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Explore the intricacies of K-moduli spaces of Fano 3-folds in this 59-minute lecture by Anne-Sophie Kaloghiros from Brunel University London. Delivered as part of the 2023 Fields Medal Symposium honoring Caucher Birkar, delve into advanced mathematical concepts and their applications in algebraic geometry. Gain insights into the latest research and developments in this specialized field of mathematics.