Explore a comprehensive lecture on new developments in algebraic geometry, focusing on rationality in algebraic varieties. Delve into the complexities of birational geometry, unirational and rationally connected varieties, and recent obstructions to rationality. Examine the powerful degeneration argument and its applications, including the decomposition of the diagonal. Investigate Chow groups, birational invariants, and unramified cohomology as tools for distinguishing between rational and unirational varieties. Learn about the Artin-Mumford invariant, cohomological decomposition of the diagonal, and their connections to the Clemens-Griffiths criterion. Gain insights into cutting-edge research in complex algebraic geometry, presented by renowned mathematician Claire Voisin from the Collège de France.