Mathematical Sciences: Projections on Banach Spaces
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Banach space theory treats infinite-dimensional phenomena                  within the framework of rigorous mathematics. It has historical                 connections to more concrete applied subjects because, for                      instance, solutions to differential equations are often                         conveniently thought of as inhabiting an appropriate Banach                     space. In physics, one frequently encounters systems with                       infinitely many degrees of freedom which must be modeled in                     Hilbert space, a special type of Banach space.                                      Two interesting things to do with a Banach space are to slice               it (technically, project it onto a complemented subspace) and to                approximate it by finite dimensional subspaces, in which one can                so to speak draw pictures and do geometry.  The principal                       investigator for this project will work on a famous open problem                that asks what the slices of a certain standard Banach space look               like, and will investigate the geometry of finite-dimensional                   subspaces of Banach spaces.
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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