Weak Hopf Symmetry Behind the 2D Topological Phases

Explore a comprehensive research seminar that delves into the fundamental connections between weak Hopf symmetry and two-dimensional topological phases. Learn about the characterization of 2D topological phases through unitary modular tensor categories (UMTC) and discover the relationships between Kitaev's quantum double models and Levin-Wen string-net models. Examine the generalization of these models to weak Hopf algebras and multifusion categories, while understanding the equivalence between these broader classes of lattice models for non-chiral 2D topological phases. Gain insights into weak Hopf gauge and charge symmetries from a lattice gauge theory perspective, with particular emphasis on the weak Hopf symmetry underlying multifusion string-net models. The presentation includes references to recent research papers, highlighting ongoing developments and open problems in this field of quantum physics and topology.