Algebra and Geometry

Group Members
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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 FussCatalan Combinatorics and Representation Theory
05/07/2021 → 29/08/2021
Research
Hausdorff Dimension Spectrum of Prop 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
Cocoordination 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 NonAssociative 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 SocietyReview & 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 infinitedimensional representations of finitedimensional 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 wellunderstood 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.