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Explore the mathematical foundations of gapped quantum systems through the lens of projective topological field theories in this conference talk from Harvard CMSA's Workshop on Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras. Delve into how gapped quantum systems can be approximated at low energy by projective topological field theories, enabling the reinterpretation of classification, symmetries, and anomalies questions through homotopy theory of moduli spaces. Learn about the construction of a moduli space for 3-dimensional TQFTs and understand how its homotopy theory provides insights into the low energy behavior of gapped systems in 2+1 dimensions. Examine how this moduli space depends on fixed target categories, built from classifying spaces of higher groups of automorphisms of ribbon categories. Focus on target categories with convenient algebraic features that maintain analytical robustness for boundary and relative theories defined through unitary representations on topological vector spaces. Gain advanced mathematical insights into the intersection of quantum field theory, topology, and operator algebras from a leading researcher in the field.
