Spectral correspondences for negatively curved Riemannian locally symmetric spaces

• Applicant: Professor Dr. Joachim Hilgert
• Subject Area: Mathematics
• Term: from 2019 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 432944415

• Final Report Year: 2023

Final Report Abstract

New instances of the close mathematical relation between the classical and quantum mechanical descriptions of moving free particles under strongly symmetry constraints were established. The methods of proof point at various possible generalizations. It was surprising that the only case of spectral correspondences for exceptional spectral parameters known so far (hyperbolic surfaces) is by no means typical, but differs analytically as well as algebraically from all the other cases.

Publications

• Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters. Journal de l’École polytechnique — Mathématiques, 10, 335-403.
  Arends, Christian & Hilgert, Joachim