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.

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: Resolution Forests and Higher Gorenstein Properties of Nakayama Algebras 

Abstract: Building on Ringel’s approach via resolution quivers, we use the more general framework of resolution forests to describe minimal projective resolutions in Nakayama algebras. For an indecomposable projective module, this description allows us to study the projective dimensions of the successive terms in its minimal injective coresolution. We derive strong restrictions on the resulting sequence. In particular, it contains at most two odd entries, and their positions are determined by the combinatorics of the forest.

We then apply these results to higher Gorenstein properties. Deleting all leaves from the resolution forest produces a smaller Nakayama algebra. We prove that, for every even integer greater than two, the original algebra has the corresponding Gorenstein property if and only if it is two-Gorenstein and the smaller algebra has the Gorenstein property two levels below. 

03.09.2026: Wei Xing (Uppsala University)

Title: Two derived equivalences for higher Auslander algebras of type A

Abstract: Given a positive integer d, a d-Auslander algebra A is characterized by the property that gldim A <= d+1 <= domdim A. Iyama showed that such an algebra is always obtained as the endomorphism algebra of a d-cluster tilting object in a module category. Starting from a linear A_n quiver, Iyama constructed an infinite family of d-Auslander algebras A_n^{d+1} called higher Auslander algebras of type A.

In this talk, I will present a derived equivalence between A_n^d and the incidence algebra of the poset of lattice paths in a d by n rectangle. Building on this combinatorial model for A_n^d, we construct a second derived equivalence between A_n^d and an nd-representation finite algebra when n and d are coprime. As a consequence, we show that the lattice of rational Dyck paths is fractionally Calabi-Yau.

17.09.2026: Sven Ulf Schmitz (Universität Bonn)

Title: Resolution Forests and Higher Gorenstein Properties of Nakayama Algebras 

Abstract: Building on Ringel’s approach via resolution quivers, we use the more general framework of resolution forests to describe minimal projective resolutions in Nakayama algebras. For an indecomposable projective module, this description allows us to study the projective dimensions of the successive terms in its minimal injective coresolution. We derive strong restrictions on the resulting sequence. In particular, it contains at most two odd entries, and their positions are determined by the combinatorics of the forest.

We then apply these results to higher Gorenstein properties. Deleting all leaves from the resolution forest produces a smaller Nakayama algebra. We prove that, for every even integer greater than two, the original algebra has the corresponding Gorenstein property if and only if it is two-Gorenstein and the smaller algebra has the Gorenstein property two levels below. 

24.09.2026 at 16:00: Marvin Plogmann and Jan Thomm (Universität zu Köln) 

Title: Spherical Algebras and their Auslander—Yoneda Algebras

Abstract: Considering a hereditary algebra A and a module M over A, Ext^n(M,A)=0 unless n is equal to the projective dimension of M. Generalising this observation to algebras of finite global dimension, Auslander and Bridger define a module M to be spherical if Ext^n(M,A)=0 unless n is the projective dimension of M (or n=0). Motivated by this, we call an algebra spherical if every indecomposable module is spherical. In this talk, we will discuss structural properties of the module category of a spherical algebra and give examples beyond the hereditary case. We will then show that representation-finite bispherical algebras, that is, algebras that are spherical with respect to both left and right modules, give rise to Auslander—Gorenstein algebras: If M is an additive generator of the module category, then its Yoneda algebra Ext^*(M,M) is Auslander—Gorenstein. In fact, an appropriate version of this property characterizes bispherical algebras, even in the representation-infinite case. Finally, we will discuss the Auslander—Reiten bijection for the Auslander—Gorenstein algebras arising in this way.