Schedule

Wen Chang (Shaanxi Normal University)

Entropy of the Serre functor for partially wrapped Fukaya categories of surfaces with stops

Abstract. I will talk about the categorical entropy of the Serre functor for partially wrapped Fukaya categories of graded surfaces with stops, as well as for perfect derived categories of homologically smooth graded gentle algebras (to which the aforementioned Fukaya categories are equivalent). We prove that the entropy of the Serre functor is a piecewise linear function determined by the winding numbers of the surface’s boundary components and the number of stops on each component. Specifically, the function takes different linear forms for non-negative and non-positive arguments, with slopes related to the minimum and maximum values derived from the ratio of each boundary component’s winding number to its stop count. We further derive the corresponding upper and lower Serre dimensions. Additionally, for ungraded homologically smooth gentle algebras, we establish a Gromov–Yomdin-like equality, linking the categorical entropy of the Serre functor to the natural logarithm of the spectral radius of the Coxeter transformation. The talk is based on the preprint arXiv:2508.14860, which is joint with A. Elagin and S. Schroll.

Haibo Jin (East China Normal University)

On the silting-discreteness of graded (skew-)gentle algebras

Abstract. Silting-discreteness is a finiteness condition on triangulated categories that governs the structure of silting objects and their mutations. It is closely related to other finiteness conditions such as tau-tilting finiteness and representation finiteness.

In this talk, we characterize silting-discreteness for the perfect derived categories of graded gentle and skew-gentle algebras via surface models. Specifically, for a graded gentle algebra, silting-discreteness is equivalent to its associated surface having genus zero and non-zero winding numbers for all simple closed curves. We further extend this geometric characterization to graded skew-gentle algebras via orbifold surface models.

Marianne Lawson (University of Hamburg)

The resolving completion of an exact category

Abstract. In 2021, Neeman showed that there is no canonical t-structure on the derived category of an additive exact category. We therefore relax the definition of a t-structure to include only Hom-orthogonality and closure under shifts. We use Rump's notion of Ext-acyclicity to obtain subcategories that satisfy the aformentioned axioms of what we call a `t-pair'. We will refer to the intersection of the two subcategories as its `heart', which in this setting is not necessarily abelian, but is exact. We establish that the ambient category is a resolving subcategory of the heart, and that the heart is maximal with this property. Employing recent work of Henrard and van Roosmalen, we show that they are derived equivalent. This generalizes classical results due to Schneiders from the 90s.

Suiqi Lu (Tsinghua University)

Quadratic Differentials as Stability Conditions of Graded Skew-gentle Algebras

Abstract. We prove that the principal component of the exchange graph of hearts of a graded skew-gentle algebra can be identified with the corresponding exchange graph of S-graphs on a graded marked surface with binary, using the geometric models and the intersection formula in [Qiu-Zhang-Zhou]. Using the similar argument in [Bridgeland-Smith, Barbieri-Möller-Qiu-So, Christ-Haiden-Qiu], we extend this identification to an isomorphism between the principal component of the space of stability conditions of the graded skew-gentle algebra and the moduli space of framed quadratic differentials.