Milman will study several related topics from the local theory of Banach spaces and the theory of convex bodies in R^n. Among them, volume estimates in finite dimensional normed spaces, random coordinate subspaces and existence of quotient spaces with good cotype constants. 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.
