Mathematical Sciences: Principal Currents

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Professor Pincus will continue his investigation of currents associated with the index structure of certain algebras of operators. In particular he will study certain bundles and sheaves which are associated to the local index which he invented as well as finer invariants. He will also study the geometric meaning of the principal function, an extension of the index which is also defined on the essential spectrum. Professor Pincus' research is in the general area of the theory of operators on Hilbert space. These operators are essentially infinite matrices of complex numbers. Such operators or linear transformations have applications in every area of applied science as well as in pure mathematics. This type of research is an attempt to classify certain important categories of such objects.