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Research Interests
I work in the Department of Mathematics at the University of Glasgow, where I do research in multiple categories, a branch of algebra connected with homotopy theory and with concurrency in Computer Science.In this subject, one constructs many interesting polyhedra; for example, the following figure shows the two-dimensional source of the four-dimensional cube:
Selected Publications
Some of my publications are:- Nerves of multiple categories (with F. A. Al-Agl), Proc. London Math Soc. (3) 66 (1993), 92-128.
- The algebra of directed complexes, Applied categorical structures 1 (1993), 247-284.
- Pasting in multiple categories, Theory and Applications of Categories 4 (1998), No. 1, 1-36 ( http://www.tac.mta.ca/tac/volumes/1998/n1/4-01abs.html).
- Multiple categories: the equivalence of a globular and a cubical approach (with F. A. Al-Agl and R. Brown), Advances in Mathematics 170 (2002), 71-118 (http://arXiv.org/math.CT/0007009).
- Omega-categories and chain complexes, Homology, Homotopy and Applications 6(1) (2004), 175-200.
- Thin fillers in the cubical nerves of omega-categories, Theory and Applications of Categories 16 (2006), No. 8, 144-173 ( http://www.tac.mta.ca/tac/volumes/16/8/16-08abs.html).
- Simple omega-categories and chain complexes, Homology, Homotopy and Applications 9(1) (2007), 451-465.
- Orientals, Contemporary Mathematics 431 (2007), 427-439 (http://arXiv.org/math.CT/0601383).
Contact Details
Department of MathematicsUniversity of Glasgow
University Gardens
GLASGOW
Great Britain
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