Séminaires : Séminaire d'Algèbre

I will discuss a replacement of the notion of homotopy cardinality in the setting of even-dimensional Calabi-Yau categories and their relative generalizations. This includes cases where the usual definition does not apply, such as Z/2-graded dg categories. As an application of the definition in the relative case, we define a version of Hall algebras for odd-dimensional Calabi-Yau categories. I will explain its relation to some previously known non-intrinsic constructions of Hall algebras. Whenever a 1CY category C is equivalent to the Z/2-graded derived category of a hereditary abelian category A, our intrinsically defined Hall algebra of C realises the Drinfeld double of the twisted Hall algebra of A. If time permits, I will also briefly discuss another application in the context of invariants of smooth and graded Legendrian links, where we prove a conjecture of Ng-Rutherford-Shende-Sivek relating ruling polynomials with augmentation categories.The talk is based on joint work with Fabian Haiden, arxiv:2409.10154.

This talk will take place in hybrid mode at the Institut Henri Poincaré.