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Explore the intricate relationship between boundary conditions and phases in quantum field theories through this comprehensive conference talk delivered at ICBS2025. Delve into the mathematical frameworks that govern how boundary conditions influence the behavior and classification of different phases in quantum field theoretical systems. Examine the theoretical foundations and advanced concepts that connect topological aspects of field theories with their boundary specifications. Investigate how different boundary conditions can lead to distinct physical phases and understand the implications for both theoretical physics and practical applications. Analyze the role of symmetries, topological invariants, and geometric structures in determining phase transitions and boundary effects. Gain insights into cutting-edge research methodologies used to study these complex interactions and their significance in modern theoretical physics, including applications to condensed matter systems, string theory, and quantum gravity.
