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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

John Bray, Tomasz Popiel
  • 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

Matt Fayers, John Bray, Abhishek Saha
  • Representations of finite groups
  • Representations of p-adic groups
  • Representations of symmetric groups and Hecke algebras

Automorphic forms

Abhishek Saha, Steve Lester, Shu Sasaki
  • Modular forms
  • Maass forms
  • Siegel modular forms
  • Representations of p-adic groups
  • Langlands programme
  • Analytic theory of automorphic forms

Algebraic Combinatorics

Alex Fink, Felipe Rincón, Matt Fayers, John Bray, Tomasz Popiel
  • Algebraic graph theory
  • Matroid theory
  • Finite geometry
  • Computation
  • Combinatorics of partitions

Homological algebra

Ivan Tomašić, Behrang Noohi
  • Higher categorical/derived structures in algebra and geometry

Model theory

Ivan Tomašić
  • Model theory of difference and differential fields
  • Stable and simple theories
  • Applications in algebraic geometry and number theory

Mathematical physics

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

Analytic Number Theory

Steve Lester, Abhishek Saha
  • Arithmetic quantum chaos
  • Analytic aspects of L-functions

Algebraic Number Theory

Abhishek Saha, Shu Sasaki, Ivan Tomašić
  • Galois representations
  • Arithmetic of L-functions
  • Special values of L-functions

Category theory

Ivan Tomašić, Behrang Noohi
  • Topos theory
  • Categorical logic

Algebraic geometry

Behrang Noohi, Alex Fink, Felipe Rincon, Shu Sasaki
  • Tropical geometry
  • Combinatorial algebraic geometry
  • Complex geometry
  • Arithmetic geometry
  • Non-Archimedean geometry

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 Fridays at 3:00pm. We aim for this seminar to be informal and accessible.

Group members

Head of Group: Dr Abhishek Saha