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Explore an algebraic framework for understanding planon-only abelian fracton orders in this 58-minute conference talk from Harvard CMSA's Workshop on Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras. Delve into three-dimensional gapped phases where fractional excitations are abelian particles constrained to move in parallel planes, with fusion and statistics data identified through finitely generated modules over Laurent polynomial rings paired with U(1)-valued quadratic forms. Learn about the excitation-detector principle as a necessary condition for physical realizability and examine the conjecture that this criterion may also be sufficient. Discover preliminary classification results and gain insights into how this elegant algebraic theory enables easily computable phase invariants and systematic classification of these quantum systems, presented through collaborative research with Michael Hermele, Wilbur Shirley, and Evan Wickenden.
