Mathematical Sciences: Topics in Operator Algebras

Vocerescu将在算子代数理论的三个不同方面继续他的工作：(I)Hilbert空间算子的赋范理想扰动和动力系统的熵不变量，(Ii)自由群的II_1因子和自由积的非交换概率方法，(Iii)拟对角C*-代数和代数的逼近。这个项目的一般数学领域以希尔伯特空间算子的代数理论为基础。运算符可以被认为是复数的有限或无限矩阵。特殊类型的运算符通常放在一个代数中，自然称为运算符代数。这些看似抽象的对象有着令人惊讶的各种应用。例如，它们在纽结理论中扮演着关键角色，而纽结理论目前正被用于研究DNA的结构。

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.