Seminar

Friday, 17 April 2026

• 13:00
  Tiago Cruz (Stuttgart): Gorenstein properly stratified algebras
  Abstract: Quasi-hereditary algebras are a class of finite-dimensional associative algebras that appear frequently in representation theory of associative algebras, but also of algebraic groups and semi-simple Lie algebras. They possess nice homological properties, like always having finite global dimension. They have inspired several generalisations, such as standardly and properly stratified algebras, which retain several homological features and stratification properties. Another important class of finite-dimensional algebras is given by Iwanaga–Gorenstein algebras, which unify algebras of finite global dimension and self-injective algebras within a common framework.
  In this talk, we provide sufficient and necessary conditions for a standardly stratified lgebra to be Iwanaga-Gorenstein and properly stratified making use of tilting theory and theory of recollements of triangulated categories. The first part is based on joint work with R. Marczinzik while the second part is based on ongoing work with S. Koenig and Y. Chen.
• 14:15
  Calvin Pfeifer (Köln): Generic modules arising from stability
  Abstract: This talk is a report on joint work in progress with Lidia Angeleri-Hügel and Rosanna Laking. Our aim is to extend parts of the theory of large modules over tame hereditary algebras to arbitrary tame algebras.
  Let A be a tame finite dimensional algebra over an algebraically closed field, and θ an additive functional on the Grothendieck group of A. Baumann, Kamnitzer and Tingley associate to θ a wide interval in the lattice of torsion classes of the category of finite dimensional A-modules, whose corresponding wide subcategory consists of the θ-semistable A-modules in the sense of King. Angeleri-Hügel, Laking and Sentieri use cosilting theory to assign to such a wide interval a closed rigid subset of the Ziegler spectrum of the unbounded derived category of all A-modules. On the other hand, Plamondon associates to θ a generically τ-regular irreducible component of the scheme of A-modules. In this talk, we will explain how the closed rigid subset of the Ziegler spectrum is determined by generic modules constructed from the generically τ-regular irreducible component.

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Future Talks

Friday, 15 May 2026

• 13:00
  Marianne Lawson (Hamburg): tba

Friday, 22 May 2026

• 13:00
  Kyungmin Rho (Bonn): Homological mirror symmetry via tensor-triangular geometry
  Abstract: Homological mirror symmetry (HMS) conjectures an equivalence between the Fukaya category of a symplectic manifold and the derived category of coherent sheaves on its mirror scheme. We discuss a tensor-triangular geometric approach and present a necessary and sufficient condition for a Fukaya category to be realized as the perfect derived category of a Noetherian scheme. This also gives a way to build a mirror scheme from purely Fukaya-categorical data and leads to a natural construction of an A∞-functor.
  
  

Friday, 29 May 2026

• 13:00
  Sam Miller (Athens, Georgia): tba

Friday, 05 June 2026

• 13:00
  Panagiotis Kostas (Thessaloniki): tba

Friday, 12 June 2026

• 13:00
  Lukas Bonfert (Hannover): tba

Seminar Archive

Friday, 30 January 2026

• 13:15, Room U2-232
  Kyoungmo Kim (Köln): Closedness under Derived Equivalence for Semi-gentle Algebras
  Abstract: The class of gentle algebras has several nice properties: its derived categories are well understood, it has deep connections with surface geometry, and it is closed under derived equivalence. A generalized class of skew-gentle algebras also has well-behaved derived categories and a geometric model. However, the class of skew-gentle algebras is not closed under derived equivalence. In this talk, we introduce a larger class of semi-gentle algebras with a geometric model and talk about closedness of the class under derived equivalence. This is a joint work with Severin Barmeier, Cheol-Hyun Cho, Kyungmin Rho, Sibylle Schroll, and Zhengfang Wang.

Friday, 23 January 2026

• 13:15, U2-232
  Viktória Klász (Bonn): Auslander-Gorenstein algebras and the Auslander-Reiten bijection
  Abstract: Auslander and Reiten discovered that every Auslander-Gorenstein algebra admits a distinguished bijection between its indecomposable projective and injective modules, now known as the Auslander-Reiten bijection. In this talk, we present a new result showing that, for certain classes of algebras, the existence of such a bijection actually characterises the Auslander-Gorenstein property. We then discuss a new, linear algebraic interpretation of the Auslander-Gorenstein property and the Auslander-Reiten bijection using Coxeter matrices and their Bruhat decompositions, based on a joint work with René Marczinzik and Hugh Thomas. This approach opens the door to extending the definition of the Auslander-Reiten bijection to algebras that are not Auslander-Gorenstein.

Friday, 16 January 2026

• 13:15, Room U2-232
  Carlo Klapproth (Stuttgart): A functorial approach to n-exact categories
  Abstract: We explain how to describe n-exact structures on a given additive category by use of its functor category. This construction is based on ideas of Enomoto and we discuss the following applications of it: First, every idempotent complete additive category has a unique maximal n-exact structure. This is a higher analogue of results going back to Crivei, Sieg-Wegner, and Rump. Second, our description allows us to explicitly construct new examples of n-exact categories on the category of (graded) projective modules over various classes of algebras including Calabi-Yau algebras and commutative rings.

Friday, 12 December 2025

• 13:15, Room U2-232
  Azzurra Ciliberti (Bochum): A multiplication formula for cluster characters in gentle algebras
  Abstract: Gentle algebras, introduced by Assem and Skowroński, are a well-loved class of algebras. They are string algebras, so their module categories are combinatorially described in terms of strings and bands, they are tiling algebras associated with dissections of surfaces, and they have many other remarkable properties. Furthermore, Jacobian algebras arising from triangulations of unpunctured marked surfaces are gentle.
  In the talk, I will present a multiplication formula for cluster characters induced by generating extensions in a gentle algebra A. This formula generalizes a previous result of Cerulli Irelli, Esposito, Franzen, Reineke. Moreover, in the case where A comes from a triangulation T, it provides a representation-theoretic interpretation of the exchange relations in the cluster algebra with principal coefficients in T.

Friday, 28 November 2025

• 13:15, Room U2-232
  Kevin Schlegel (Stuttgart): Constructible subcategories and unbounded representation type
  Abstract: For a wide range of subcategories of the module category of a finitely generated algebra, we show a variant of the inductive step of the second Brauer-Thrall conjecture. That is, if there are infinitely many non-isomorphic indecomposable modules of the same finite dimension in the subcategory, then there are infinitely many dimensions that each admit infinitely non-isomorphic indecomposable modules in the subcategory. This also implies a variant of the first Brauer-Thrall conjecture in this context. The subcategories in question are the constructible subcategories, which are those that consist of all modules that vanish on a finitely presented functor. A key ingredient of the proof is a new connection between the Ziegler spectrum and schemes of finite dimensional modules that allows for a geometric approach. An important step is to find a suitable curve inside a constructible subset of the scheme. This result is contributed by Andres Fernandez Herrero.
• 14:30, Room U2-232
  Isambard Goodbody (Glasgow): Strong generation of the derived category by injectives
  Abstract: The notion of strong generation can be used to extract properties of a geometric or algebraic object from its derived category. For example, the global dimension of a Noetherian ring is equal to the minimum number of steps it takes to generate every object from the regular module. A result of Neeman shows that a Noetherian separated scheme is regular and of finite dimension if and only if its perfect derived category admits a strong generator. However, unlike the algebraic situation, there is no candidate generator playing the role of the regular module. This means that the problem of extracting the precise dimension of a scheme using this technique remains open. Orlov has conjectured that the dimension of a smooth projective variety is equal to the smallest generation time ranging across all possible generators. We take a different approach, motivated from the algebraic situation, by taking our candidate generator to be all of the indecomposable injectives. We’ll present some results showing that one can bound the dimension of the scheme in this way.
• 16:00, Room U2-232
  Tilman Bauer (Stockholm): Abelian Hopf algebras in positive characteristic
  Abstract: In this talk, I will adress the question of classification of commutative and cocommutative (a.k.a. abelian) Hopf algebras over a field. From an algebro-geometric point of view, these are abelian group schemes, and thus any classification must be at least as hard as the classification of not necessarily finitely generated abelian groups. In characteristic 0, it is in fact about equally hard, but in characteristic p, the question becomes significantly more complicated. As abelian Hopf algebras form an abelian category, their classification can be reduced to the classification of modules over certain rings. Under stronger assumptions, namely the presence of a grading, a perfect ground field, and p-torsion pure-injective Hopf algebras, I will present a complete classification via certain string modules along with inroads to a classification without the p-torsion assumption.
  

Friday, 21 November 2025

• 13:15, Room U2-232
  Fabian Januszewski (Paderborn): Rational structures on quivers and a generalization of Gelfand's equivalence
  Abstract: The representation theory of quivers, well-understood over algebraically closed fields, presents deeper challenges over general fields K. The established approach in this setting, developed by Dlab and Ringel, utilizes the framework of K-species. Separately, a celebrated result by Gelfand connects the representation theory of Lie groups to quivers, establishing an equivalence between a block of Harish-Chandra modules for SL(2,R) and representations of the Gelfand quiver. This talk presents a new framework designed to unify and generalize these concepts in a rational setting.
  We introduce the notion of a K-rational structure on a quiver, which endows a quiver with a compatible action of a Galois group. We link this concept to a refinement of K-species, which we term étale K-species. There is a categorical anti-equivalence between K-rational quivers and étale K-species, which extends to an equivalence of their respective representation categories. This framework also provides a canonical notion of base change for these objects.
  As the primary application, we use this machinery to generalize Gelfand's equivalence to a Q-rational setting. We define a Q-rational structure on the Gelfand quiver and construct a functor from the category of Q-rational Harish-Chandra modules to the category of nilpotent Q-rational quiver representations. A key technical tool, which we call unipotent stabilization, is necessary to construct this functor and prove that it is an equivalence.

Friday, 14 November 2025

• 13:15, Room U2-232
  Jan Stovicek (Prague): Torsion and complete dualizable objects in tt-categories with a Noetherian ring action
  Abstract: The main object of interest in this talk is a rigidly compactly generated tensor triangulated category with an action of a graded commutative Noetherian ring R making (graded) homomorphism groups between compacts finitely generated R-modules. There are various examples of this setup coming from commutative algebra, modular representation theory of groups or homotopy theory.
  In joint work with Jun Maillard, we studied the categories of dualizable objects inside the mutually equivalent categories of a-torsion and a-complete objects with respect to a homogeneous ideal a of R. This is a surprisingly well behaved setup. For example, the categories of a-torsion/complete dualizable objects are always Hom-finite over the a-adic completion of R and we can recover them using a form of Cauchy completions from the categories of a-torsion/comlete compact objects. The best results are achieved when we in addition assume that the category of compact objects is strongly generated (or equivalently, has finite Rouquier dimension). Then so is the category of a-torsion/complete dualizable objects and the so-called local regularity condition introduced by Benson, Iyengar, Krause and Pevtsova is automatically satisfied. Moreover, there are Brown representability results providing a "perfect pairing" between the categories of a-torsion/complete compact objects and a-torsion/complete dualizable objects which are formally very similar to Neeman's arXiv:1804.02240.

Friday, 07 November 2025

• 13:15, Room U2-232
  Mateusz Stroinski (Hamburg): Algebras, quivers and species in fusion and tensor categories
  Abstract: By results of Etingof and Ostrik, the theory of module categories over a finite tensor category C is equivalent to that of modules over algebras inside C. Hence it is a generalisation of the representation theory of finite-dimensional algebras, internal to C.
  The aim of this talk is to build on this observation: I will explain how to define Jacobson radicals, quivers, species and their representations, all internal to C.
  Applications I will present include a proof of a conjecture of Etingof-Ostrik on (semi)simple algebras in C, based on joint work with Kevin Coulembier (University of Sydney) and Tony Zorman (TU Dresden), as well as a variant of Gabriel's theorem on basic Morita representatives given by species in C, based on an ongoing collaboration with Edmund Heng (University of Sydney).
  
  

Friday, 31 October 2025

• 13:15, Room U2-232
  Gopinath Sahoo (Mumbai): Tensor t-structures and perversity functions
  Abstract: For a Noetherian scheme X admitting a dualizing complex, Bezrukavnikov-Deligne and independently Gabber and Kashiwara showed that any monotone comonotone perversity function on X gives rise to a t-structure on the bounded derived category of X. In a recent preprint (arXiv:2412.18009), we introduced the notion of tensor t-structures via the action of perfect complexes on the bounded derived category, and proved that these coincide exactly with those coming from perversity functions. This work builds on our earlier results on t-structures for unbounded derived categories of Noetherian schemes. In this talk, I will explain how these results are related and briefly review their history.

Friday, 17 October 2025

• 09:00, Room M4-122/126
  Igor Burban (Paderborn): Exceptional curves and real curve orbifolds
  Abstract: An exceptional hereditary non-commutative curve over an algebraically closed field is a weighted projective line of Geigle and Lenzing. However, over arbitrary fields, the theory of exceptional curves is significantly richer. In my talk I am going to explain the definition, examples and key properties of this class of non-commutative curves, including their invariants and their relation to squid algebras. I shall also explain a connection between real exceptional curves of tubular type and wallpaper groups, which was discovered by Lenzing many years ago. My talk is based on arXiv:2411.06222 as well as on an ongoing work in progress with Baumeister, Neaime and Schwabe.
• 10:30, Room M4-122/126
  Daniel Perniok (Paderborn): Coxeter-Dynkin algebras of canonical type
  Abstract: In this talk we will see a new definition of Coxeter-Dynkin algebras of canonical type. This generalises the existing definition in the special case where it can be described via quivers and relations. The main goal is to establish a derived equivalence to Ringel's squid algebra (and hence to the corresponding canonical algebra). Finally, we will build a bridge to geometric group theory via Saito's classification of marked extended affine root systems of codimension one.
  
• 11:30, Room M4-122/126
  Andrew Hubery (Bielefeld): Tame hereditary algebras, non-commutative curves, and preprojective algebras
  Abstract: The category of finite dimensional representations of a tame hereditary algebra has a discrete part, related to the roots of an affine Kac-Moody Lie algebra, and a continuous part. The simplest case is for the Kronecker quiver, when the continuous part is precisely the projective line. Lenzing and coauthors generalised this and showed that this continuous part has the structure of a non-commutative curve, constructed using the preprojective algebra. We will revisit this important construction, strengthening their results, and providing further connections between the geometry and certain infinite dimensional representations.
• 14:00, M4-122/126
  Georges Neaime (Bielefeld): Reflection groups of canonical type and their non-crossing partitions
  Abstract: We introduce the notion of reflection groups of canonical type. These groups are related to the K-theoretic study of the canonical algebras of Ringel. We use the notion of a symbol introduced by Lenzing to define them. We also introduce the associated non-crossing partitions of canonical type, which are intervals of Coxeter elements equipped with a poset structure. These notions will appear in a joint work in progress with Barbara, Charly, and Igor. If time permits, I will present a research programme for the sequel in order to study these groups from a geometric group theory point of view.
• 15:30, Room M4-122/126
  Barbara Baumeister (Bielefeld): Extended Weyl groups and their hyperbolic covers
  Abstract: I will explain the problem appearing in the Hurwitz action on the set of reduced reflection factorizations of a Coxeter element, and present a solution to this problem. I will also explain the choice of the name "hyperbolic cover".
• 16:30, Room M4-122/126
  Charly Schwabe (Paderborn): Simplicity beneath the complexity: a categorification of non-crossing partitions for exceptional curves
  Abstract: In this talk, I will report on ongoing joint work with Baumeister, Burban and Neaime. I will explain how the proofs of Hurwitz transitivity and the categorification of non-crossing partitions become very simple under the right assumptions. In other words, I will show exactly what the technical difficulties are, that were unclear when we started this project.
  

Wednesday, 15 October 2025

• 11:00, Room B2-218
  Cyril Matousek (Aarhus): Hereditary rings and metric completions of their derived categories
  Abstract: A metric on a triangulated category, as developed by Neeman, provides a recipe for constructing a metric completion of the category. These completions are guaranteed to be triangulated categories as well and have recently been used to study, among other things, derived Morita theory, cluster categories, and t‑structures. The aim of this talk is to examine metric completions of bounded derived categories of hereditary rings and their connection to the concept of universal localisation. Notably, we explicitly describe the completions of bounded derived categories of hereditary finite dimensional tame algebras and hereditary commutative noetherian rings with respect to additive good metrics.

For information on earlier talks please check the complete seminar archive.