Local Definitions of Gapped Hamiltonians and Topological and Invertible States I

Explore the mathematical foundations of quantum many-body systems in this conference talk from the Workshop on Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras. Delve into the local characterizations of gapped Hamiltonians and examine how topological and invertible quantum states can be rigorously defined through local properties. Learn about the intersection of quantum field theory, condensed matter physics, and advanced mathematical frameworks including homotopy theory and operator algebras. Discover how local definitions provide powerful tools for understanding the global properties of quantum systems, particularly in the context of topological phases of matter and their classification. Gain insights into the mathematical structures that underlie some of the most exotic states of quantum matter and their potential applications in quantum computation and topology.