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Explore the intricacies of minimal free resolutions in this 58-minute lecture by Karim Adiprasito from the Hebrew University of Jerusalem. Delve into open questions and recent findings regarding the "shape" of minimal resolutions, and gain insights into both established and innovative methodologies employed in this field of study. Discover the complexities of algebraic geometry and homological algebra as Adiprasito surveys various approaches to understanding these fundamental mathematical structures.