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Explore the fundamental concepts and mathematical structures of topological field theory through this comprehensive master class series from NCCR SwissMAP's Mathematical Physics program. Delve into the intersection of topology and quantum field theory, examining how topological invariants arise in physical systems and their applications in modern theoretical physics. Learn about the mathematical foundations that underpin topological quantum field theories, including their categorical structures, functorial properties, and connections to knot theory and low-dimensional topology. Investigate key examples such as Chern-Simons theory, topological sigma models, and their role in understanding quantum invariants of manifolds. Discover how these theories provide powerful tools for studying phase transitions, quantum Hall effects, and other condensed matter phenomena where topology plays a crucial role. Gain insights into the relationship between topological field theories and algebraic structures, including their connections to representation theory and algebraic geometry.
