Classification of Disordered Insulators in One Dimension

Explore the mathematical aspects of disordered topological insulators in this comprehensive lecture. Delve into the characteristics of novel materials that insulate in their bulk but potentially conduct along their edges, with a focus on the integer quantum Hall effect as a prime example. Examine the concept of topological indices, their experimental measurability, and macroscopic quantization. Gain insights into the application of algebraic topology to quantum mechanical Hamiltonians. Survey recent findings, primarily concentrating on the classification problem in one dimension, which involves studying spaces of unitaries and orthogonal projections that essentially commute with a fixed projection. Learn about the collaborative research conducted with Jui-Hui Chung in this hour-long talk presented by Jacob Shapiro from Princeton University.