Explore the intricate relationship between antiferromagnetism and superconductivity in the electron Hubbard model through this comprehensive lecture. Delve into advanced concepts such as the Hamiltonian, quantum states, ground states, symmetry breaking, and doping. Gain insights from Harvard University professor Subir Sachdev as he presents the sixth installment of "The Quantum Phases of Matter" series. Examine the Vanilla VCS Theory and its factorization in this joint course offering from the Institute for Advanced Study and the Tata Institute of Fundamental Research. Enhance your understanding of quantum physics and condensed matter theory in this 92-minute presentation designed for graduate-level physics students and researchers.