This project is for mathematical research on singular integral operators and related matters. These operators transform functions which may be quite chaotic in their behavior into functions which are very smooth. The study of their continuity properties, that is, how small changes in the input function show up in the transformed function, is basic to much of mathematical analysis. Such investigations are part of the research which Professor Semmes will undertake. Surfaces in space give rise to singular integral operators; these will be studied with the aim of relating continuity properties of the operators to geometric properties of the surfaces. A collateral group of problems to be pursued has to with the complex method of interpolation of Banach spaces from the viewpoint of differential geometry and differential equations.