Ferry will study a number of topics in controlled topology and differential geometry. Most of these problems bear on the problem, "How much control is enough to force simple homotopy equivalence between polyhedra or homeomorphism between topological manifolds?" An interesting testing ground for controlled theories is on the borderline between topology and differential geometry, where there are problems which are obviously controlled in some way but for which there is no obvious control space. Ferry has already solved one such problem by, in some sense, letting the problem construct its own control space. He plans to explore further ramifications of these techniques.
