Toward an Algebraic Theory of Fracton Orders

This conference talk by Mike Hermele from CU Boulder explores the development of an algebraic theory for fracton orders, presented during the Generalized Symmetries: High-Energy, Condensed Matter and Mathematics KITP conference held at UC Santa Barbara in April 2025. Delve into the cutting-edge research connecting quantum field theory with topological defects and their action on operator spaces, which has revolutionized our understanding of symmetries over the past decade. Learn how these generalized symmetry concepts have revealed unexpected physical phenomena across condensed matter, high energy physics, and quantum gravity. The talk is part of a conference coordinated by experts Maissam Barkeshli, Michele Del Zotto, Sakura Schafer-Nameki, and Shu-Heng Shao, designed to bring participants up to speed with recent advances and open problems in this rapidly evolving field.