## Mathematical Sciences: C*-Algebra Extensions and Homomorphisms

##### Abstract

Lin will work to obtain an extension of the Weyl-von Neumann theorem which will be used to give a complete classification of C*- algebra extensions of C(X), X a compact subset of the plane, by a sigma unital simple C*-algebra. He will also investigate whether every C*-algebra of real rank zero has weak (FN), as has been shown by Lin in many cases. A final problem to be studied is that of classifying certain equivalence classes of homomorphisms from one C*-algebra to another. 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 non-commutative geometry, which is becoming increasingly important in physics.