Algebra

The traditional objects of study in algebra are algebraic structures such as groups, rings, and modules. However, the developments of the last decades have increasingly emphasised the subject's connections with other areas of mathematics and science, such as number theory, geometry, topology, classical and quantum field theory, integrable systems, and theoretical computing science.

Here in Glasgow, we study both classical and modern problems and questions in algebra. The research interests of our staff members include geometric group theory, number theory (algebraic and analytic), both commutative and noncommutative ring theory, as well as topics in representation theory and homological algebra.  All information about our group, our members, our activities, and a full list of our expertise, can be found at our Core Structures webpage.

Our group has an active PhD student community, and every year we admit new PhD students.  We welcome applications from across the world, and we encourage you to browse our available supervisors, and also to consult our general advice on how to navigate the application process.

The non-exhaustive list under Postgraduate Opportunities contains a sample of the types of PhD projects that our group offers.

Staff

Dr Spiros Adams-Florou : Lecturer

Algebraic K-theory, L-Theory

Member of other research groups: Geometry and Topology

  • Personal Website
  • Publications
  • Prof Alex Bartel : Professor of Mathematics

    • Algebraic number theory:
      • Galois module structures, e.g. the structure of the ring of integers of a number field as a Galois module, or of its unit group, or of the Mordell-Weil group of an abelian variety over a number field;
      • Arithmetic statistics, especially the Cohen―Lenstra heuristics on class groups of number fields and their generalisations;
      • Arithmetic of elliptic curves over number fields.
    • Representation theory of finite groups:
      • Integral representations of finite groups;
      • Connections between the Burnside ring and the representation ring of a finite group;
      • Applications of the above to number theory and geometry.
    • Geometry and topology:
      • Actions of finite groups of low-dimensional manifolds.

    Member of other research groups: Geometry and Topology
    Research student: Ross Paterson

  • Personal Website
  • Prof Gwyn Bellamy : Professor of Mathematics

    My research interests are in geometric representation theory and its connections to algebraic geometry and algebraic combinatorics. In particular, I am interested in all aspects of symplectic representations, including symplectic reflection algebras, resolutions of symplectic singularties, D-modules and deformation-quantization algebras.

    Member of other research groups: Geometry and Topology
    Research students: Niall Hird, Samuel (Sam) Lewis, Kellan Steele, Simone Castellan, Ross Paterson

  • Personal Website
  • Publications
  • Dr Tara Brendle : Professor of Mathematics

    Geometric group theory; mapping class groups of surface

    Member of other research groups: Geometry and Topology
    Research students: Tudur Lewis, Luke Jeffreys

  • Personal Website
  • Publications
  • Dr Kenneth A Brown : Professor of Mathematics

    Noncommutative algebra; Hopf algebras; homological algebra

    Member of other research groups: Geometry and Topology
    Research student: Miguel Couto

  • Personal Website
  • Publications
  • Dr Mikhail Feigin : Senior lecturer

    Representations of Cherednik algebras; rings of quasi-invariants

    Member of other research groups: Integrable Systems and Mathematical Physics, Geometry and Topology
    Research students: Maali Alkadhem, Leo Kaminski, Georgios Antoniou, Johan Wright

  • Personal Website
  • Publications
  • Dr Vaibhav Gadre : Lecturer

    Teichmuller Dynamics, Mapping Class Groups. 

    Member of other research groups: Geometry and Topology
    Research students: Luke Jeffreys, Tudur Lewis

  • Personal Website
  • Publications
  • Dr Sira Gratz : Lecturer

    representation theory of algebras, cluster algebras and cluster categories, triangulated categories

    Research students: David Murphy, James Rowe, Damian Wierzbicki

  • Personal Website
  • Publications
  • Dr Dinakar Muthiah : Lecturer

    I work in Representation Theory and Algebraic Geometry. I am interested in geometric representation theory inspired by the Langlands program and mathematical physics. A few topics that particularly interest me: affine Grassmannians, p-adic groups, loop and double loop groups, Hecke algebras, intersection cohomology, Coulomb branches, symplectic varieties.

  • Personal Website
  • Dr Franco Rota : Research Associate

    Algebraic geometry. In particular, derived categories, moduli spaces of sheaves, the McKay correspondence, Bridgeland stability conditions, the stability manifold and its relation with mirror symmetric questions.

    Member of other research groups: Geometry and Topology

  • Personal Website
  • Dr Greg Stevenson : Lecturer

    Member of other research groups: Geometry and Topology
    Research students: David Murphy, James Rowe, Hao Zhang

  • Personal Website
  • Publications
  • Dr Christian Voigt : Senior lecturer

    Noncommutative geometry; K-theory; Quantum groups

    Member of other research groups: Geometry and Topology, Analysis
    Research students: Jamie Antoun, Owen Tanner

  • Personal Website
  • Publications
  • Prof Michael Wemyss : Professor of Mathematics

    Algebraic geometry and its interactions, principally between noncommutative and homological algebra, resolutions of singularities, and the minimal model program.  All related structures, including: deformation theory, derived categories, stability conditions, associated commutative and homological structures and their representation theory, curve invariants, McKay correspondence, Cohen--Macaulay modules, finite dimensional algebras and cluster-tilting theory.

    Member of other research groups: Geometry and Topology
    Research students: Sarah Kelleher (Mackie), Ogier Van Garderen, Hao Zhang, Samuel (Sam) Lewis

  • Personal Website
  • Publications
  • Dr Mike Whittaker : Lecturer

    Operator algebras, self-similar groups, and Zappa-Szep products.

    Member of other research groups: Geometry and Topology, Analysis
    Research students: Dimitrios Gerontogiannis , Kate Gibbins, Mustafa Ozkaraca, Jamie Antoun, Cheng Chen

  • Personal Website
  • Publications
  • Dr Joachim Zacharias : Reader

    C*-algebras, their classification and amenability properties; special examples of C*-algebras; K-theory and non commutative topology, noncommutative dynamical systems, geometric group theory with applications to C*-algebras.

    Member of other research groups: Integrable Systems and Mathematical Physics, Geometry and Topology, Analysis
    Research student: Dimitrios Gerontogiannis

  • Personal Website
  • Publications

  • Postgraduates

    Simone Castellan : PhD Student

    Research Topic: Short star products in (Poisson) vertex algebras
    Member of other research groups: Integrable Systems and Mathematical Physics, Geometry and Topology
    Supervisors: Daniele Valeri, Gwyn Bellamy

  • Cheng Chen : PhD Student

    Research Topic: Semigroup C*-algebras for examples coming from group theory
    Supervisors: Brendan Owens, Mike Whittaker

  • Miguel Couto : PhD Student

    Supervisor: Kenneth A Brown

  • Kate Gibbins : PhD Student

    Research Topic: The Ledrappier shift, one-dimensional tilings and continuous fields of C*-algebras.
    Supervisors: Mike Whittaker, Runlian Xia

  • Niall Hird : PhD Student

    Supervisor: Gwyn Bellamy

  • Luke Jeffreys : PhD Student

    Research Topic: Teichmüller dynamics
    Member of other research groups: Geometry and Topology
    Supervisors: Vaibhav Gadre, Tara Brendle

  • Personal Website
  • Leo Kaminski : PhD Student

    Research Topic: Special solutions of WDVV equations
    Member of other research groups: Integrable Systems and Mathematical Physics, Geometry and Topology
    Supervisor: Mikhail Feigin

  • Sarah Kelleher (Mackie) : PhD Student

    Supervisor: Michael Wemyss

  • Tudur Lewis : PhD Student

    Research Topic: Mapping class groups and related structures.
    Member of other research groups: Geometry and Topology
    Supervisors: Tara Brendle, Vaibhav Gadre

  • David Murphy : PhD Student

    Research Topic: Representations of finite dimensional algebras This project studies representations of finite dimensional algebras via a homological approach. The central idea is to study structures and properties of categories coming from representations of finite dimensional algebras, with possible focus on thick subcategories, Serre functors, lattice theory, and (tau-)tilting.
    Supervisors: Sira Gratz, Greg Stevenson

  • Ross Paterson : PhD Student

    Supervisors: Alex Bartel, Gwyn Bellamy

  • James Rowe : PhD Student

    Supervisors: Sira Gratz, Greg Stevenson

  • Kellan Steele : PhD Student

    Member of other research groups: Geometry and Topology
    Supervisor: Gwyn Bellamy

  • Owen Tanner : PhD Student

    Research Topic: Topological full groups and continuous orbit equivalence.
    Member of other research groups: Geometry and Topology
    Supervisors: Xin Li, Christian Voigt

  • Ogier Van Garderen : PhD Student

    Member of other research groups: Geometry and Topology
    Supervisor: Michael Wemyss

  • Damian Wierzbicki : PhD Student

    Research Topic: cluster algebras
    Supervisors: Christian Korff, Sira Gratz

  • Hao Zhang : PhD Student

    Research Topic: Bridgeland stability manifolds of Divisor to Curve Contractions
    Member of other research groups: Geometry and Topology
    Supervisors: Michael Wemyss, Greg Stevenson