Geometry and Topology

  • A deformation of a singularity

    Singularity

    The study of such objects brings together ring theory, topology and algebraic geometry and has applications in integrable systems and mathematical physics.

  • A braid

    Braid

    Braids appear spontaneously in both topology and category theory, for reasons that turn out to reveal deep connections between these subjects.

Research activity in Geometry and Topology occurs in several areas, including that of Category Theory.

Our interests in Geometry cover a broad range of topics including: algebraic geometry; differential geometry; geometric group theory; and interactions with differential equations, representation theory and string theory.

Our interests in Topology encompass low-dimensional topology and algebraic topology. While the study of these subjects often involves geometric intuition, Topologists tend to study much less `rigid' geometric situations than Geometers.

Category theory looks at mathematics on a large scale. The aim is to strip away inessential details in order to get to the essence of things.

Dr Chris Athorne Senior lecturer

Geometric representation theory; algebraic curves;soliton theory

Member of other research groups: Integrable Systems and Mathematical Physics
Research student: Sophie Rachel Norman

Dr Andrew J Baker Reader

Hopf algebras and formal groups; stable homotopy theory;structured ring spectra and derived algebraic geometry; Morava K-theory for classifying spaces of finite groups and fusion systems

Member of other research groups: Algebra

Dr Gwyn Bellamy Lecturer

D-module, symplectic algebraic geometry, deformation-quantization algebras

Member of other research groups: Algebra

Dr Tara Brendle Lecturer

Geometric group theory; mapping class groups of surfaces; low-dimensional topology

Member of other research groups: Algebra
Research students: Neil Fullarton, Charalampos Stylianakis, Alan Logan

Prof Kenneth A Brown Professor of Mathematics

Noncommutative algebra; Hopf algebras; homological algebra

Member of other research groups: Algebra
Research students: Astrid Jahn, Paul Gilmartin

Dr Mikhail Feigin Lecturer

Quantum integrable systems; Hadamard's problem; WDVV equations; random matrices; Representations of Chrednik algebras; rings of quasi-invariants

Member of other research groups: Integrable Systems and Mathematical Physics, Algebra

Dr James Griffin Research Associate

Operads;  Loop spaces; (Co)homology theories of algebras

Member of other research groups: Algebra
Supervisor: Ulrich Kraehmer

Dr Brendan Owens Lecturer

Low-dimensional topology: knots, 3-manifolds, smooth 4-manifolds

Research students: Andrew Donald, Duncan Mc Coy

Dr Daniel Stevenson Lecturer

Abstract homotopy theory; category theory; gerbes

Research student: Pouya Adrom

Prof Ian A B Strachan Professor of Mathematical Physics

Geometry and integrable systems; Frobenius manifolds; twistor theory and self-duality

Member of other research groups: Integrable Systems and Mathematical Physics
Research student: Richard Stedman

Dr Christian Voigt Lecturer

Noncommutative geometry; K-theory; Quantum groups

Member of other research groups: Analysis, Algebra

Dr Raymond Vozzo Lecturer

Differential geometry; gerbes; infinite-dimensional geometry.

Dr Stuart White Senior Lecturer

Non-commutative geometry

Member of other research groups: Algebra, Analysis
Research students: Liam Dickson, Tomasz Pierzchala, Jorge Castillejos Lopez

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, Analysis, Algebra
Research students: Andrew Hawkins, Gabriel Tornetta

Pouya Adrom PhD Student

Research Topic: Topics in abstract homotopy theory
Supervisor: Daniel Stevenson

Barry Devlin PhD Student

Research Topic: Category Theory
Member of other research groups: Algebra

Andrew Donald PhD Student

Research Topic: Seifert manifolds which embed in the four-sphere
Supervisor: Brendan Owens

Neil Fullarton PhD Student

Research Topic: Mapping class groups and related groups
Member of other research groups: Algebra
Supervisor: Tara Brendle

Astrid Jahn PhD Student

Research Topic: Hopf algebras
Member of other research groups: Algebra
Supervisor: Kenneth A Brown

Duncan Mc Coy PhD Student

Research Topic: Knots and Smooth Four-Dimensional Manifolds
Supervisor: Brendan Owens

Ana Rovi PhD Student

Research Topic: Lie algebroids
Member of other research groups: Algebra
Supervisor: Ulrich Kraehmer

Charalampos Stylianakis PhD Student

Research Topic: Mapping Class Groups and Related Groups
Member of other research groups: Algebra
Supervisor: Tara Brendle

Friday 10th May14:00-15:00Mathematics 417
Prof. F. Quinn (Virginia Polytechnic Institute and State Universit)
Monday 13th May16:00-17:00Mathematics 325
Dr C. Wendl (University College London)
Monday 20th May16:00-17:00Mathematics 325
Dr A. Wilson (University of Glasgow)
Monday 3rd June16:00-17:00Mathematics 325
Dr J. Giansiracusa (Swansea University)

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