Wintersemester 2025/26
Wintersemester 2025/26
23.09.2025 um 10:00 Uhr in 69/E23
Tarek Emmrich (Universität Osnabrück)
Minors of algebraic matrices
Motivated by applications to the recovery of sparse signals on graphs, we study conditions under which minors of algebraic matrices are nonvanishing. For eigenvector matrices, we establish a sufficient criterion ensuring nonvanishing minors. For Vandermonde matrices, and in particular for Fourier matrices (a special case), we build on Chebotarev’s theorem. We further extend this framework in two directions: a real version and a finite field version. The latter, in particular, yields new results for Fourier matrices of squarefree order.
09.10.2025 um 14:00 Uhr in 69/117
Bentje Jantzen (Universität Osnabrück)
Symmetrische Seitenpolytope - eine Erweiterung von Symmetrischen Kantenpolytopen auf Simplizialkomplexe
Symmetrische Kantenpolytope (engl.: Symmetric Edge Polytopes) sind Polytope, die sich aus der Kantenstruktur eines Graphen ableiten und sie spielen eine wichtige Rolle in verschiedenen Bereichen der Mathematik. Doch Graphen bieten nur eine begrenzte Möglichkeit Informationen zu halten, weil sie auf Knoten und Kanten beschränkt sind. Fassen wir einen Graphen jedoch als 1-dimensionalen Simplizialkomplex auf, stellt sich die Frage, was in höheren Dimensionen passiert und wie man dies in einer verallgemeinerten Definition abbilden kann.
Im Laufe des Vortrags werden wir eine mögliche Verallgemeinerung des Symmetrischen Kantenpolytops einführen, das sogenannte Symmetrische Seitenpolytop, das sich aus der Seitenstruktur eines Simplizialkomplexes ableitet, und ein paar grundlegende Eigenschaften vorstellen. Dabei werden wir insbesondere den Fall des Standardsimplex als zugrundeliegenden Simplizialkomplex im Rahmen der Ehrharttheorie genauer betrachten.
22.10.2025 um 09:00 Uhr in 69/E15
Christian Ahring (Universität Osnabrück)
Semistability for Filtered Modules
Semistability of vector bundles was introduced by Mumford in the 60's in order to construct nice moduli spaces of vector bundles on curves. The concept of semistability has been generalized to coherent sheaves on higher dimensional varieties but also adopted to other areas of mathematics (e.g. representations of quivers, normed lattices etc.). Categorical frameworks for semistability theories have been developed. A key property of these semistability theories is the existence of a unique Harder-Narasimhan filtration for every object. In this talk we present how the category of filtered modules over a local ring does (not) fit into this framework. However, we show that every purely d-dimensional filtered module admits a non-unique Harder-Narasimhan filtration.
29.10.2025 um 09:00 Uhr in 69/E15
Fynn Pörtner (Universität Osnabrück)
Extension Problem for Semistable Filtered Modules
0→A→E→B→0, it remains an open question whether E is again semistable. We provide additional conditions on A and B that guarantee the semistability of E. We demonstrate that, even in the case of a local domain R, the proof of semistability of R^2 involves subtle and nontrivial arguments.
In the second part of the talk, we present a criterion for determining whether a local reduced ring is semistable. Finally, we use the close connection between Stanley-Reisner rings and graphs to introduce a natural notion of semistability for graphs.
12.11.2025 um 09:00 Uhr in 69/E15
Mieke Fink (Universität Osnabrück)
TBA
19.11.2025 um 09:00 Uhr in 69/E15
Prof. Dr. Holger Brenner (Universität Osnabrück)
TBA
26.11.2025 um 09:00 Uhr in 69/E15
Georgy Scholten (MPI CBG Dresden)
TBA
17.12.2025 um 09:00 Uhr in 69/E15
Se Eun Choi (Universität Osnabrück)
Revealing RL Cognitive Structure: A Tensor Decomposition Framework Grounded in Algebraic Geometry
Introduces geometric approach by applying Canonical Polyadic (CP) tensor decomposition to reinforcement learning behavioral data. By contructing two-armed bandit data as an Agent x Trial x Behavioral Feature tensor, the framework preserves multilinear interactions lost in matrix methods like Principal Component Analysis (PCA). The central finding is the discovery of functional similarity that organizes agent phynotypes. The mathematical reliability of this structure is secured by the principle of generic identifiability, rooted in Algebraic Geometry, which guarantees the latent factors are essentially unique and thus interpretable.