Schedule

Azzurra Ciliberti

Title: A multiplication formula for cluster characters in gentle algebras

Abstract: Gentle algebras, introduced by Assem and Skowroński, are a well-loved class of algebras. They are string algebras, so their module categories are combinatorially described in terms of strings and bands, they are tiling algebras associated with dissections of surfaces, and they have many other remarkable properties. Furthermore, Jacobian algebras arising from triangulations of unpunctured marked surfaces are gentle. In the talk, I will present a multiplication formula for cluster characters induced by generating extensions in a gentle algebra A. This formula generalizes a previous result of Cerulli Irelli, Esposito, Franzen, Reineke. Moreover, in the case where A comes from a triangulation T of an unpunctured marked surface, it provides a representation-theoretic interpretation of the exchange relations in the cluster algebra with principal coefficients in T. Finally, I will explore an additional application of this formula to cluster algebras of type B.

Mikhail Gorsky

Title: Counting in Calabi-Yau categories, with applications to Hall algebras

Abstract: 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 construction in the relative case, we define a version of Hall algebras for odd-dimensional Calabi-Yau categories. I will briefly explain its relation to some previously known non-intrinsic constructions of Hall algebras. Whenever a 1CY category C is equivalent to 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, thus resolving a long standing problem in this CY case. The talk is based on joint work with Fabian Haiden, arxiv:2409.10154.

Wassilij Gnedin

Title: Derived representation theory of gentle orders 

Abstract: Gentle algebras have attracted significant interest in recent years, particularly due to their appearance in homological mirror symmetry. The derived representation theory of certain subclasses of gentle algebras — in particular that of finite-dimensional gentle algebras — is by now thoroughly understood. My talk is concerned with a class of lesser-studied infinite-dimensional gentle algebras called gentle orders. Prototypical examples of gentle orders arose in connection with tame categories of Harish-Chandra modules in Lie theory. Adopting a predominantly homological approach, I will present a factorization of the derived Nakayama functor of a gentle order, discuss its fractionally Calabi-Yau objects and exceptional cycles, and show that certain combinatorial invariants of its underlying quiver are preserved under derived equivalences — analogous to results known for finite-dimensional gentle algebras. This talk is based primarily on the arXiv preprint 2502.14852.