International Workshop on Operator Theory and Applications 2020

该奖项将为16位早期职业数学家参加将于2020年8月17日至21日在英国兰开斯特大学举行的算子理论与应用国际研讨会（IWOTA）提供旅费。该会议不仅是世界上最大的算子理论会议，而且被认为是将算子理论与其他运用算子理论技术和相关数学结果的学科联系起来的首要事件。IWOTA 2020将致力于算子理论及其应用的各个方面，并将汇集来自世界各地的顶尖研究人员。在兰开斯特举办这样一个大型活动也将提供一个独特的机会，加强美国和英国该领域一些最好的专家之间的研究联系。物理、数学和工程中的许多问题都可以通过将复杂的物理实体表示为称为矩阵的大型数字和数学符号数组来最好地描述。矩阵帮助我们可视化线性变换如何作用于向量空间；确定它们的结构揭示了转换的重要性质。希尔伯特空间算子是矩阵的无限维推广。向量的泛化通常是一个函数，因此，运算符经常被建模为函数空间上的乘法。目前，IWOTA 2020将由4位全体演讲嘉宾、14位半全体演讲嘉宾和几场特别会议组成。特别会议的主题包括算子空间、量子化函数理论和非交换勒贝格空间、算子代数和量子理论、非交换概率和随机矩阵、算子半群和泛函微积分、谱理论和微分方程、解析函数空间上的算子及其应用、复几何和算子理论、自由代数几何、量子群和代数量子场论、线性系统、以及为早期职业研究人员举办的研讨会。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，认为值得支持。

This award will cover travel for sixteen early-career mathematicians to attend the International Workshop in Operator Theory and Applications (IWOTA), to be held at Lancaster University in the United Kingdom, during August 17 - 21, 2020. The conference is not only the largest operator theory in the world, but it is also considered the premier event that connects operator theory to other disciplines that employ operator theoretic techniques and related mathematical results. IWOTA 2020 will be devoted to all aspects of operator theory and its applications and will feature top researchers from all around the world. Having such a major event organized in Lancaster will also provide a unique opportunity to reinforce research ties between some of the best experts in the field in the United States and United Kingdom.Many problems in physics, mathematics, and engineering can be best described by representing complex physical entities as large arrays of numbers and mathematical symbols, called matrices. Matrices help us visualize how linear transformations act on vector spaces; determining their structure reveals important properties of the transformations. Hilbert space operators are infinite-dimensional generalizations of matrices. The generalization of a vector is often a function and, as a result, operators are frequently modeled as multiplications on spaces of functions. At present, IWOTA 2020 will consist of four plenary speakers, fourteen semi-plenary speakers, and several special sessions. The topics of the special sessions include operator spaces, quantized function theory and noncommutative Lebesgue spaces, operator algebras and quantum theory, noncommutative probability and random matrices, operator semigroups and functional calculus, spectral theory and differential equations, operators on analytic function spaces and related applications, complex geometry and operator theory, free algebraic geometry, quantum groups and algebraic quantum field theory, linear systems, and a workshop for early-career researchers. The conference website is https://www.lancaster.ac.uk/maths/iwota2020/.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.