Non-Invertible Symmetries and Dualities from the Ground Up - Class 1

Learn the fundamentals of non-invertible symmetries and dualities in this comprehensive lecture delivered by Paul Fendley from the University of Oxford. Explore the mathematical foundations and physical principles underlying these advanced concepts in theoretical physics, starting from basic principles and building toward more sophisticated applications. Discover how non-invertible symmetries differ from traditional symmetries and understand their role in modern field theory and condensed matter physics. Examine the connections between dualities and symmetry structures, with particular emphasis on their implications for quantum field theories and statistical mechanics systems. Gain insights into the mathematical tools and techniques used to analyze these symmetries, including their representation theory and algebraic structures. This foundational class serves as the first installment in a comprehensive series on anomalies, topology, and quantum information in field theory and condensed matter physics, providing essential background for understanding advanced topics in theoretical physics and their applications to quantum many-body systems.