RESEARCH INTERESTS

My main areas of research are algebraic topology and geometry, with more specialised interests in algebraic combinatorics and Hopf algebras. Recently, I have helped to instigate the amalgamation of several threads into the emerging discipline of toric topology. I have listed some key words below; there are many further details in the description of my projects for postgraduate supervision. Electronic versions of recent preprints & offprints are available for downloading.

Last updated: 5 March 2007 Construction of the new School: Nick Higham's photos


Algebraic topology

Cobordism theory, complex oriented cohomology theory, homotopy limits and colimits, real and complex K-theory, loop spaces, model category theory, operations and cooperations, rational homotopy theory, stable homotopy theory, quaternionic constructions

Geometry

Polytopes, toric varieties, weighted projective space

Algebraic combinatorics,

Stanley-Reisner algebras, incidence coalgebras, umbral calculus, chromatic polynomials

Toric topology

Torus actions, quasitoric manifolds, Davis-Januszkiewicz constructions, moment-angle complexes, Bott towers

Hopf algebras

Hopf algebroids, quantum doubles


Work in progress

I am working on several documents with various coauthors (and, occasionally, on my own). They are not yet in a fit state for general consumption, but here are some of the working titles:

Victor M Buchstaber and Nigel Ray
Iterated doubling constructions and multiple cobordism theory

Dietrich Notbohm and Nigel Ray
On Davis-Januszkiewicz homotopy types II: completion and globalisation

Nigel Ray and William Schmitt
Combinatorial models for Steenrod comodules

Victor M Buchstaber, Nigel Ray, and William Schmitt
Lattice path models for formal group laws

Nigel Ray
Beyond ImJ: hypersurfaces and chromatic elements in stable homotopy


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