Mathematical Sciences: Topics in Operator Algebras

Voiculescu将继续他的工作，在三个不同的 算子代数理论的几个方面：（i）赋范理想 Hilbert空间算子的扰动与熵 动力系统的不变量，（ii）自由群的II_1因子 以及自由积的非对易概率方法， （iii）拟对角C ~*-代数与代数的逼近。 这个项目的数学的一般领域有其 希尔伯特空间算子的代数理论的基础。 算子可以被认为是有限或无限的矩阵， 复数 特殊类型的运算符通常被放置在 在一个代数中，自然称为算子代数。 这些看似抽象的物体有着惊人的多样性， 应用. 例如，它们在纽结理论中起着关键作用， 这反过来又被用来研究 DNA.

Voiculescu will to continue his work in three different aspects of operator algebra theory: (i) normed-ideal perturbations of Hilbert space operators and entropic invariants of dynamical systems, (ii) II_1 factors of free groups and the noncommutative probability approach to free products, (iii)quasidiagonal C*-algebras and approximation of 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.