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Explore a colloquium talk delving into the intricacies of interpolation and sampling in analytic function spaces. Join John McCarthy from Washington University as he presents a comprehensive overview of the subject, covering topics from the prehistory of interpolation to the Omega Theorem. Gain insights into the general problem, the concept of buying disks, retraction techniques, and the local extension property. Discover how a shift in perspective led to removing restrictions and considering all sets. Engage with this in-depth discussion that forms part of the Focus Program on Analytic Function Spaces and their Applications at the Fields Institute.