Fractional Calabi-Yau lattices

Abstract: F. Chapoton made public in 2023 an intriguing conjecture linking combinatorial formulas, symplectic geometry, and representation theory of fractional Calabi-Yau posets. After exposing recent progress around this conjecture, I shall present the fractional Calabi-Yau property for lattices and how to prove it. If time permits, I'll consider the poset of plane partitions, for which the conjecture remains open

machine learningcommutative algebraalgebraic geometryalgebraic topologycombinatoricscategory theoryoperator algebrasrings and algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

Algebraic and Combinatorial Perspectives in the Mathematical Sciences

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