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Explore the fascinating world of hyperkähler varieties derived from CY2 categories in this illuminating lecture by Alex Perry from the University of Michigan. Delivered as part of the 2023 Fields Medal Symposium honoring Caucher Birkar, delve into the intricate mathematical concepts and theories surrounding these complex geometric structures. Gain insights into the latest research and developments in this field, and understand how these varieties relate to broader topics in algebraic geometry and mathematical physics.