Partial Symmetries of Braided Categories and Fusion of Gapped Boundaries in Topological Orders

Explore partial symmetries of braided categories and the fusion of gapped boundaries in topological orders through this mathematical physics seminar delivered by Professor Dmitri Nikshych from the University of New Hampshire. Delve into advanced concepts at the intersection of category theory, quantum field theory, and condensed matter physics as part of the "Quantum field theory with boundaries, impurities, and defects" research programme at the Isaac Newton Institute. Examine how partial symmetries manifest in braided categorical structures and understand their role in describing topological phases of matter. Investigate the mathematical framework governing gapped boundaries and their fusion properties, which are crucial for understanding edge states and boundary phenomena in topological quantum systems. Gain insights into the categorical approach to topological order and its applications to quantum many-body systems, with particular emphasis on the mathematical structures that encode topological information and symmetry properties.