TRR 358 - Hereditary categories, reflection groups and non-commutative curves (Subproject C02)
There are deep connections between quiver representations and Coxeter groups involving the associated root systems, Lie algebras and quantum groups. We will study a parallel situation in which coherent sheaves on certain non-commutative curves, called exceptional curves, correspond to other types of reflection groups. Such exceptional curves ...
Duration: 01/2023 - 12/2026
TRR 358 - Geodesic flows and Weyl chamber flows on affine buildings (B04)
Affine buildings and their quotients are geometric objects which come along with interesting dynamical systems. This project studies geodesic flows and Weyl chamber flows on such buildings. More precisely, the project aims to develop a spectral theory of joint Ruelle-Taylor resonances for the Weyl chamber flows and study equidistribution properties ...
Duration: 01/2023 - 12/2026
TRR 358 - Spectral theory in higher rank and infinite volume (B02)
Spectral theory is a fundamental tool for the investigation of locally symmetric spaces which, in the classical context, usually have finite volume. Already for spaces real rank one, say quotients of the upper half plane by a discrete group of infinite covolume, very interesting and characteristic spectral phenomena happen. The case of higher rank ...
Duration: 01/2023 - 12/2026
TRR 358 - Affine Kac–Moody groups: algebra, analysis and arithmetic (Subprojct A05)
Affine Kac-Moody groups and related groups (like loop groups) will be studied from several perspectives. We shall investigate finiteness properties of special linear groups over Laurent polynomials over the ring of integers. We also strive to classify certain maximal Lie orders corresponding to trigonometric solutions of the classical Yang-Baxter ...
Duration: 01/2023 - 12/2026
TRR 358; TP A04: Combinatorial Euler products
Euler products are the incarnation of local-global principles. They often arise as leading constants of an asymptotic formula describing a counting problem in algebra or number theory, and they encode the underlying integral structures. Prototypes are the conjectures of Manin and Malle. The Euler products and their associated zeta functions ...
Duration: 01/2023 - 12/2026
TRR 358; TP A02: Algebraic and arithmetic aspects of aperiodicity
This project aims at the analysis and classification of certain topological dynamical systems of geometric and number-theoretic origin. In particular, the systems induced by k-free integers in orders of algebraic number fields will be investigated via their generalised symmetries, their topological entropy and other number-theoretic invariants. ...
Duration: 01/2023 - 12/2026
TRR 358 - Integral structures in geometry and representation theory
Integral structures arise in many places throughout mathematics: as lattices in Euclidean space, as integral models of reductive groups and algebraic schemes, or as integral representations of groups and associative algebras. Even questions about the most basic example of an integral structure, the ring of integers Z, very soon lead into the fields ...
Duration: 01/2023 - 12/2026
Symplectic discretizations for optimal control problems in mechanics
The optimal control of mechanical problems is omnipresent in our technically affected daily living as well as in many scientific questions. As analytical solutions of optimal control problems are in general not available, applications rely on numerical simulations that are robust and accurate, and directly utilizable by engineers. For general ...
Duration: 01/2023 - 12/2025
Change.WorkAROUND
Steigerung der Wandlungsfähigkeit industrieller Dienstleistungssysteme durch Workarounds (Change.WorkAROUND)Wandlungsfähigkeit ist die Eigenschaft eines Unternehmens, Veränderungen, die ein ursprünglich planbares oder vorhersehbares Ausmaß überschreiten, rechtzeitig wahrzunehmen und technisch wie auch organisatorisch zu beherrschen. Zum Auf- und ...
Duration: 01/2023 - 12/2025
Contact: Prof. Dr. Daniel Beverungen, Prof. Dr. Martin Schneider
3D-Rekonstruktion des Ozonwasserwerkes an der Börnepader
Von 1902 bis 1937 stand in Paderborn ein unscheinbares Fabrikgebäude am Flussarm Börnepader, das ein bahnbrechendes Ozonwasserwerk beherbergte. Dieses Werk, erprobt von Ingenieuren der Siemens & Halske AG, setzte erstmals elektrisch generiertes Ozon zur Entkeimung von Trinkwasser ein, was bei Fachleuten europaweit Interesse fand. Es trug maßgeblich ...
Duration: 01/2023 - 12/2024