Skein Theory and the Quantum A-Polynomial - Part 4

Explore advanced concepts in skein theory and the quantum A-polynomial in this 46-minute lecture delivered by J. Brown from the University of Edinburgh as part of the 2025 SCGCS School on Topological Symmetries and Defects in Quantum Field Theory. Delve into the mathematical foundations that connect knot theory with quantum field theory, examining how skein relations provide algebraic tools for studying knots and links through polynomial invariants. Investigate the quantum A-polynomial as a powerful invariant that encodes geometric and topological information about knot complements, building upon classical A-polynomial theory. Learn how these mathematical structures relate to topological quantum field theories and their applications in understanding quantum symmetries and defects. This fourth installment continues the comprehensive exploration of these interconnected topics, providing essential knowledge for researchers and advanced students working at the intersection of topology, algebra, and quantum physics.