Mathematical Sciences: C*-Algebras of Singular Integral Operators and Toeplitz Operators Associated with N-Densional Flows

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Professor Xia will study the C*-algebras of random singular integral operators and Toeplitz operators associated with n- dimensional flows. He will analyze the ideal structure in these algebras and address questions such as their solvability. He will compute the K-groups of certain important sub-C*-algebras and their ideals with the goal of classifying these kinds of algebras. Professor Xia's project deals with C*-algebras. These algebras are families of Hilbert space operators each of which can be thought of as an infinite matrix of complex numbers. The algebras which Professor Xia will consider consist of operators which arise in more applied fields such as the study of partial differential equations.