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Explore the fundamental role of symmetries and anomalies in modern physics through this comprehensive summer school from the Institut des Hautes Etudes Scientifiques. Delve into the mathematical and physical foundations of anomalies across quantum systems, from condensed matter to high-energy particle physics, examining how these phenomena constrain dynamics and reveal insights into Standard Model extensions and topological quantum materials. Master the interdisciplinary approach connecting algebraic topology, topological quantum field theory, and characteristic classes with cutting-edge applications in supersymmetric quantum field theories and string theory. Learn from expert perspectives spanning mathematics (topological field theory, category theory), high-energy physics (chiral anomalies, 't Hooft anomaly matching), and condensed matter physics (symmetry-protected and symmetry-enhanced topological order). Cover essential topics including continuous flavor symmetry anomalies, conformal anomalies, lattice symmetries, CPT symmetries, higher-form and higher-group symmetries, non-invertible symmetries, and categorical frameworks. Engage with specialized lecture series on string theory symmetries and anomalies, generalized symmetries in 2D conformal field theories, higher symmetry in particle physics, anomalies in condensed matter physics, generalized symmetries and gauge theory phases, non-invertible symmetries, nonrelativistic conformal field theory, and non-invertible symmetries in quantum lattice models. Benefit from the expertise of leading researchers including organizing committee members Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki, alongside scientific committee advisors Anton Kapustin, Yuji Tachikawa, and Xiao-Gang Wen.
