Mathematical Sciences: "Invariants of Operator Algebras"

Dadarlat将研究一个渐近的非稳定理论， C ~*-代数同态，~*-代数的同伦分类 次齐次C ~*-代数同态与扰动 同态理论到真实的秩为零的C*-代数。 这将 提供了C* 的几何性质之间的联系， 代数及其代数不变量，并将奠定 核简单可分分类理论的基础 C*-代数 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。 这些抽象 物体的应用范围之广令人惊讶。 比如说， 它们在纽结理论中起着关键作用，而纽结理论目前 被用来研究DNA的结构， 在非对易几何中的重要性， 在物理学中变得越来越重要。

Dadarlat will investigate a nonstable theory of asymptotic homomorphisms of C*-algebras, a homotopy classification of *- homomorphisms of subhomogeneous C*-algebras, and a perturbation theory of homomorphisms into real rank zero C*-algebras. This will provide connections between the geometrical properties of C*- algebras and their algebraic invariants, and will lay the foundation for a classification theory of nuclear simple separable C*-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 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 noncommutative geometry, which is becoming increasingly important in physics.