Zhang will continue his research on various invariants of C*- algebras, including the real rand, the topological stable rand, the exponential rand and length, the C*-projective length of the Grassmann space, and the homotopy groups of the unitary group and the Grassmann space of certain C*-algebras. He will also continue his investigation on the internal structure of the multiplier algebras in terms of the K-theory and its torsion subgroup of the associated C*-algebra. The general area of mathematics of this project has its basis in the theory of algebras of Hilbert space operators. Operators can be thought of as finite or infinite matrices of complex numbers. Special types of operators are often put together in an algebra, naturally called an operator algebra. These abstract objects have a surprising variety of applications. For example, they play a key role in knot theory, which in turn is currently being used to study the structure of DNA, and they are of fundamental importance in noncommutative geometry, which is becoming increasingly important in physics.
