number fields
  • Analytic number theory
  • L-functions
  • Multiplicative functions
  • Classical automorphic forms
  • Classical and higher rank modular forms
  • Automorphic representations

Algebraic Combinatorics

  • Algebraic graph theory
  • Matroids and tropical geometry
  • Finite geometry
  • Computation

Homological algebra

  • Higher categorical/derived structures in algebra and geometry

Model theory

  • Model theory and its applications in algebraic geometry and number theory

Mathematical physics

  • Exceptional groups and Lie algebras and applications to physics, quantum chaos

Group seminars

In conjunction with Imperial College, City University and Birkbeck University of London we run the weekly London Algebra Colloquium, which has been running continuously since 1950. 

When it's not our turn to host the LAC, we normally hold our Algebra and Number Theory Seminar during term on Mondays at 4.30pm. We aim for this seminar to be informal and accessible.

Group members

Head of Group: Matt Fayers