Algebra and Representation theory seminar

23.07.2026 at 16:00: Yilin Wu  (University of Luxembourg) 

Title: Graded Higgs categories

Abstract: Let A be a differential bigraded k-algebra and let e be an idempotent of A. Under suitable assumptions on the pair (A,e), we define the graded Higgs category H and the graded relative cluster category C. We show that H carries a Frobenius extriangulated structure, and that its stable category admits a silting object. Examples arise from Keller-Scherotzke's work on graded singular Nakajima categories and from graded maximal Cohen-Macaulay modules over isolated singularities. This is a report on ongoing joint work with Li Fan. 

23.07.2026 at 17:00: Judith Marquardt  (Université Grenoble Alpes) 

Title: Degenerations of chain complexes

Abstract: Riedtmann and Zwara have characterized degenerations of orbits in module varieties in terms of certain short exact sequences.  In this talk, we study degenerations of orbits in varieties of chain complexes of projective modules. We show that degenerations are characterized in terms of certain admissible short exact sequences in the exact category of complexes of projectives. We then extend our study to the homotopy category. In this context, complexes of projectives with a given g-vector form an ind-variety, and we prove that degenerations of orbits are characterized using distinguished triangles in the category. This links to an algebraic definition of degeneration for triangulated categories introduced by Jensen, Su and Zimmermann.

30.07.2026 at 16:00: Noémi Nagy  (Bachelor Thesis Seminar) 

Title: Bruhat-decomposition and Coxeter-permutation of gentle tree algebras 

30.07.2026 at 17:00: Carolin Hartung and Sven Ulf Schmitz (Universität Bonn) 

Title: TBA 

16.04.2026: Fang Yang  (MPIM Bonn)

Title: Degenerations in graded quiver varieties and derived categories of Dynkin quivers

Abstract:  For any acyclic quiver, Keller–Scherotzke provided a stratifying functor from the category of finite-dimensional modules of the singular Nakajima category to the derived category of the quiver. Under this functor, a degeneration of strata of a graded quiver variety corresponds to a degeneration, in the sense of Jensen–Su–Zimmermann, in the derived category. In this article, for any Dynkin quiver, we further investigate Jensen–Su–Zimmermann’s partial order and show that any degeneration of objects in the derived category can be obtained in this way.

23.04.2026: Carolin Hartung  (Universität Bonn)

Title: Projective Presentations over quasicompact algebras

Abstract:  In a joint work with Christoph Geiss, Daniel Labardini-Fragoso and Jan Schröer we give a general formula for minimal projective presentations of finite-dimensional modules over quasicompact basic algebras. This result generalizes a description of minimal projective presentations for modules over Jacobian algebras proven by Weyman, Derksen and Zelevinsky. In particular, we are able to drop their finiteness assumptions and work over fields of arbitrary characteristics.

30.04.2026: Veronica Calvo Cortes  (MPI MiS Leipzig)

Title: Dyck Paths, Configuration Spaces and Polytopes for Linear Nakayama Algebras 

Abstract: We present a combinatorial model of configuration spaces and polytopes associated to linear Nakayama algebras. Such configuration spaces were recently introduced for more general algebras by Arkani-Hamed, Frost, Plamondon, Salvatori and Thomas. In our special setting, we provide elementary proofs and explicit combinatorial constructions. From a Dyck path we define three related objects: a finite-dimensional algebra, an affine algebraic variety, and a polytope. Moreover, our constructions are natural: each relation in the poset of Dyck paths gives a morphism between the corresponding objects.

13.05.2026 (Wednesday) at 18:00 in room 0.008: Ricardo Canesin  (Université Paris Cité)

Title: Additive categorification of the monoidal Lambda-invariant 

Abstract: The Lambda-invariant for quantum affine algebras was introduced by Kashiwara-Kim-Oh-Park as an important tool in their study of the monoidal categorification of cluster algebras. It yields a quantization of the associated cluster algebra, and it was recently shown to coincide with Peigen Cao’s tropical invariant.

In this talk, we interpret these invariants via the additive categorification of cluster algebras using Higgs categories in the sense of Yilin Wu. Whenever the relative Ginzburg algebra is proper, we show that the Higgs category admits a canonical quantum structure generalizing those of Geiss-Leclerc-Schröer and Grabowski-Pressland, and we provide a homological interpretation of the corresponding tropical invariant.

For certain finite-rank cluster algebras categorified by Kashiwara-Kim-Oh-Park, we show that the associated relative Ginzburg algebra is indeed proper, and that our additive Lambda-invariant agrees with their monoidal one.

This is joint work with Peigen Cao and Geoffrey Janssens. 

28.05.2026 in room 0.011: Emily Poelders  (University of Bonn) 

Title: The Reduced Incidence Algebra of a Divisor Lattice 

Abstract: We investigate the structure of reduced incidence algebras, with a primary focus on divisor lattices, by developing a combinatorial framework using Young diagrams to represent isomorphism classes of intervals. Furthermore, we describe the multiplication via colored Young diagram concatenations and prove that, over a field of characteristic zero, the reduced incidence algebra of a divisor lattice is Frobenius if and only if it is unmixed. 

09.07.2026 Jiayang Zhang (Bachelorarbeit-Seminar)

Titel: Generische Galoisgruppen von rationalen Polynomen

16.07.2026 Carolin Hartung (Master Thesis Seminar)

Title: E-symmetry in Special Biserial Algebras

Abstract: The Auslander–Reiten formula gives a symmetry condition for stable Hom-spaces involving a module and its Auslander–Reiten translates. The analogous condition for ordinary, non-stable Hom-spaces is called E-symmetry. Derksen, Weyman and Zelevinsky proved that Jacobian algebras satisfy E-symmetry. In this thesis, we generalise their result to the broader class of generalized Jacobian algebras. Moreover, for special biserial algebras, we prove the converse: every E-symmetric special biserial algebra is generalized Jacobian.