This award will support research in the geometry of Banach spaces. In finite dimensions, all vector spaces are essentially the same. But in the infinite dimensional situation of interest here, this is far from the case. Banach spaces are infinite dimensional spaces with the additional structure introduced by varying notions of distance between points in the space. Such spaces have wide application in mathematics, both pure and applied. The particular problems which Professors Johnson and Pisier will address include the Lipschitz theory of finite metric spaces, operator theory and the factorization of operators, weak Hilbert spaces, probability theory, factorization of operator valued analytic functions, and completely bounded maps.
