Module #1 Introduction to Advanced Quantum Theory Overview of the course, review of basic quantum mechanics, and importance of advanced quantum theory
Module #2 Mathematical Preliminaries Review of relevant mathematical tools:linear algebra, differential equations, and group theory
Module #3 Quantum Operators and Algebras Introduction to quantum operators, algebras, and their representations
Module #4 Symmetries in Quantum Mechanics Symmetries, conservation laws, and Noethers theorem
Module #5 Quantum Field Theory:Introduction Basic concepts of quantum field theory, including fields, particles, and interactions
Module #6 Free Fields and Greens Functions Free fields, Greens functions, and their applications
Module #7 Interacting Fields and Feynman Diagrams Interacting fields, Feynman diagrams, and perturbation theory
Module #8 Renormalization Group and Running Couplings Introduction to renormalization group, running couplings, and asymptotic freedom
Module #9 Topological Quantum Field Theory Introduction to topological quantum field theory, topological invariants, and applications
Module #10 Integrable Systems and Quantum Inverse Scattering Introduction to integrable systems, quantum inverse scattering, and Bethe ansatz
Module #11 Black Holes and Quantum Gravity Introduction to black holes, event horizons, and quantum gravity
Module #12 Quantum Information and Entanglement Introduction to quantum information, entanglement, and quantum computing
Module #13 Quantum Error Correction and Fault Tolerance Quantum error correction, fault tolerance, and quantum error correction codes
Module #14 Many-Body Localization and Quantum Chaos Introduction to many-body localization, quantum chaos, and ergodicity
Module #15 Superconductivity and Superfluidity Introduction to superconductivity, superfluidity, and the BCS theory
Module #16 Quantum Phase Transitions and Criticality Introduction to quantum phase transitions, criticality, and universality
Module #17 Nonequilibrium Quantum Systems Introduction to nonequilibrium quantum systems, quantum transport, and dissipative dynamics
Module #18 Quantum Thermodynamics and Resource Theory Introduction to quantum thermodynamics, resource theory, and thermodynamic cost
Module #19 Topological Insulators and Superconductors Introduction to topological insulators, topological superconductors, and their applications
Module #20 Quantum Field Theory in Higher Dimensions Quantum field theory in higher dimensions, AdS/CFT correspondence, and holography
Module #21 Conformal Field Theory and Bootstrap Introduction to conformal field theory, bootstrap, and their applications
Module #22 Numerical Methods in Quantum Field Theory Introduction to numerical methods in quantum field theory, lattice gauge theory, and Monte Carlo simulations
Module #23 Applications of Advanced Quantum Theory Applications of advanced quantum theory to condensed matter physics, particle physics, and cosmology
Module #24 Current Research and Open Problems Overview of current research and open problems in advanced quantum theory
Module #25 Course Wrap-Up & Conclusion Planning next steps in Advanced Quantum Theory career
