The study of such objects brings together ring theory, topology and algebraic geometry and has applications in integrable systems and mathematical physics.
Geometry and Topology
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A deformation of a singularity
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A 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
Postgraduate opportunities: An equivariant approach to higher genus Weierstrass P-functions
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-modules, 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 student: Duncan Mc Coy
Dr Richard J Steiner Senior lecturer
Category theory
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 Anne Thomas Lecturer
Geometric group theory; rigidity; buildings; Coxeter groups
Member of other research groups: Algebra
Dr Christian Voigt Lecturer
Noncommutative geometry; K-theory; Quantum groups
Dr Raymond Vozzo Lecturer
Differential geometry; gerbes; infinite-dimensional geometry.
Dr Liam Watson Lecturer
Low-dimensional topology
Dr Stuart White Senior Lecturer
Non-commutative geometry
Member of other research groups: Algebra, Analysis
Research students: Tomasz Pierzchala, Jorge Castillejos Lopez , Liam Dickson
Dr Andrew Wilson University Teacher of Mathematics
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 student: Gabriel Tornetta
Pouya Adrom PhD Student
Research Topic: Topics in abstract homotopy theory
Supervisor: Daniel Stevenson
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
An equivariant approach to higher genus Weierstrass P-functions (PhD)
Supervisors: Chris Athorne
Relevant research groups: Integrable Systems and Mathematical Physics, Geometry and Topology
To obtain information about P-functions associated with planar curves of genus 4 and more using representation theory within an equivariant framework. Methods developed by the supervisor considerably simplify singularity based methods and illuminate the geometric structures of differential relations between these multi-periodic, Abelian functions. The functions themselves are of use in the theory of Integrability.
Whittaker Prize of the Edinburgh Maths Society
Friday 7th June, 2013
Dr Stuart White has been awarded the Whittaker Prize of the Edinburgh Maths Society. It is a very prestigious award and very hard to win,...
Monday 7th October16:00-17:00Maths 204
Ryan Budney (University of Victoria)
Monday 14th October16:00-17:00Maths 204
Mauro Mauricio (Alfred Renyi Institute of Mathematics)
Monday 21st October16:00-17:00Maths 204
Andrew Lobb (University of Durham)
Tuesday 29th October15:00-16:00Maths 515
Christian Klein (University of Bourgogne)
Monday 25th November16:00-17:00Maths 204
Behrang Noohi (Queen Mary University of London)