Mathematical Sciences: Joint K-spectral Sets and Subnormal Operators

算子论是现代分析的中心学科。它起源于二十世纪初对数学物理和偏方程的研究。当时，人们可以看到，平衡论、振动、量子理论等中的许多物理问题可以通过模拟这些现象的积分方程组进行富有成效的研究。在接下来的几年里，算符理论的主题已经成长为此类研究的中心位置，在核心数学中也是如此。现代分析的核心也是算子代数的相关学科，在该学科中，人们同时研究算子的集合。作为最好地将概率、测度论、拓扑学和几何学的概念转移到非对易环境中的数学构造，算子代数涉及到从数学本身到物理和微生物学的丰富而重要的一系列应用。保尔森教授的研究在算子理论和算子代数之间架起了桥梁。仔细分析算子代数的内部结构理论和它们之间的映射是一个日益重要的课题，保尔森教授就是这方面的专家。在以前的研究中，Paulsen教授得到了关于C*-代数之间完全有界映射的重要结果。他最近出版的关于这一主题的书有望为单算子理论家和算子代数学家开辟新的研究领域。在他目前的课程中，Paulsen教授将研究联合K-谱集、次正态模型和函数代数上的Hilbert模。前面的研究应该会导致对非自伴算子代数的张量积的深入了解。第二个领域探索膨胀理论的各个方面，后一个项目涉及到算子理论中的几个主题。

Operator theory is a central discipline in Modern Analysis. Its origins lie in the study of mathematical physics and partial equations in the early twentieth century. At that time, it was seen that numerous physical problems in the theory of equilibria, vibration, quantum theory, etc. could be studied productively via the integral equations that model the phenomena. In the ensuing years, the subject of operator theory has grown to a central position in such investigations, and in core mathematics as well. Also central to Modern Analysis is the related discipline of operator algebras in which one studies collections of operators simultaneously. As the mathematical construct which best transfers the concepts of probability, measure theory, topology, and geometry to noncommutative contexts, operator algebras relate to a rich and important array of applications, from within mathematics itself to physics and microbiology. The research of Professor Paulsen bridges both operator theory and operator algebras. A careful analysis of the internal structure theory of operator algebras and the maps between them is an increasingly important subject, and Professor Paulsen is an expert in such matters. In prior research, Professor Paulsen obtained important results concerning completely bounded maps between C*-algebras. His recent book on this subject is expected to open new areas of research for both single operator theorists as well as operator algebraists. In his current program, Professor Paulsen will study joint K-spectral sets, subnormal models, and Hilbert modules over function algebras. The former study should lead to insights into tensor products of nonself-adjoint operator algebras. The second area explores aspects of dilation theory, and the latter project relates to several topics in operator theory.