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In this lecture, Zsolt Patakfalvi presents a mathematical counter-example to the log-canonical Beauville-Bogomolov decomposition. Learn how for each integer d > 3, there exists a K-trivial log canonical variety over complex numbers of dimension d that does not admit a Beauville-Bogomolov decomposition. Discover why this means that for the universal cover X of the variety, no decomposition exists as a product of an affine space and three types of projective varieties: strict Calabi-Yau, symplectic and rationally connected varieties. The presentation emphasizes that this counter-example is sharp, as the decomposition does hold for Kawamata log terminal varieties. This talk was recorded during the thematic meeting "Families of Kähler spaces" on April 24, 2025, at the Centre International de Rencontres Mathématiques in Marseille, France.
