Local Definitions of Gapped Hamiltonians and Topological and Invertible States III

Explore advanced concepts in quantum field theory and topological phases through this third installment of a specialized lecture series delivered at Harvard CMSA's Workshop on Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras. Delve into the intricate mathematical framework surrounding local definitions of gapped Hamiltonians, examining how these fundamental quantum mechanical operators can be characterized through topological and algebraic methods. Investigate the properties and classifications of topological states of matter, focusing on their invariant characteristics that remain unchanged under continuous deformations. Analyze invertible states and their role in understanding quantum phases, exploring how these special quantum states relate to the broader landscape of topological quantum field theories. Gain insights into the intersection of homotopy theory and operator algebras as powerful tools for studying quantum many-body systems, with particular emphasis on how these mathematical frameworks provide rigorous foundations for understanding gapped quantum phases and their topological properties.