Mathematical Sciences: Operator Algebras and Geometry

Sheu教授将研究C* 代数与几何之间的相互关系，包括代数量子化、涉及Toeplitz C* 代数和群C* 代数的K理论问题、幂零群上的Wiener-Hopf C* 代数和奇异叶状C* 代数。C* 代数的概念是空间上线性变换族概念的抽象。这些变换也可以被认为是在空间的某些状态中具有值的对象，而这个族的属性是负责符号 * 的，它是由在这些状态中的值是真实的数的变换生成的代数。事实上，这些对象自然地出现在数学和物理的许多分支，使他们重要的研究。

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.