Professor Xia will study a number of topics in the theory of almost commuting n-tuples of Hilbert space operators. He will investigate cyclic cohomology and trace formulas for almost commuting n-tuples. He will study the theory of n-tuples of almost unperturbed Schrodinger operators and he will try to find a complete set of unitary invariants for subnormal tuples of operators. This research involves the theory of Hilbert space operators. These operators can be thought of as infinite matrices of complex numbers. They find application in almost every branch of pure and applied mathematics. The object of Professor Xia's research is to classify and understand important families of these operators.
