Conference Agenda

The decomposition theorem of Beilinson, Bernstein, Deligne, and Gabber is among the deepest known facts about the topology of complex projective varieties. For a map from a smooth complex projective variety X to a projective variety Y , the theorem imposes strong structural constraints on the cohomology H(X) as an H(Y )-module. Our results show that many of these constraints are linear-algebraic consequences of classically known properties of H(X).

By formalizing this structure through the notion of Lefschetz modules, we obtain analogous decomposition statements in settings where the classical decomposition theorem does not apply, such as in combinatorial Hodge theory and for Chow rings modulo numerical equivalence. Joint work with Omid Amini and Matt Larson.