Mathematical Sciences: Local Index Invariants for Rings of Type I & II

凯里教授将继续他在算子理论方面的工作 关于主流、局部指数和弗雷德霍姆 多变量谱理论中的互易性。 对于运算符环 类型II，这项工作涉及行列式之间的关系 算子代数与多重次调和函数理论。 这个项目涉及希尔伯特空间算子，可以是 被认为是复数的无限矩阵。 教授 凯里的项目将集中在一个更几何的方式来看待 这些运营商。 最终目标是能够分类和 对这些物体的大家族有更深入的了解， 因为它们在几乎所有的纯理论和应用科学分支中都很重要， 数学

Professor Carey will continue his work in operator theory concerning principal currents, local index, and Fredholm reciprocity in multivariable spectral theory. For operator rings of type II, this work involves relationships between determinant theory in operator algebras and plurisubharmonic functions. This project concerns Hilbert space operators which can be thought of as infinite matrices of complex numbers. Professor Carey's project will focus on a more geometric way of looking at these operators. The ultimate goal is to be able to classify and obtain a deeper understanding of large families of these objects, for they are important in almost all branches of pure and applied mathematics.