Winter Semester 2023/2024
23.10 Aran Tattar
Title: Bound quiver minors
Abstract: In graph theory, the notion of a graph minor allows one to characterise many properties (e.g. planarity, tree width) of graphs with respect to 'forbidden minors'. We introduce an analog of graph minors for bound quiver algebras and discuss some properties and potential applications.
06.11 Haibo Jin
Title: Silting theory in partial wrapped Fukaya categories of graded marked surfaces
Abstract: In this talk I will explain some new developments in studying silting theory in partial wrapped Fukaya categories based on my previous work joint with Sibylle Schroll and Zhengfang Wang, arXiv:2303.17474.
In the previous paper we work on partial wrapped Fukaya categories of graded marked surfaces without punctures (=fully marked boundaries), or equivalently, we work on the perfect derived categories of homologically smooth and proper graded gentle algebras. We show that among the derived equivalence classes of homologically smooth and proper graded gentle algebras there is only one class whose perfect derived category does not admit silting objects. Using this, we confirm a conjecture by Lekili and Polishchuk.
Today I will generalize the results above to non-proper case, that is, we allow the graded surfaces contain punctures. I will show that in this case, the conjecture by Lekili and Polishchuk still holds. This is joint work with Sibylle Schroll and Zhengfang Wang.
13.11 Maximilian Kaipel
Title: The canonical perverse schober on the g-vector fan
Abstract: Based on the recent introduction of perverse schobers by Kapranov-Schechtman and Bondal-Kapranov-Schechtman, we are interested in defining an analogous structure on the g-vector fan.
20.11 Lang Mou
Title: Measured laminations as stability conditions
Abstract: Various surface models have emerged for understanding algebraic structures, such as cluster algebras and representations of gentle algebras. Closed curves and arcs are among the most commonly used objects in these models. Measured laminations, introduced by Thurston in his study on surface diffeomorphisms, are generalizations (or limits) of multi-curves. In this talk, we will discuss the roles measured laminations can play in surface models of algebras. In particular, we view measured laminations as King’s stability conditions on modules of the Jacobian algebra associated to an ideal triangulation. This approach allows us to provide a complete description of the decomposition of the stability vector space into cones, each having constant Baumann-Kamnitzer-Tingley torsion pairs. This is a report on work in progress with Eric Babson.
11.12 Mikhail Gorsky (University of Vienna)
Title: Valuations and rank functions on categories
Abstract: Degenerations of quantized enveloping algebras can be studied via quantum degree cones. In my work with Xin Fang, we interpreted such cones from the perspective of relative homological algebra and functor categories. In this setting, degenerations of quantized enveloping algebras and more general Hall algebras are induced by certain functions on objects in exact categories, which we call valuations, which give points in quantum degree cones. Chuang and Lazarev recently introduced another class of functions on objects in categories: rank functions on triangulated categories, generalizing, in particular, Sylvester rank functions and mass functions of Bridgeland stability conditions. In my talk, I will present some parts of my recent work with Teresa Conde, Frederik Marks, and Alexandra Zvonareva on the functorial approach to rank functions and will try to explain a connection between these frameworks.
05.02 Xiao-Chuang Wang (USTC)
Title: Gentle algebras with one maximal path
Abstrct: For a gentle algebra A with one maximal path, it can be glued by one quiver of type An. There is a natural quasi-chord diagram α associated to A. In this talk, we show that we can check if A has finite global dimension by counting the specific faces of α. Then we study the dihedral group action on the set of quasi-chord diagrams. At last, we discuss the special case of maximal chord diagrams. This is a joint work with Haigang Hu (USTC) and Yu Ye (USTC).