Cubical homotopy theory: a beginning

A cubical complex is the analogue of a simplicial complex, but built with cubes rather than tetrahedra. Cubical complexes appeared in the early descriptions of homology theory and combinatorial homotopy theory in the middle of the twentieth century, but development of the subject area stopped as simplicial sets became the dominant combinatorial model for homotopy theory as a result of the work of Kan and later Quillen. Cubical complexes have recently resurfaced as objects of fundamental interest in Pratt's theory of higher dimensional automata in concurrency theory, and have appeared in some discussions of higher categorical structures. This talk will display an approach to the still unanswered question of the existence of an intrinsic combinatorial homotopy theory for these objects.

The speaker is a candidate for the position of Head, Department of Mathematics.