Mathematical Sciences: Index Theory and K-Theory of Group C*-Algebras

希格森将继续他的研究有关的几个问题 Baum-Connes猜想断言，对于局部紧的 G的约化C ~*-代数的K-理论是等变的 它的普适真G空间的K理论。 这 调查将涉及使用一个指标定理为适当的 行动，椭圆算子的建筑物，和等变E理论。 这是算子代数更一般的K-理论的一部分。 这个项目的一般数学领域有其基础 希尔伯特空间算子的代数理论。 运营商 可以被认为是复数的有限或无限矩阵 号码 特殊类型的运算符通常放在 代数，自然称为算子代数。 这些看似 抽象对象具有令人惊讶的多种应用。 为 例如，它们在纽结理论中起着关键作用，而纽结理论又是 目前被用来研究DNA的结构。 **//

Higson will continue his study of several problems related to Baum-Connes conjecture which asserts that for a locally compact group G, the K-theory of the reduced C*-algebra of G is equivariant to the K-theory of its universal proper G-space. This investigation will involve the use of an index theorem for proper actions, elliptic operators on buildings, and equivariant E-theory. This is part of the more general K-theory for operator algebras. 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 seemingly 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. **//