Algebraic techniques in 3-cateories of (2+1)D topological defects

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• Peter Huston (University of Leeds)
• Thursday 30 October 2025, 11:30-12:30
• Seminar Room 1, Newton Institute.

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BIDW02 - Diving Deeper into Defects: On the Intersection of Field Theory, Quantum Matter, and Mathematics

Topological phases of matter in (2+1)D should naturally form a 3-category, in which k-morphisms represent defects of codimension k. By the cobordism hypothesis, the 3-categories of (2+1)D topological order with a fixed anomaly are each equivalent to the 3-category of fusion categories enriched over a corresponding UMTC . In ongoing work with Fiona Burnell, we introduce algebraic techniques for concrete computations in 3-categories of (2+1)D topological order, including a tunneling approach to the classification of point defects which generalizes the use of braiding to identify anyon types. We then apply these techniques to compute ground state degeneracy and classify low energy excitations in a class of fracton-like (2+1)D topological defect networks.

This talk is part of the Isaac Newton Institute Seminar Series series.

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