Professor Szarek will study the isomorphic theory of Banach spaces, some problems from finite dimensional operator theory, and scientific computation linked to these areas. One of the problems to be investigated is whether extremely rigid infinite dimensional Banach spaces exist where for example the Calkin algebra is abelian or consists only of multiples of the identity operator. 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.
