Seminar

No talks have been announced for this week.

For a regular email announcement please contact birep.

Future Talks

Friday, 16 October 2026

  • 13:15, Room X-E0-228
    Anna Rodriguez Rasmussen (Uppsala): Keller reconstruction for pointed Hopf algebras
    Abstract: Keller's reconstruction theorem, also known as A-infinity Koszul duality, describes how to reconstruct a finite-dimensional (co)algebra B from the Ext-infinity algebra of its simple (co)modules. If B is a pointed Hopf algebra, then the category of B-comodules becomes a tensor category where the tensor product of two simple comodules is again a simple comodule. This gives rise to additional structure on an appropriate version of the Ext-infinity algebra of the simple comodules. In this talk, I will discuss how to reconstruct the bialgebra B by taking into account this additional structure.
    This is work in progress, partly based on a collaboration with Gregor Schaumann.

Friday, 23 October 2026

  • 14:30, X-E0-228
    Katy Waddle (Hannover): tba

Friday, 30 October 2026

  • 13:15, X-E0-228
    Esha Gupta (Bonn): tba

Friday, 13 November 2026

  • 13:15, X-E0-228
    Xiaofa Chen (Köln und Hefei): tba
  • 16:00, Room X-E0-228
    Merlin Christ (Bonn): tba

Friday, 27 November 2026

  • 13:15, X-E0-228
    Can Wen (Köln und Beijing): tba
  • 14:30, X-E0-228
    Jan Thomm (Köln): tba
  • 16:00, X-E0-228
    Daniel Perniok (Paderborn): tba

Friday, 11 December 2026

  • 13:15, X-E0-228
    Erlend Børve (Aarhus): tba

Friday, 09 April 2027

  • 13:15, X-E0-228
    José Vivero (Montevideo, Uruguay): tba

Seminar Archive

Friday, 10 July 2026

  • 13:00, D2-136
    Jonathan Gruber (Bonn): Monoidal Ringel duality
    Abstract: Ringel duality is a duality on highest weight categories that interchanges tilting objects and projective objects. There are many interesting examples of highest weight categories that additionally carry a monoidal structure, e.g. arising from representations of algebraic groups, quantum groups or affine Lie algebras, or from Deligne's interpolation tensor categories. In this talk, I will explain how Ringel duality can be upgraded to a duality between monoidal highest weight categories. Time permitting, I will also discuss two applications where (1) monoidal Ringel duality defines new monoidal structures for representations of affine Lie algebras at positive levels, and (2) monoidal Ringel duality shows that the abelian envelopes of interpolation tensor categories are highest weight categories.
    This is based on joint work with Johannes Flake.

Friday, 19 June 2026

  • 13:00, D2-136
    Esther Banaian (Paderborn): A cluster character map for the derived category of a gentle algebra
    Abstract: Caldero and Chapoton described a function which sends representations of an ADE quiver to elements of the associated cluster algebra. This transformative work paved the way for many more interesting studies, and in particular this CC map has been generalized to a variety of settings. We propose a CC map for the derived category of a gentle algebra. A main feature of our definition is how it interacts with the geometric model of the derived category, and a key property is that our CC functions respect skein relations from (graded) intersections of curves. This is based on ongoing joint work with Azzurra Ciliberti, Ilaria Di Dedda, Khrystyna Serhiyenko, Yadira Valdivieso-Diaz and Kayla Wright.

Friday, 12 June 2026

  • 13:00, D2-136
    Lukas Bonfert (Hannover): Serre functor and P-objects for perverse sheaves on P^n
    Abstract: The constructible derived category of P^n is equivalent to the bounded derived category of the principal block of parabolic category O for sl(n+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. In this talk, I will explain a nice description of the Serre functor from the perspective of the constructible derived category, using the P-twists introduced by Huybrechts–Thomas. I will also discuss the classification of P-like objects in the category of perverse sheaves, which is the heart of a certain t-structure. The talk is based on joint work with Alessio Cipriani (arXiv:2506.06051).
  • 14:15, D2-136
    Markus Kleinau (Bonn): Cambrian lattices are fractionally Calabi-Yau via 2-cluster combinatorics
    Abstract: Cambrian lattices originate in the theory of Coxeter groups. They appear as 1-skeletons of generalised associahedra or as lattices of torsion classes of representation finite hereditary algebras. Rognerud has shown that Cambrian lattices of linear type A, better known as Tamari lattices, are fractionally Calabi-Yau. That is a power of the Serre functor on the derived category of their incidence algebra agrees with a power of the shift.
    The m-cluster categories are an m+1 Calabi-Yau version of cluster categories. They contain a family of m-cluster tilting objects connected by a notion of mutation. In this talk I will introduce a family of intervals in crystallographic Cambrian lattices that exhibit the same combinatorics as 2-cluster tilting objects in 2-cluster categories. As a consequence I will show that Cambrian lattices are fractionally Calabi-Yau.

Friday, 05 June 2026

  • 12:45, Room D2-136
    Chris Hone (Copenhagen): Smoothness and intersection cohomology
    Abstract: The cohomology of a compact oriented manifold satisfies Poincare duality, and in many contexts one may view the property of being self dual as an abstract incarnation of smoothness. In many settings, one has singular (non self dual) objects which admit resolutions by smooth ones. In this talk I'll discuss a simple procedure for constructing invariants of singular objects from smooth ones in this setting. This provides an alternate construction of rational intersection cohomology for singular varieties without using t structures, a mod two intersection cohomology for real varieties, and some modules over certain finite dimensional commutative algebras.
  • 14:15, Room D2-136
    Panagiotis Kostas (Thessaloniki): Intrinsic homological algebra for triangulated categories
    Abstract: It has long been observed that in the derived category of a ring, all the subcategories of interest are intrinsic. Based on this, we introduce far-away orthogonality -- a concept which allows us to systematically associate a list of intrinsic subcategories to any compactly generated triangulated category. We will explain how to utilize these subcategories in order to produce reasonable homological notions in this context and examine those attributes for common triangulated categories in representation theory. This is based on joint work with C. Psaroudakis and J. Vitória.
  • 15:30, Room D2-136
    Baptiste Rognerud (Paris): The extra slow Tamari lattice on faithfully balanced modules
    Abstract: Faithfully balanced modules appear in various places in the literature on ring theory, such as Schur-Weyl duality, Thrall's notion of a QF-1 algebra. They also appear in relation with many endo-correspondences, such as the Auslander correspondence. Even though they are very natural objects, they remain quite mysterious.
    For the Nakayama algebras, they were classified by Crawley-Boevey, Ma, Rognerud and Sauter in 2021. The classification is relatively simple, it involves tableaux combinatorics on the Auslander-Reiten quiver of the algebra. In this talk, we will only consider the path algebra of an equioriented quiver of type A. In that case, a simple formula for the number of faithfully balanced modules was found be these authors. Moreover, this combinatorics turned out to be related to other kinds of tableaux (e.g permutation tableaux or tree-like tableaux) which are objects that appear in other areas of mathematics.
    The goal of the talk is to introduce a partial order on the set of faithfully balanced modules and see that it naturally extends the Tamari lattice on the tilting modules. We will study its lattice properties and see that it behaves like a 3-color version of the Tamari lattice.
    This is a joint work with Sylvie Corteel and Jihyeug Jang.

Friday, 29 May 2026

  • 13:00, D2-136
    Sam Miller (Athens, Georgia): The classification of integral endotrivial complexes
    Abstract: Endotrivial complexes are the invertible objects in the derived category of permutation modules for a finite group. Previously, we classified the endotrivials over a field of positive characteristic. In this talk, we will describe how to extend the classification to endotrivials over a commutative Noetherian ring using techniques from representation theory, homotopy theory, and tensor-triangular geometry. This is joint work with J. Omar Gomez.
  • 14:15, D2-136
    Odysseas Giatagantzidis (Stuttgart): Homological aspects of cyclic Nakayama algebras via minimal zero paths
    Abstract: This talk revisits key homological aspects of cyclic Nakayama algebras using a new combinatorial framework based on minimal zero paths. As a consequence, we provide a criterion that determines the exact value of their finitistic dimension, which has to be one of two consecutive integers by work of Ringel (2021) building on results of Madsen (2005). Furthermore, we offer novel characterizations for well-studied homological properties, including Iwanaga-Gorensteinness, finite global dimension, and quasi-heredity, recovering prior results in this direction.

Friday, 22 May 2026

  • 13:00, D2-136
    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, 15 May 2026

  • 13:00, D2-136
    Marianne Lawson (Hamburg): The resolving completion of an exact category
    Abstract: In 2024, Neeman showed that there exist Quillen exact categories whose derived category does not admit a t-structure. We therefore relax the definition of a t-structure by dropping the triangle axiom (TS3). We use Rump's notion of Ext-acyclicity to obtain subcategories that satisfy the aforementioned definition of what we call a `t-pair'. We will refer to the intersection of the two subcategories as its `heart', which in this setting is not necessarily abelian, but is exact. We establish that the ambient exact category is a resolving subcategory of the heart, and that the heart is maximal with this property. Employing recent work of Henrard and van Roosmalen, we show that the heart and ambient category are derived equivalent. This generalizes classical results due to Schneiders from the 90s.


Saturday, 09 May 2026

Friday, 08 May 2026

Friday, 24 April 2026

  • 13:00, Room D2-136
    Wassilij Gnedin (Bielefeld): Derived representation theory of the Gelfand quiver
    Abstract: In 1970, Gelfand observed that the principal block of Harish-Chandra modules for SL(2,R) is equivalent to the category of nilpotent representations of a certain skew-gentle quiver, and posed the problem of classifying its indecomposable objects. Explicit solutions were obtained in the late 1980s by Bondarenko and independently by Crawley-Boevey.
    In my talk, I will sketch a classification of the indecomposable objects in the bounded derived category of nilpotent representations of the Gelfand quiver in terms of band and string complexes, following an approach of Burban and Drozd. The main combinatorial classes can be characterized in Lie-theoretic as well as homological terms. Moreover, the derived Auslander-Reiten translation, the sign involution, and the contragredient duality admit concrete descriptions in terms of band and string data.
    A further elaboration of this approach yields projective resolutions of the indecomposable nilpotent representations of the Gelfand quiver, as well as their main homological invariants and their explicit representation matrices. Finally, I will briefly discuss generalizations of the preceding results to other skew-gentle quivers. The talk is based on joint work with Burban (arXiv:2604.00274).

Friday, 17 April 2026

  • 13:00, D2-136
    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, D2-136
    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.

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