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Delve into the advanced mathematical concepts of compact quantum surfaces in this comprehensive two-hour lecture presented by Elmar Wagner from Universidad Michoacana, Mexico. Explore the intricate theories and applications of quantum geometry, building upon the foundations established in Part I. Gain insights into the latest developments in this cutting-edge field of mathematical physics, and enhance your understanding of the complex interplay between quantum mechanics and geometry. Engage with challenging concepts and problem-solving techniques as you navigate through this in-depth exploration of compact quantum surfaces.