Professor Sheu will conduct research on the interrelation between C* algebras and geometry, including the areas of algebraic quantization, K-theoretic problems involving Toeplitz C* algebras and group C* algebras, Wiener-Hopf C* algebras on nilpotent groups, and singular foliation 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 objects that have values in certain 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.
