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Explore the non-abelian generalization of the classical Rees construction in this advanced mathematics lecture from the Workshop on Special Cycles and Related Topics at the Institute for Advanced Study. Delve into how the traditional Rees construction, commonly used in commutative algebra and Hodge theory, interpolates between filtrations as Gm-equivariant vector bundles on the affine line and their associated gradings. Examine various non-abelian versions where Gm is replaced by a reductive group, and discover a Galois correspondence between prehomogeneous spaces and certain monodical categories. Learn how this theoretical framework applies to monoidal categories of motives with concrete applications to algebraic cycles, presented by Yves Andre from Institut de Mathématiques de Jussieu - Paris Rive Gauche.
