Mathematical Sciences: Index Theory and Cyclic Cohomology

尼斯特将继续他的工作，在这一部分的理论， 与非交换几何有关的算子代数，以及 特别是指数理论和循环上同调。 他的直系 目标包括双变Chern-Connes特征的公式 以及Atiyah-Singer被积函数的鉴定， 计算叶状代数的循环上同调 Bott的单纯形方法，以及这两种方法的组合， 叶理指数定理 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。 这些抽象对象有着令人惊讶的多种应用。 例如，它们在纽结理论中起着关键作用， 目前正被用于研究DNA的结构， 在非对易几何中具有根本的重要性， 在物理学中变得越来越重要

Nistor will continue his work in that part of the theory of operator algebras relating to noncommutative geometry, and particularly index theory and cyclic cohomology. His immediate goals include a formula for the bivariant Chern-Connes character and the identification of the Atiyah-Singer integrand, computation of the cyclic cohomology of foliation algebras using Bott's simplicial methods, and a combination of these two into an index theorem for foliations. 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.