Projects from Prof. Dr. Joachim Hilgert
Lie Theory
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
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
SPP 1388: Representation Theory
Representation theory is a cross-disciplinary branch of mathematics with a wide range of applications in mathematics and in the sciences. Chemistry uses representation theory for instance to investigate symmetries of molecules, while quantum mechanics is a classical area of applications in physics. Further applications in physics and related areas ...
Duration: 01/2012 - 12/2016
Funded by: DFG