Algebra and Representation theory seminar

29.01.2026:  Maximilian Kaipel (University of Bielefeld) 

Title: Exceptional versus tau-exceptional sequences

Abstract: Exceptional sequences are classical objects in algebraic geometry and representation theory. They are particularly useful when they generate their ambient triangulated category, in which case we call them complete. While complete exceptional sequences always exist for hereditary algebras, they generally fail to exist for other finite dimensional algebras.

Motivated by this observation and the generalisation of classical tilting theory to tau-tilting theory, Buan—Marsh introduce tau-exceptional sequences. For these sequences of modules, complete versions always exist. However, while exceptional and tau-exceptional sequences coincide for hereditary algebras, essentially no relationship between these two notions is known beyond this setting.

In my talk I will present first results that establish a connection between these two types of sequences for Auslander algebras of K[x]/(x^t), where t is some positive integer. In particular, I will show that complete exceptional sequences form a proper subset of complete tau-exceptional sequences and compare their mutation theories.

05.02.2026:   Pia Falkenburg and Carolin Hartung (University of Bonn) 

Title: THE HOMOLOGICAL BIJECTION BY RINGEL IS STABILIZED INTERVAL FREE

Abstract: Ringel introduced homological permutations in his study of the finitistic dimension of Nakayama algebras. There he established, among other results, the left-right symmetry and observed that the homological permutations associated to linear Nakayama algebras are fixed-point free. Building on this, Vincent Gelinas carried out further experiments and formulated the conjecture that these permutations satisfy the much stronger SIF property (Stabilized-Interval-Free). As a main theorem of this talk we prove this conjecture. To achieve this goal we also find a bijection between so called „special“ permutations and irreducible set partitions.

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.

08.01.2026:  Henning Krause (University of Bielefeld) 

Title: Ordnung muss sein - ruminations on posets and their linear representations

Abstract: For any finite totally ordered set and any field, the finite dimensional linear represenations form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some cases new integer sequences arise. The formulation of this counting problem leads to a universal construction which assigns to any poset a finitely cocomplete additive category; it is abelian when the poset is finite and does not depend on the choice of any ring of coefficients. Conversely, one may request for an abelian category the existence of an underlying partial order, following the rule „Ordung muss sein“; an answer to this question involves the distributivity of certain lattices.

15.01.2026:  Martin Rubey (Technische Universität Wien) 

Title: The global dimension of Nakayama Algebras, trees and Dyck paths

Abstract: We show that the global dimension of linear Nakayama algebras has the same distribution as the height of Dyck paths. To do so, we consider a slight modification of Ringel's resolution quiver and a mix of enumerative and bijective arguments.

This is joint work with Viktória Klász, René Marczinzik, Anton Mellit and Christian Stump. 

22.01.2026:  Buyan Li  (Tsinghua University) 

Title: Root Category and Simple Groups of Lie Type

Abstract: Ringel used the representation theory of finite-type hereditary algebra and Hall polynomials to obtain the positive part of the simple Lie algebra. Peng and Xiao generalized Ringel's result to root category and obtained the whole Lie algebra. Based on their constructions, we construct the compact real form of the complex semisimple Lie algebra, and the Chevalley group of the root category, as well as its maximal compact subgroup. On the other hand, we use Lusztig's results to recover the classical representation theory of compact Lie groups, such as Peter-Weyl theorem and Plancherel theorem.