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Explore a 43-minute conference talk by Colleen Delaney from Purdue University discussing complexity-theoretic hierarchies of topological order, presented at the Generalized Symmetries: High-Energy, Condensed Matter and Mathematics KITP conference held at UC Santa Barbara's Kavli Institute for Theoretical Physics in April 2025. The talk contributes to a decade of progress in quantum field theory where symmetries are interpreted through topological defects acting on operator spaces, creating a generalized understanding of symmetries with applications across condensed matter, high energy physics, and quantum gravity. The conference brought together leading experts to share recent advances and open problems in the field, coordinated by Maissam Barkeshli, Michele Del Zotto, Sakura Schafer-Nameki, and Shu-Heng Shao.
