Schlumprecht will continue his study of the structure theory and local theory of Banach spaces, and specifically, the distortion problem. Schlumprecht's recent work in this area contributed significantly to the solutions of several long standing problems, including the unconditional basis problem, the hyperplane problem, and the prime Banach space problem, and additional results in these and related areas will be pursued. Banach space theory is that part of mathematics that attempts to generalize to infinitely many dimensions the structure of 3-dimensional Euclidean (i.e.ordinary) space. The axioms for the distance function in a Banach space are more relaxed than those for Euclidean distance (For example, the "parallelogram law" is not required to hold.), and as a result, the "geometry" of a Banach space can be quite exotic. Much of the research in this area concerns studying the structure theory of Banach spaces.
