Explore advanced concepts in quantum field theory through this seminar lecture delivered by Professor Shinsei Ryu from Princeton University. Delve into the intricate connections between higher Berry phases, tensor networks, and boundary conformal field theory, examining how these fundamental concepts intersect in modern theoretical physics. Learn about the mathematical frameworks that describe quantum systems with boundaries, impurities, and defects, and discover how tensor network approaches can provide new insights into conformal field theories at boundaries. Investigate the role of higher Berry phases in characterizing topological properties of quantum many-body systems and their relationship to boundary phenomena. Gain understanding of cutting-edge research methodologies that bridge quantum information theory, condensed matter physics, and mathematical physics, with particular emphasis on systems exhibiting non-trivial boundary conditions and topological features.