Projects from Prof. Dr. Tobias Weich
Institute of Mathematics
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
Funded by: DFG
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
Funded by: DFG
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: 01/2022 - 12/2026
Funded by: DFG
PhoQC: Photonic Quantum Computing
Photonic Quantum Computing (PhoQC): The aim is to research the fundamentals for the realization of photonic quantum computers. For this purpose, an internationally leading research center is to be created at the University of Paderborn in perspective, in which the fields of physics, mathematics, engineering sciences, computer science and electrical ...
Duration: 11/2021 - 12/2024
Funded by: MKW NRW, EIN Quantum NRW
Microlocal Methods for Hyperbolic Dynamics
A fundamental paradigm of statistical physics states that sufficiently complex systems tend very quickly to equilibrium. In the 80s Pollicott and Ruelle developed the notion of resonances for a certain class of dynamical systems (Axiom A systems) in order to prove this convergence towards equilibrium rigorously. These resonances, nowadays often ...
Duration: 08/2019 - 07/2025
Funded by: DFG
Spectral correspondences for negatively curved Riemannian locally symmetric spaces
The central goal of this project is to describe Pollicott-Ruelle resonances of locally symmetric spaces using a - to be established - correspondence between these resonances and quantum resonances.There are close connections between the dynamical properties of a free particle on a negatively curved Riemannian locally symmetric space in the ...
Duration: 01/2019 - 12/2023
Funded by: DFG