Operator Algebras, Dynamics, and Classification

Texas A&M Research Foundation, College Station TX

Investigators

Abstract

Kerr The 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 theme will 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