Publication Areas

• Algebraic topology, including
• algebraic homotopy,
• homotopy coherence,
• strong shape theory and proper homotopy theory,
• global actions, groupoid atlases and their applications,
• fractafolds -fractal analogues of manifolds'
• topological quantum field theory,
and
• abstract homotopy theory.

• Category theory, including:
• enriched and lax category theory,
• n- and infinity categories,
• higher dimensional algebra and its applications,
• applications of category theory in computer science and information technology,

and
• categorical models of spatial phenomena
• AI and Theoretical Computer Science, including Multiagent Systems, the geometry of Information and Topological Data Analysis.
  • Multiagent systems.  Several papers on this area are listed in my publication list.
  • Geometry of Information:  This grew out of the fractafolds project.  Some indication of what I mean by the title can be gained from the report on that project (see `fractafolds' above) and also the papers on the Dagstuhl website ( http://drops.dagstuhl.de/portals/04351/).
  • Topological Data Analysis.