24.04.2025: Yulia Mukhina (École polytechnique, Paris)

Title: A new algorithm for differential elimination 

Abstract: For a polynomial dynamical system, we study the problem of computing the minimal differential equation satisfied by a chosen coordinate. We give a bound for the Newton polytope of the support of such an equation and show that our bound is sharp in "more than half of the cases". We show the algorithm bases on this bound and demonstrate that our implementation of the algorithm can tackle problems which are out of reach for the state-of-the-art software for differential elimination.

15.05.2025: Azzurra Ciliberti (University of Bochum)

Title: 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.

05.06.2025: Iacopo Nonis (University of Leeds)

Title: Tau-exceptional sequences for representations of quivers over local algebras   

Abstract:  Exceptional sequences were first introduced in triangulated categories by the Moscow school of algebraic geometry. Later, Crawley-Boevey and Ringel considered exceptional sequences in the module categories of hereditary finite-dimensional algebras. Motivated by tau-tilting theory introduced by Adachi, Iyama, and Reiten, Jasso’s reduction for tau-tilting modules, and signed exceptional sequences introduced by Igusa and Todorov, Buan and Marsh developed the theory of (signed) tau-exceptional sequences – a natural generalization of (signed) exceptional sequences that behave well over arbitrary finite-dimensional algebras.

In this talk, we will study (signed) tau-exceptional sequences over the algebra 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 (signed) tau-exceptional sequences over Λ can be fully understood in terms of (signed) exceptional sequences over kQ. 

10.07.2025: Nicolás López Funes (University of Bonn)

Title: On tau-exceptional sequences

17.07.2025: Tiago Cruz (University of Stuttgart)

Title: Understanding Schur algebras S(p, 2p) via a generalisation of higher Auslander algebras 

Abstract: Schur algebras of the form S(n, n) are well understood from

the homological point of view. In particular, their global and dominant

dimensions are known. The story is completely different for Schur

algebras S(n,d) with n < d in positive characteristic.

In this talk, we explain several homological properties of Schur

algebras S(p,2p) over a field of positive characteristic p. In

particular, we refine our understanding of Schur-Weyl duality for these

algebras by placing them within an Auslander-type correspondence. In

doing so, we find a new duality for these class of algebras in terms of 

tilting theory. This is based on joint work with Karin Erdmann.

17.07.2025: Markus Kleinau (University of Bonn)

Title: Cambrian lattices are fractionally Calabi Yau via 2-cluster combinatorics

Abstract: The crystallographic Cambrian lattices are the 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 generalizations of cluster categories which

exhibit very similar combinatorics. In particular there is a family of

m-cluster tilting objects connected by a notion of mutation. In this

talk we will describe the Serre functors of crystallographic Cambrian

lattices using the combinatorics of 2-cluster tilting objects in

2-cluster categories. As a consequence we show that all crystallographic 

Cambrian lattices are fractionally Calabi Yau.

01.08.2025 (10:00-13:00 in SR 0.011): Javier Herrero, Javier San Martín, and Masa Zaucer (University of Bonn)

Title: Reflexive Modules in Nakayama Algebras

Abstract: It is well-known that self-injective Artin algebras are characterized by the property that all of its finitely generated modules are reflexive. Under certain circumstances, self-injectivity reduces to check reflexivity of a smaller class of modules. Following this idea, we will begin presenting some positive results in a general context by Marczinzik. We will then address this problem in the case of Nakayama algebras, which have a combinatorial interpretation via Dyck paths. We thus give a criterion to test reflexivity of modules via purely combinatorial formulas, which we have used to prove two conjectures relating the number of non-projective simple reflexive modules with combinatorial properties of the Dyck path. We will conclude by presenting a more general conjecture generalizing from the setting of simple modules to the case of arbitrary non-projective indecomposable reflexive modules. 

21.08.2025: Sven Ulf Schmitz and Finn Bauwens (University of Bonn)

Title: On selforthogonal algebras with cyclic quiver 

Abstract: A selforthogonal module M is characterized by the property Ext^i(M,M)=0 for all i>0. We aim to look at selforthogonal algebras, i.e. algebras where every module is selforthogonal. For algebras with acyclic quiver, a lot of examples are known, e.g. hereditary algebras of Dynkin quivers and linear Nakayama algebras. We show that selforthogonal algebras have finite representation type and finite global dimension. We then classify all selforthogonal cyclic Nakayama algebras using a generalization of Ringel's resolution quiver. We also discuss some classes of selforthogonal algebras with cyclic quiver that are not Nakayama algebras. 

18.09.2025: Master thesis talks

16:15 Jonas Walter: Canonical decompositions for dimension vectors of n-subspace quivers

17:15 Paul Berners: A generalization of preprojective algebras

25.09.2025: Juri Kaganskiy, Samuel Meyer, and Henrik Schlüter (University of Bonn)

Title: Reduced Incidence Algebras

Abstract: Our project deals with questions concerning reduced incidence algebras and Frobenius algebras. The reduced incidence algebra R(P) is defined for every poset. A natural question to pose is: For which P is R(P) Frobenius. An interesting subclass of posets are the finite distributive lattices. Our main result is: For P a finite distributive lattice: R(P ) is a Frobenius algebra iff P is an unmixed divisor lattice.