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Explore the intriguing question of rationality in smooth complex projective varieties through this illuminating lecture by Brendan Hassett from Brown University. Delve into general structure theorems and examine guiding examples such as cubic fourfolds to understand which members of a family of varieties are rational or stably rational. Gain insights into the complex world of algebraic geometry and expand your knowledge of rational varieties in this hour-long talk presented at the University of Miami.