Mathematical Sciences: Principal Currents

平卡斯教授将继续研究与某些算子代数的索引结构相关的电流。特别是，他将研究与他所发明的局部指标有关的束和束，以及更精细的不变量。他还将研究主函数的几何意义，这是指数的延伸，也定义在本质谱上。平卡斯教授的研究领域是希尔伯特空间的算子理论。这些算子本质上是复数的无限矩阵。这样的算子或线性变换在应用科学的各个领域以及纯数学中都有应用。这种类型的研究是试图对这类物体的某些重要类别进行分类。

Professor Pincus will continue his investigation of currents associated with the index structure of certain algebras of operators. In particular he will study certain bundles and sheaves which are associated to the local index which he invented as well as finer invariants. He will also study the geometric meaning of the principal function, an extension of the index which is also defined on the essential spectrum. Professor Pincus' research is in the general area of the theory of operators on Hilbert space. These operators are essentially infinite matrices of complex numbers. Such operators or linear transformations have applications in every area of applied science as well as in pure mathematics. This type of research is an attempt to classify certain important categories of such objects.