Séminaires : Séminaire d'Algèbre

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.

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