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 |
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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

Polytopes, toric varieties, weighted projective space

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

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

Hopf algebroids, quantum doubles

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 Im*J*: hypersurfaces and chromatic elements in stable
homotopy

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