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
National Research Data Infrastructure for and with Computer Science
The main goal of the consortium NFDIxCS is to identify, define and finally deploy services to store complex domain specific data objects from the specific variety of sub-domains from Computer Science (CS) and to realize the FAIR principles across the board. This includes to produce re-usable data objects specific to the various types of CS data ...
Duration: 01/2023 - 12/2028
Near-field coupled nonlocal optical metasurface for versatile polarization and bandstructure manipulations
Recent advances in the modern nanotechnology gave birth to ‘thin-flat-optics’ elements (the so-called optical metasurfaces), based on nanoscale structures, capable of versatile tailoring on the responses to light such as wave-fronts, amplitudes, polarization, and frequency. Despite the extremely reduced dimensions of the ‘flat-optics’ elements, the ...
Duration: 01/2023 - 12/2026
Musicological Markup with the mei-friend Editor
As the only music encoding format, MEI natively supports not only various types of notation, but also fine-grained cross-references?both within a document and to other digital objects?as well as complex transcription-related and editorial markup. At the same time, there is a great need for suitable tools that are graphically oriented and enable ...
Duration: 01/2023 - 12/2023