Analytic and Geometric Aspects of Operator Algebras

抽象的安德森 主要研究者将继续发展一个几何谱理论的n元组的自伴算子在有限冯诺依曼代数。 一个目标是使用这种新的方法，试图开发一个连贯的理论，这些运营商的联合频谱。 另一个目的是利用它来加深我们对无理旋转代数和冯诺依曼代数等算子代数的结构的理解。 这个项目是关于算子代数某些方面的研究。这些物体在研究各种各样的问题，包括数学物理、量子力学和纽结理论等领域的问题时，都证明是卓有成效的。 首席研究员和他的同事发现了一种新的方法来查看某些分析数据（矩阵的特征值及其无限维类似物-运营商的频谱）。 该项目的一个主要目标是解决一个困难的问题（非通勤运营商的联合频谱），到目前为止，这个问题已经经受住了反复的猛烈攻击。众所周知，本征值和其他光谱数据对于理解工程和科学中的许多真实的世界问题是必不可少的。 因此，这个项目有可能产生解决应用数学中以前无法解决的问题的方法。

Abstract Anderson The principal investigator will continue to develop a geometric spectral theory for n-tuples of self-adjoint operators in finite von Neumann algebras. One goal is to use this new approach to try to develop a coherent theory of the joint spectrum of such operators. Another aim is to use it to deepen our understanding of the structure of such operator algebras as irrational rotation algebras and von Neumann algebras determined by free groups. This project is concerned with the study of certain aspects of operator algebras. These objects have proved fruitful in the study of a wide variety of questions, including problems in such fields as mathematical physics, quantum mechanics and knot theory. The principal investigator and his coworkers have discovered a new way to view certain analytic data (eigenvalues of matrices and their infinite dimensional analogues - spectra of operators). A major goal of the project is to solve a difficult problem (joint spectrum for non-commuting operators), which thus far has withstood repeated vigorous attacks. It is well known that eigenvalues and other spectral data are essential in understanding many real world problems in engineering and science. Thus, it is possible that this project could produce methods for attacking questions in applied mathematics that have not been previously accessible.