I work in the
School of Mathematics and Statistics at
the University of Glasgow, where I do research in multiple
categories, a branch of algebra connected with homotopy theory and with concurrency in
In this subject, one constructs many interesting polyhedra;
for example, the following figure shows the two-dimensional source of the four-dimensional
The cubical branch of this theory involves studying maps between cubes which map each face into a union of faces of the same or of smaller dimension and which are in a sense order-preserving. These maps can be represented by chain maps between chain complexes and can therefore be investigated algebraically. The investigation of these maps might be a suitable project for a PhD student.
Some of my publications are:
Nerves of multiple categories (with F. A. Al-Agl), Proc. London Math Soc. (3) 66 (1993),
The algebra of directed complexes, Applied categorical structures 1 (1993), 247-284.