Operator Algebras, Dynamics, and Classification

该项目将包括一系列相互关联的研究和教育活动，围绕算子代数和动力系统的主题。主要的驱动主题将是分类的概念，既作为内部结构的调查框架，也作为外部观点，其中关于某些现象的普遍性和它们发生的复杂性的问题可以使用描述性集合论的工具来解决。 该计划将桥梁活动在Banach空间理论，几何和组合群论，凸几何，集合论和代数拓扑。 数学结构研究的主要目标之一是对可能出现的各种可能性进行分类，事实上，数学中的许多重要结果都是一种或另一种形式的分类定理。然而，当人们处理无限维现象时，例如经典力学和量子力学中出现的现象，可分类性显然是有限的。这些可分类性问题本身构成了一个理论，尽管它很抽象，但涉及人们在物理系统中经常看到的对称性和混乱的概念。 该项目的目的是研究各种类型的无限维结构的分类极限，这些结构起源于经典和量子物理学的几何和概率方面

KerrThe project will consist of a host of interconnected research and educational activities centered around the subjects of operator algebras and dynamical systems. The principal driving themewill be the notion of classification, both as a framework for the investigation of internal structure and as an external viewpoint where questions about the prevalence of certain phenomena and the complexity with which they occur can be addressed using the tools of descriptive set theory. This program will bridge to activity in Banach space theory, geometric and combinatorial group theory, convex geometry, set theory, and algebraic topology. One of the main goals in the investigation of mathematical structure is to classify the variety of possibilities that may occur, and indeed many of the significant results in mathematics are classification theorems of one form or another.It has become apparent however that there can be limits to classifiability when one is dealing with infinite-dimensional phenomena such as those that arise in classical and quantum mechanics. These issues of classifiability themselves comprise a theory which, despite its abstraction, involves the very notions of symmetry and chaos that one often sees in physical systems. The aim of the project is to study the limits of classification for various types of infinite-dimensional structures that have their origin in the geometric and probabilistic aspects of classical and quantum physics