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 |
|---|
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 ImJ: hypersurfaces and chromatic elements in stable
homotopy