Mathematical Sciences: Some Topological Aspects of C*-Algebras

菲利普斯教授将研究C*-代数中指数秩的概念。特别是，他将(a)更好地理解矩阵值函数的代数的指数秩，以及与实秩的可能联系，(b)确定稳定C*-代数的指数秩，(C)进一步研究实秩零与性质弱（FU）之间的关系。此外，菲利普斯教授将研究C*-代数逆极限的同伦理论。C*代数的概念是对空间上一系列线性变换的抽象。这些变换也可以被认为是在空间的状态中有值，这个族的性质是负责符号*的是代数是由这些状态中的值是实数的变换生成的。这些对象在数学和物理的许多分支中自然出现的事实，使它们成为研究的重要对象。

Professor Phillips will investigate the concept of exponential rank in C*-algebras. In particular he will (a) obtain a better understanding of the exponential rank of algebras of matrix valued functions, and the possible connections with real rank, (b) determine the exponential rank of stable C*-algebras, and (c) further investigate the relation between real rank zero and the property weak (FU). In addition Professor Phillips will investigate the homotopy theory of inverse limits of 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 having values in the 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.