Algebra

Queen Mary earned a reputation for excellence in algebra early on through our work in group theory, including the finite simple groups project; our staff have included such names as Kurt Hirsch, Karl Gruenberg and Ian G. Macdonald. Our research in algebra now covers a broad range of areas.

  • Tropical and combinatorial algebraic geometry is an exciting area growing worldwide, with a 2022 Fields Medal awarded to June Huh, and is a key tool in enumerative geometry and moduli theory. CeCANT has a critical mass in this area, funded through multiple EPSRC grants, in Prof. Fink, Dr Nabijou, and Dr Rincón, and strong connections to teams at Warwick, Durham, Cambridge, and elsewhere. Algebraic geometry also features in the work of Dr Noohi, Dr Sasaki, and Dr Tomašić, and algebraic combinatorics that of Dr Fayers.
  • In representation theory, our emphases are representations of symmetric groups and allied finite groups, real and complex reflection groups, and Hecke algebras (Dr Fayers), and representations of p-adic groups and automorphic representations (Dr Saha).
  • In category theory and logic our strengths lie in topos theory, categorical logic, model theory of difference and differential fields, higher categorical and derived structures in algebra and geometry, and homological algebra. Working in these areas are Dr Noohi and Dr Tomašić, funded through the EPSRC grant "Model theoretic and topos theoretic view of difference algebra and applications to dynamics".

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. We also hold internal seminars in termtime, and aim for these to be informal and accessible.

Various algebraic and combinatorial representations of a matroidVarious algebraic and combinatorial representations of a matroid