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
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
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 student: Neil Fullarton
Prof Kenneth A Brown Professor of Mathematics
Noncommutative algebra; Hopf algebras; homological algebra
Member of other research groups: Algebra
Research students: Astrid Jahn, Steven O'Hagan
Dr Alastair Craw Senior lecturer
Algebraic geometry; symplectic geometry; the McKay correspondence
Member of other research groups: Algebra
Research staff: Alexander Quintero Velez
Research students: Nathan Prabhu-Naik, Jesus Tapia Amador
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 Ulrich Kraehmer Lecturer
Noncommutative geometry; Hopf algebras and quantum groups; homological algebra
Member of other research groups: Algebra, Analysis
Research students: Jake Goodman, Ana Rovi
Dr Tom Leinster EPSRC Advanced Research Fellow/Reader
Category theory; analogues of Euler characteristic; metric and integral geometry; self-similarity
Member of other research groups: Algebra
Research student: Barry Devlin
Dr Brendan Owens Lecturer
Low-dimensional topology: knots, 3-manifolds, smooth 4-manifolds
Research student: Andrew Donald
Dr Alexander Quintero Velez Postdoctoral Research Fellow
Algebraic geometry; symplectic geometry; the McKay correspondence
Member of other research groups: Algebra
Supervisor: Alastair Craw
Dr Constanze Roitzheim EPSRC Postdoctoral Fellow
Stable homotopy theory; model categories
Member of other research groups: Algebra
Dr Richard J Steiner Senior lecturer
Category theory
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: Ewan Kenneth Morrison
Dr Stuart White Lecturer
Non-commutative geometry
Member of other research groups: Algebra, Analysis
Research students: Liam Dickson, Tomasz Pierzchala
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
Supervisor: Tom Leinster
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
Steven O'Hagan PhD Student
Research Topic: Hopf algebras
Member of other research groups: Algebra
Supervisor: Kenneth A Brown
Nathan Prabhu-Naik PhD Student
Research Topic: Tilting theory and quivers
Supervisor: Alastair Craw
Ana Rovi PhD Student
Research Topic: Lie algebroids
Member of other research groups: Algebra
Supervisor: Ulrich Kraehmer
Jesus Tapia Amador PhD Student
Frobenius manifolds
Research Topic: Quiver flag varieties
Supervisor: Alastair Craw
Dr Alastair Craw awarded EPSRC grant
Tuesday 27th March, 2012
Dr Alastair Craw was awarded an EPSRC grant for working on Bridgeland stability and the moveable cone. ...
Dr Ulrich Kraehmer awarded EPSRC grant to study Hopf algebroids and operads
Friday 10th February, 2012
Ulrich Kraehmer has won an EPSRC First Grant that will fund a project studying Hopf algebroids and operads. These are research areas in algebra and...