Noncommutative Topology, Operator Algebras and Theoretical Physics

Noncommutative topology is an extension of classical topology that emerged in the second half of the twentieth century, adapting tools from operator algebras, algebraic and topological K-theory, and generalized index theory to the study of algebraic objects such as those that arise naturally in quantum physics: noncommutative algebras. The purpose of the School and Conference on Noncommutative Topology, Operator Algebras and Theoretical Physics is to bring graduate students and researchers (in physics and mathematics) into contact with the latest developments in this area of research in two different ways: through specialized courses and through a series of research conferences in which recent results of these techniques in different areas will be presented. On the physics side, the program will explore two main directions: applications of operator algebras to topological phases of quantum matter, on the one hand, and connections with quantum field theory on the other. On the mathematical side, the school will also feature applications of noncommutative topology and operator algebras in pure mathematics.