Mathematical Sciences: C*-algebras, Operator Theory and Applications

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Professor Salinas will pursue his research on multivariable operator theory, including Toeplitz C* algebras on bounded domains in n variables, weighted Wiener-Hopf operators, and joint quasitriangularity of operators and quasidiagonality of C* algebras. Professor Upmeier will continue and expand his work on multivariable Toeplitz operators, C* algebras, and index theory. He will also study quantization procedures on manifolds. Dr. Zhang will continue his work on the structure of certain simple C* algebras and multiplier and corona algebras of certain types of C* algebras. The notion of a C* algebra is an abstraction of the idea of a family of linear transformations on a space. These transformations can also be thought of as having values in the states of the space, and the property of this family which is responsible for the symbol * is that the algebra is generated by transformations whose values in these states are real numbers. The fact that these objects appear naturally in many branches of mathematics and physics make them important to study.