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 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 (supervisor in brackets)
Matt Fayers (Head of Group) Imen Belmokhtar (Matt Fayers)
John Bray Félicien Comtat (Abhishek Saha)
Alex Fink Natalie Evans (Steve Lester)
Steve Lester Rhys Evans (Leonard Soicher)
Thomas Müller Antonino Iannazzo (Ivan Tomašić)
Behrang Noohi Scott Kemp (Alex Fink)
Tomasz Popiel Rachael King (Ivan Tomašić)
Felipe Rincon Diego Millan Berdasco (Matt Fayers)
Abhishek Saha Ben Smith (Alex Fink)
Ivan Tomašić Yegor Stepanov (John Bray)
Leonard Soicher (Emeritus) Dean Yates (Matt Fayers)
Rob Wilson (Emeritus)  

Shahn Majid (GA), Xin Li (GA) and Hugo Maruri-Aguilar (PA) also undertake research in algebra.

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.

News

  • 3 December 2018: Abhishek Saha's Leverhulme grant for the project 'New investigations in automorphic forms: analytic and arithmetic interfaces' will start in March 2019.  The grant will fund a postdoctoral researcher and a PhD student.  Then value of the award is £293,685.
  • 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.