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Explore the groundbreaking applications of topology and topological defects in phase transitions within two-dimensional systems in this Nobel Prize-winning lecture by J. Michael Kosterlitz. Delve into the theoretical predictions and experimental verifications in 2D superfluids, superconductors, and crystals, showcasing the quantitative agreement with topological defect theories. Gain insights into the Heisenberg model, vortex schematics, and scaling methods while examining compelling experimental results that validate these concepts. Learn why this research matters and how it contributed to Kosterlitz and Thouless receiving half of the 2016 Physics Nobel Prize.