Algebra and Representation theory seminar

08.01.2026:  Henning Krause (University of Bielefeld) 

Title: TBA

29.01.2026:  Maximilian Kaipel (University of Cologne) 

Title: Tau-tilting finiteness under base field extension

Finite dimensional algebras come in two families. On the one hand, representation finite algebras are those which admit only finitely many indecomposable modules up to isomorphism. They are generally well understood and controllable. On the other hand, representation infinite algebras are generally the opposite. For this reason, it often makes sense to restrict one’s attention to a smaller class of modules over these algebras.

The modules I will focus on in this talk are called tau-rigid modules and are closely related to classical tilting modules and cluster algebras. In the context of tau-tilting theory, they have played a dominant role in representation theory over the past 15 years. It is remarkable, that many representation infinite algebras are actually tau-tilting finite, that is, have only finitely many indecomposable tau-rigid modules up to isomorphism. 

Let L:K be a field extension. A theorem of Jensen and Lenzing from 1982 states that a K-algebra A is representation finite if and only if the L-algebra $A \otimes_K L$ is representation finite, provided L:K is “nice enough”. In my talk I will discuss the question of whether tau-tilting finite algebras are similarly preserved under base field extension, illustrating the theory on many examples. This is based on joint work with Erlend D. Børve.

19.02.2026:  Matthew Pressland  (Université de Caen Normandie)

Title: TBA

02.10.2025: Bachelor/Master thesis talks

16:15: James Turesson: The g-vector fan of a finite-dimensional algebra

17:15: Marlon Huestege: Irreducible polynomials over finite fields

16.10.2025: Tal Gottesman (University of Bochum)

Title: Counting Boolean antichains

Abstract: We say that an antichain of a Lattice L is boolean if it generates a boolean sublattice in L, in a particularly nice way. These purely combinatorial objects play a role in the representation theory of the incidence algebra of the lattice L as indicated by recent results of Rognerud, Yıldırım and by an on going project with Klász, Kleinau and Marczinzik. Given these motivations, it seemed natural to ask: how many boolean antichains does a lattice actually have? Recently, students participating in a "Dive into Research" at the university of Bochum counted boolean antichains in famous lattices and discovered some familiar formulas. The goal of this talk is to present these results, but with enough motivations to suit an algebraically inclined audience.

06.11.2025:  Sven Ulf Schmitz (University of Bonn)

Title: Counting cyclic Nakayama algebras of finite global dimension

Abstract: For a Nakayama algebra A, we introduce additional structure on the Resolution quiver R(A), first introduced by Ringel, to obtain a purely combinatorial classification of Nakayama algebras of finite global dimension. We give explicit counting formulas for the number of both arbitrary and cyclic Nakayama algebras of finite global dimension with n simple modules.

04.12.2025:  Andreas Bode (University of Wuppertal)

Title: Auslander regularity of p-adic differential operators

The theory of D-modules provides an important geometric tool in the representation theory of Lie algebras and reductive groups. This talk is a gentle introduction to the ring-theoretic properties of rings of differential operators, particularly in a p-adic analytic setting. We prove Auslander regularity and Bernstein’s inequality for completed Weyl algebras over any complete nonarchimedean field of mixed characteristic (generalizing work by Ardakov-Wadsley in the case of discretely valued fields) and use Kashiwara’s equivalence to establish Auslander regularity for completed rings of differential operators on more general spaces. This allows us to develop a well-behaved dimension theory for p-adic Dcap-modules and establish various fundamental properties of Dcap-module operations, like adjunction and projection formulae.