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Explore the fundamental concepts of non-invertible symmetries and dualities in this comprehensive lecture delivered by Paul Fendley at the Galileo Galilei Institute. Delve into advanced theoretical physics topics as Fendley introduces the basic principles underlying non-invertible symmetries, examining their mathematical foundations and physical implications. Learn how these symmetries differ from traditional invertible symmetries and discover their role in modern quantum field theory and condensed matter physics. Investigate the connection between non-invertible symmetries and various duality transformations, understanding how these concepts reshape our understanding of symmetry in physical systems. Gain insights into the mathematical structures that govern these symmetries and their applications in describing phase transitions and topological phases of matter. This foundational lecture serves as an essential introduction to cutting-edge developments in theoretical physics, providing the groundwork for understanding more advanced topics in the field of non-invertible symmetries and their dualities.
