Posters

Xiuli Bian (Universität zu Köln)

Classifying recollements of derived module categories for derived discrete algebras 

Abstract. We investigate a class of derived discrete Nakayama algebras. All indecomposable compact objects in their derived module categories are determined and we classify all recollements generated by indecomposable compact exceptional objects. Our results show that every such recollement is derived equivalent to a stratifying recollement. Moreover, we can provide a geometric interpretation of these results. As a byproduct, this confirms a question posed by Xi for these recollements. [Poster] 

Pierre Bodin (Université de Versailles Saint-Quentin-en-Yvelines and Université de Sherbrooke)

Surfaces with conical singularities: Fukaya categories as A∞-localizations

Abstract. The partially wrapped Fukaya category of a smooth graded marked surface was introduced by Haiden, Katzarkov and Kontsevich. In a more general setting, Auroux and Jeffs defined the Fukaya category of a singular surface to be a certain A∞-quotient of the Fukaya category of a smooth surface. On this poster, we define the notion of a graded admissible dissection on a marked surface with conical singularities, and associate to these data a quiver with relations. We then show that it describes the endomorphism ring of a formal generator for a certain A∞-quotient of the associated smooth marked surface. By construction, the perfect derived category of this algebra is a Verdier quotient of the perfect derived category of a gentle algebra, and it provides a categorification for the contraction of a simple closed curve on a smooth surface. This is analogous to a recollement established by Chang, Jin and Schroll, which categorifies the notion of cutting and pasting of surfaces. [Poster] 

Lukas Bonfert (Universität Bonn)

Serre functor and P-objects for perverse sheaves on Pⁿ

Abstract. The constructible derived category of Pⁿ is equivalent to the bounded derived category of the principal block of parabolic category O for slₙ₊₁ and also to the bounded derived category of a certain special biserial algebra. In both of these languages, the Serre functor can be explicitly described: from the perspective of category O, results of Mazorchuk–Stroppel describe it as a concatenation of shuffling functors, and from the perspective of finite-dimensional algebras, results of Happel and Bondal–Kapranov describe it as the Nakayama functor. On my poster I explain a nice description of the Serre functor from the perspective of perverse sheaves, using the P-twists introduced by Huybrechts–Thomas. The poster is based on joint work with Alessio Cipriani (arXiv:2506.06051). [Poster] 

Ricardo Canesin (Université Paris Cité)

A categorification of combinatorial Auslander–Reiten quivers

Abstract. Combinatorial Auslander–Reiten quivers, introduced by Oh and Suh, serve as an important tool in the representation theory of quantum affine algebras. These quivers generalize the AR quiver associated with a Dynkin quiver Q, but are defined purely in terms of the Coxeter combinatorics of the Weyl group of Q. This naturally raises the question of whether these combinatorial objects admit a representation-theoretic interpretation analogous to that of classical AR quivers. In this poster, we provide such a categorification using the derived category of the derived preprojective algebra of the same Dynkin type. We construct two categories that generalize the category of Q-representations and its derived category, and present some of their properties. [Poster] 

Tomasz Ciborski (Nicolaus Copernicus University in Toruń)

Entropy of derived autoequivalences of derived discrete algebras

Abstract. The notion of entropy of exact endofunctors of triangulated categories originates from the study of the entropy of dynamical systems and has been introduced by Dimitrov, Haiden, Katzarkov and Kontsevich. Having a generator and an endofunctor of the said category, we define the entropy of the endofunctor as a measure of the exponential growth of "distance in exact triangles" between the generator and its images under consecutive powers of the endofunctor. Additionally, Fan, Fu and Ouchi introduced a notion of polynomial entropy, which is meant to measure the polynomial growth of that distance. In my work I consider triangulated categories Dᵇ(mod Λ) and per(Λ), where Λ is a derived discrete algebra over an algebraically closed field. The aim of the poster is to provide a formula for both the entropy and the polynomial entropy of an arbitrary autoequivalence of the considered categories. [Poster] 

Azzurra Ciliberti (Ruhr-Universität Bochum)

A categorification of cluster algebras of type B and C through symmetric quivers

Abstract. This poster presents a combinatorial way to associate a symmetric quiver with relations Q to any seed of a cluster algebra of type B and C. Under this correspondence, cluster variables of type B (resp. C) correspond to orthogonal (resp. symplectic) indecomposable representations of Q. [Poster] 

Darius Dramburg (Uppsala Universitet)

A classification of n-representation infinite algebras of type Ã

Abstract. We present a classification of n-representation infinite algebras of type Ã. These algebras are an analogue of the hereditary type à algebras in Iyama’s higher Auslander–Reiten theory, and they are defined by requiring that their higher preprojective algebra is a certain skew-group algebra R ∗ G. The proof amounts to constructing and classifying the correct gradings on the McKay quiver of G. These gradings naturally form equivalence classes under a certain kind of mutation, which induces derived equivalences. We classify these equivalence classes using convex geometry. Furthermore, we can turn every mutation class into a finite distributive lattice. We also present results for extensions of type Ã, especially for n = 3. 

Kateřina Fuková (Charles University in Prague)

Multiplicative bases and commutative semiartinian von Neumann regular algebras

Abstract. This poster overviews the joint work with Jan Trlifaj [1]. Let R be a semiartinian (von Neumann) regular ring with primitive factors artinian. The dimension sequence DR (described in [2]) is an invariant that captures the various skew-fields and dimensions occurring in the layers of the socle sequence of R. Though DR does not determine R up to an isomorphism even for rings of Loewy length 2, we prove that it does so when R is a commutative semiartinian regular K-algebra of countable type over a field K. The proof is constructive. Moreover, we prove that the K-algebras coming from the same extended construction (which are subalgebras of K ^κ for some cardinal κ) possess conormed strong multiplicative bases despite the fact that the ambient K-algebras K ^κ do not even have any bounded bases for any infinite cardinal κ. [Poster]
[1] K. F., J. Trlifaj, Multiplicative bases and commutative semiartinian von Neumann regular algebras, arXiv:2501.06018, 2025
[2] P. Ružicka, J. Trlifaj, J. Žemliačka, Criteria of steadiness, pp. 359–372, Abelian groups, module theory and topology, Marcel Dekker, 1998

Jordan Haden (University of East Anglia)

3-Preprojective algebras of type D

Abstract. Over an algebraically closed field, Gabriel’s theorem states that the path algebra kQ of a connected quiver is representation-finite if and only if the underlying graph of Q is an ADE Dynkin diagram. Equivalently, kQ is representation-finite precisely when the preprojective algebra of Q is finite-dimensional. d-Representation-finite algebras, introduced by Iyama and Oppermann, are a generalisation of representation-finite path algebras. Attached to each d-representation-finite algebra is a (d +1)-preprojective algebra. Grant showed that a d-representation-finite algebra is fractional Calabi–Yau if and only if the Nakayama automorphism of its (d +1)-preprojective algebra has finite order. We present a family of algebras which arise from the well-studied 3-preprojective algebras of type A by “taking orbifolds”. We show that a subset of these are themselves 3-preprojective algebras (of type D). Thus we provide new examples of 2-representation-finite algebras, which we show are also fractional Calabi–Yau. [Poster] 

Maximilian Kaipel (Universität zu Köln)

Mutating τ-exceptional sequences

Abstract. Recently a mutation operation for τ-exceptional sequences was introduced by Buan, Hanson and Marsh. This generalises the classical mutation of exceptional sequences for hereditary algebras. On my poster I will recall this mutation, present some of its properties and open conjectures. My focus will lie on the alternative way of understanding this mutation as a mutation of TF-ordered τ-rigid modules, as introduced in joint work with Buan and Terland. I will showcase applications of this viewpoint to answering questions about transitivity and braid relations of the mutation. [Poster] 

Markus Kleinau (Universität Bonn)

Lattices of torsion classes and 2-cluster categories

Abstract. Rognerud had shown that the incidence algebra of the Tamari lattice, that is the lattice of torsion classes of a linear type A algebra, is fractionally Calabi-Yau. We extend this result to the lattice of torsion classes of any representation finite hereditary algebra. To that end we relate the combinatorics of the Serre functor of these lattices with the combinatorics of 2-cluster tilting objects in 2-cluster categories, providing new interpretations for the shift and mutation. [Poster] 

Amit Kuber (Indian Institute of Technology Kanpur)

Linear orders, automata and stable ranks for string algebras

Abstract. The poster depicts a striking application of computer science apparatus in the representation theory of string algebras, and hopes to bridge the gap between these two seemingly distant fields. Theoretical computer science has rich literature on the connections between word problems, automata theory and linear orders. Sarah Rees (2008) first noted that the sets of strings for a string algebra form regular sets, and hence are defined by finite state automata. In the context of string algebras, we show how to automate the computation of (order-isomorphism classes of) certain linear orders called hammocks, which encode factorisations of the so-called graph maps. This computation, previously achieved combinatorially in a work with Sinha et al. (2024), is a key step in the stable rank computation for a string algebra — the smallest ordinal for which the sequence of the powers of the radical of the module category stabilises. The computation of the stable rank in the domestic case was done by Schröer (2000) while in the non-domestic case in a work with Srivastava and Sinha. (This is joint work with S. Srivastava.) [Poster] 

Jonathan Lindell (Uppsala Universitet)

Corings, their dual rings and (co)Hochschild cohomology

Abstract. Corings were first defined by Sweedler and simultaneously by Roiter under name of bocs, generalising coalgebras to when we have a non-commutative ground ring. They appear naturally in the context of non-commutative descent theory, entwining structures and in the theory of quasi-hereditary algebras. Associated to any coring, there is the right algebra, also called the opposite of the left dual algebra. We show that there is a map from the coHochschild cohomology of the coring to the opposite of the relative Hochschild cohomology of the right algebra, which moreover is an isomorphism if the coring is finitely generated projective as a left module over the ground ring. Further, we show that this morphism lifts to the B∞ level, thus inducing a map of Gerstenhaber algebras on the level of cohomology. 

Judith Marquardt (Université Grenoble Alpes and Université de Versailles Saint-Quentin-en-Yvelines)

Degenerations of families of bands and strings for gentle algebras

Abstract. Let A be a gentle algebra. For every collection of string and band diagrams, we consider the constructible subset of the variety of representations containing all modules with this underlying diagram. For instance, to a band we associate the set of corresponding band modules with all choices of parameters. We study degenerations of such sets and show that some of them are induced by kissing of string and band diagrams. [Poster] 

Cyril Matoušek (Aarhus University)

Metric completions from finite dimensional algebras

Abstract. A metric on a triangulated category, as developed by Neeman, provides a recipe for constructing a metric completion of the category in a pattern analogous to the completion of a metric space. In our project, we study metric completions of triangulated categories arising in a representation theory of algebras. We fully describe completions of bounded derived categories of hereditary finite dimensional tame algebras and hereditary commutative noetherian rings with respect to additive good metrics. We also provide a way how to pull-back metrics across categories using a triangulated functor, in order to induce triangulated equivalences between completions. [Poster] 

David Nkansah (Aarhus University)

Homological algebra without grading

Abstract. Complexes are central objects in homological algebra, and as such, grading is very present within the subject. But what if we discard the grading of a complex? This leads us to the notion of a differential module. In this poster, we explore how the finiteness of the injective dimension of a finitely generated module over a local commutative Noetherian ring can be detected through this ungraded framework. As an application, we give a new characterisation of when such a ring is Cohen–Macaulay. [Poster] 

Iacopo Nonis (University of Leeds)

τ-Exceptional sequences for representations of quivers over local algebras

Abstract. In the early 1990s, Crawley-Boevey and Ringel studied exceptional sequences and their mutation in the module categories of hereditary finite-dimensional algebras. More recently, Buan and Marsh introduced τ-exceptional sequences — a natural generalization of exceptional sequences that behaves well over arbitrary finite-dimensional algebras. Together with Hanson, the authors also developed a notion of mutation for τ-exceptional sequences, extending the classical concept of mutation in the hereditary setting. In this poster, we study τ-exceptional sequences and their mutation over algebras of the form Λ = RQ, where R is a finite-dimensional local commutative algebra over an algebraically closed field, and Q is an acyclic quiver. I will explain how τ-exceptional sequences and their mutation over Λ can be fully understood in terms of exceptional sequences and their mutation over kQ. [Poster] 

Marvin Plogmann (Universität zu Köln)

A characterization of A∞-Yoneda algebras of simple objects

Abstract. Yoneda algebras of simple modules over finite-dimensional algebras form a notable class of A∞-algebras in representation theory. This raises a natural question: How can these be distinguished among all A∞-algebras? I will present a bijective correspondence – arising via Koszul duality – between finite-dimensional algebras and the class of coconnective, augmented, locally finite, homologically smooth A∞-algebras that are coherently generated in degrees 0 and 1. The key technical tool is the use of dg realisation functors. I will explain how these allow for such a classification, when they induce equivalences, and how this framework extends to proper connective dg algebras and, more generally, to certain connective exact dg categories. [Poster] 

Kyungmin Rho (Max Planck Institute for Mathematics in Bonn)

Derived-equivalence classes of associative algebras and Fuss–Catalan numbers

Abstract. We answer the following question for some Dynkin-type algebras: How many algebras (up to isomorphism) are derived equivalent to a given algebra? It is well known that the number of tilting modules over a path algebra of type Aₙ coincides with the n-th Catalan number. Using geometric models, we show that the number of tilting complexes (up to grading shift) in its derived category coincides with the Fuss–Catalan number, which enables us to count the number of derived-equivalent algebras. We also discuss how to generalize this to certain extended Aₙ-type and Dₙ-type algebras using their corresponding geometric models. [Poster] 

Kevin Schlegel (Universität Stuttgart)

The first Brauer–Thrall conjecture for constructible subcategories

Abstract. The classical first Brauer–Thrall conjecture states that if the dimension of indecomposable finite dimensional modules over a finite dimensional algebra can be bounded, then there are only finitely many of them up to isomorphism. The first solution of the conjecture was provided by Roiter and a different proof relies on Auslander–Reiten theory. Both approaches are homological in nature. We extend the first Brauer–Thrall conjecture to constructible subcategories of the module category of a finitely generated algebra over an arbitrary field. A subcategory is constructible if it can be described as all modules vanishing on a single finitely presented functor. For example, Hom- and Ext-orthogonals of a finitely presented module are constructible. In general, these subcategories lose the homological properties of the module category, so a new approach is necessary to tackle the problem. We are able to solve it using the Ziegler spectrum of a ring and its connection to the spectrum of a commutative ring. The first step is to find a suitable curve inside the scheme of finite dimensional modules. This result is contributed by Andres Fernandez Herrero. [Poster] 

Anastasios Slaftsos (Università di Padova)

The Q-shaped homotopy category of a ring

Abstract. A (co-)chain complex over a k-algebra A, can be viewed as an A-Mod-valued representation of the repetitive quiver of the linear oriented Dynkin quiver A₂ modulo the mesh relations. Formally speaking, this situation implies an equivalence between the category of (co-)chain complexes Ch(A) and the category of k-linear functors from the mesh category Q of A₂ to A-Mod. This abstract perspective allows one to consider different “shapes” of Q and study all of them collectively. In 2022, Holm and Jørgensen introduced the notion of the “Q-shaped derived category” that studies such phenomena and generalises the concept of the usual derived category. However, when someone studies categories of complexes, it is well known that there exists an intermediate step between the category of complexes and the derived category, the one known as the homotopy category of complexes. In our work, we replace the abelian exact structure with the object-wise split exact structure and prove that there exists an exact model structure, whose homotopy category we call the “Q-shaped homotopy category”, which generalises the concept of the usual homotopy category of complexes. Finally, mimicking the category of complexes, we prove that the Q-shaped homotopy category shows up as a gluing of the Q-shaped derived category and the category of the Q-shaped acyclic objects, generalising the recollement situation of Krause. Based on a joint work in progress with Henrik Holm and Jorge Vitória. [Poster] 

Jan Thomm (Universität zu Köln)

Auslander–Reiten sequences in minimal A∞-structures of the module category of a representation finite algebra

Abstract. The Auslander–Reiten sequences of a representation finite algebra may be seen as the building blocks of its module category. However, any Yoneda product of a radical morphism with an Auslander–Reiten sequence will automatically be split. Considering this, the Auslander–Reiten sequences seem to be unable to "generate" any other short exact sequences. Enhancing the Yoneda product to an A∞-structure helps us to overcome this discrepancy. We show that for a representation finite algebra the Ext-algebra of any basic additive generator is in fact always generated by the irreducible morphisms and Auslander–Reiten sequences as an A∞-algebra. [Poster] 

Haoyu Wang (Institut de Mathématiques de Jussieu – Paris Rive Gauche)

Quasi-cluster morphisms via decategorification

Abstract. In 2017, Chris Fraser discovered an action of the extended affine braid group on d strands on the Grassmannian of k-subspaces in n-space, endowed with its cluster structure due to Scott (2006). Here, we write d for the greatest common divisor of k and n. Building on work by Fraser and Keller we construct a categorical lift of this action using Jensen–King–Su’s (additive) categorification of the Grassmannian via Cohen–Macaulay modules over a singular quotient of the preprojective algebra P of extended type Aₙ₋₁. A key ingredient is Seidel–Thomas’s braid group action (2000) on the derived category of P. [Poster] 

Can Wen (Universität zu Köln)

Hochschild cohomology of skew-gentle algebras

Abstract. Skew-gentle algebras are a natural generalization of gentle algebras. The Tamarkin–Tsygan calculus for gentle algebras was calculated by Chaparro, Schroll, Solotar and Suárez-Álvarez in 2024. They gave a complete description of the structure of the Hochschild cohomology ring of a gentle algebra, both as a graded commutative algebra and as a Gerstenhaber algebra, and related these structures to the geometric model of gentle algebras. Motivated by this, we calculate the Hochschild cohomology of skew-gentle algebras, as well as their cup products and Gerstenhaber brackets. Similar to the gentle cases, we can also give a geometric interpretation for the algebraic generators of the Hochschild cohomology of skew-gentle algebras. This is a joint work with Xiuli Bian, Sibylle Schroll, Andrea Solotar and Xiaochuang Wang. [Poster] 

Wei Xing (Uppsala Universitet)

A derived equivalence for higher Auslander algebras of type A

Abstract. I will present a derived equivalence for certain d-Auslander algebras of type A. Such a derived equivalence is induced by a tilting complex whose endomorphism algebra admits an ndℤ-cluster tilting subcategory in its module category. As an application, an ndℤ-cluster tilting subcategory can be constructed for certain higher d-Nakayama algebras. [Poster] 

Hao Zhang (University of Glasgow)

Gopakumar–Vafa invariants associated to cAₙ singularities

Abstract. We describe Gopakumar–Vafa (GV) invariants associated to cAₙ singularities. We (1) generalise GV invariants to crepant partial resolutions of cAₙ singularities, (2) show that generalised GV invariants also satisfy Toda’s formula and are determined by their associated contraction algebra, (3) give filtration structures on the parameter space of contraction algebras associated to cAₙ crepant resolutions with respect to generalised GV invariants, and (4) numerically constrain the possible tuples of GV invariants that can arise. We further give all the tuples that arise from GV invariants of cA₂ crepant resolutions. [Poster]