School of Mathematical Sciences

Algebra and Number Theory

The Algebra and Number Theory Group at QMUL 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, it now covers a range of areas in group theory, representation theory, number theory, algebraic combinatorics, algebraic geometry, logic, homological/categorical algebra, and computational methods.

Please click on a member's name to see their profile and publications. 

FACULTY MEMBERS PhD STUDENTS
John Bray Imen Belmokhtar
Matt Fayers (Head of Group) Rhys Evans
Alex Fink Scott Kemp
Steve Lester Rachael King
Shahn Majid Diego Millan Berdasco
Thomas Müller Ben Smith
Behrang Noohi Yegor Stepanov
Tomasz Popiel  
Abhishek Saha  
Leonard Soicher  
Ivan Tomašić  
Rob Wilson (Emeritus)  

High levels of Algebra also feature in the research of Xin Li (GA) and Hugo Maruri-Aguilar (PA).

Seminars

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.

In conjunction with Imperial College and City University we run the weekly London Algebra Colloquium(link is external), which has been running continuously since 1950.

News

  • 14 May 2018: Alex Fink's Marie Skłodowska-Curie Individual Fellowship award for the project 'Tropical Differential Geometry' will start in June 2018 when the fellow Zeinab Toghani will join the Algebra and Number Theory Group for two years.The value of the award is €195,455.
  • 11 August 2017: We are pleased to announce that the newly appointed lecturers in number theory, Steve Lester and Abhishek Saha have joined the Algebra and Number Theory Group.

    Steve is interested in analytic number theory, especially L-functions, multiplicative functions, classical automorphic forms, and mathematical physics, especially quantum chaos.

    Abhishek is interested in classical and higher rank modular forms, automorphic representations and the L-functions attached to them.

  • 17 March 2017: We are pleased to announce that Behrang Noohi and Ivan Tomašić have joined the Algebra and Number Theory Group.

    Behrang is interested in higher categorical/derived structures in algebra and geometry. More specifically: algebraic/differentiable/topological stacks, moduli problems, higher dimensional groups and higher Lie theory, and string topology.

    Ivan studies model theory and its applications in algebraic geometry and number theory. More specifically, his interests include difference algebra and geometry (relating to the arithmetic aspects of the Frobenius automorphism), measurable structures, (nonstandard) cohomology theories, and motivic integration.

Main areas of research

  • 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 and its applications in algebraic geometry and number theory;
  • mathematical physics: exceptional groups and Lie algebras and applications to physics, quantum chaos.