A geometrical model

Algebra and Geometry

Projects

New Frontiers in Symplectic Topology
01/09/2022 → 31/08/2026
Research

LMS Research School on Rigidity, Flexibility and Applications
18/07/2022 → 22/07/2022
Research

Mackey Functors for Topological Groups
13/02/2022 → 19/02/2022
Research

Schubert Calculus via Cluster Categories
01/01/2022 → 31/12/2022
Research

Positive Fuss-Catalan Combinatorics and Representation Theory
05/07/2021 → 29/08/2021
Research

Hausdorff Dimension Spectrum of Pro-p Groups
28/06/2021 → 20/08/2021
Research

LMS - Research in Pairs (Prof Serge Bouc)
07/03/2021 → 31/07/2021
Research

Research in Pairs - Scheme 4 - Support of collaborative research with Professor Walter Whiteley at York University, Toronto
01/02/2021 → 31/05/2021
Research

Rank Functions on Triangulated Categories, Homotopy Theory and Representations of Finite Groups (RANKS)
01/12/2020 → 30/11/2023
Research

Co-coordination of LMS Online Lecture Series
01/09/2020 → 31/10/2020
Other

Combinatorial and Geometric Methods in Representation Theory
20/01/2020 → 19/01/2022
Research

host the LMS Prospects in Mathematics Meeting 2019 (additional funding)
01/09/2019 → 30/09/2019
Research

Honey Bee Municipal Pesticide Exposure
01/08/2019 → 31/12/2020
Research

Singularities and symplectic topology
25/03/2019 → 13/12/2020
Research

LIMITS: Limits of Structures in Algebra and Combinatorics
01/02/2019 → 31/01/2024
Research

Supplementary Issue of Glasgow Mathematical Journal on Non-Associative Algebras
01/12/2018 → 30/11/2020
Research

Linearly constrained frameworks
01/11/2018 → 31/01/2019
Research

Functor categories for groups
01/10/2017 → 31/12/2018
Other

London Mathematical Society-Review & Final Approvals Travel to Delaware
25/09/2017 → 05/10/2017
Research

LMS Scheme 4 - 41434
01/09/2015 → 30/09/2015
Other

Comibinatorial Rigidity, Symmetric Geometric Constraint Systems and Applications
01/06/2015 → 31/08/2016
Research

Reconstructing Broken Symmetry
28/11/2014 → 27/03/2016
Research

London Mathematical Society - Visitor Grant (Scheme 2)
01/10/2014 → 28/10/2014
Research

EPSRC - Interpretation functors and infinite-dimensional representations of finite-dimensional algebras
09/09/2013 → 08/09/2016
Research

Research Activity

The research interests of our group cover a wide range of topics on the interface between algebra and geometry.

Geometric objects can be conveniently encoded using algebra. For example, a circle or ellipse in the plane can be described by a quadratic polynomial equation. Higher degree polynomials give more interesting spaces called "algebraic varieties", which we can study using tools from ring theory, or using more advanced tools like derived categories. The symmetries of a geometric object form a group, which can be studied using pure algebra and representation theory.

Conversely, geometric techniques can often be applied to algebraic objects. For example, you can often deform algebraic objects in families called moduli spaces, which have natural notions of geometry and topology. Or you can deduce something about a group by letting it act on a well-understood metric space.

In our department, the algebra and geometry group conducts research mainly in:

  • representation theory of groups and algebras,
  • group theory and geometric group theory,
  • Lie algebras and algebraic groups,
  • homotopical and homological algebra,
  • algebraic topology,
  • deformation theory,
  • noncommutative geometry,
  • symplectic topology.