Forschungsinteressen

  • Spektralgeometrie: Insbesondere mittels des Studiums von Resonanzen (sowohl des Laplace-Beltrami Operators als auch des geodätischen Flusses).

  • Mathematische Physik: Spektraltheorie chaotischer deterministischer Systeme (Ruelle-Pollicott Resonanzen) sowie komplexer (chaotischen) Quantensystemen.

  • Harmonische Analysis von Lie-Gruppen: Insbesondere das Studium der Wellenfrontmengen unitärer Darstellungen von Lie-Gruppen

Ausgewählte Publikationen der Arbeitsgruppe

Higher rank quantum-classical correspondence
J. Hilgert, T. Weich, L.L. Wolf,  Analysis&PDE (to appear).

Ruelle-Taylor resonaces of Anosov actions
T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, Journal of the EMS (to appear).

The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
M. Cekić, B. Delarue, S. Dyatlov, G.P. Paternain, Inventiones Mathematicae 229 (2022) 303–394.

Ruelle–Pollicott resonances for manifolds with hyperbolic cusps
Y. Guedes Bonthonneau, T. Weich, Journal of the European Mathematical Society 24 (2022) 851–923.

Geförderte Forschungsprojekte

Logo

Emmy Noether-Gruppe

Mikrolokale Methoden für Hyperbolische Dynamiken

Logo

Sonderforschungsbereich TRR 358

Wir sind mit zwei Projekten am gemeinsamen Sonderforschungsbereich "Ganzzahlige Strukturen in Geometrie und Darstellungstheorie" der Universitäten Bielefeld und Paderborn beteiligt.

Logo

PhoQC

Wir sind am vom Land NRW geförderten Forschungsprojekt "PhoQC: Photonisches Quantencomputing" beteiligt.

Logo

SPP

Benjamin Dealrue leitet das Projekt "Resonances for non-compact locally symmetric space" im Rahmen des DFG-geförderten Schwerpunktprogramms "Geometry at Infinity".

Vollständige Liste der Publikationen der AG Spektralanalysis

SRB Measures of Anosov Actions
T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, Journal of Differential Geometry (to Appear) --  ArXiv:2103.12127 (2024).
Ruelle-Taylor resonaces of Anosov actions
T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, J. Europ. Math. Soc. (2024) 1–36.
Absence of principal eigenvalues for higher rank locally symmetric spaces
T. Weich, L.L. Wolf, Communications in Mathematical Physics 403 (2023).
Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems
P. Schütte, T. Weich, S. Barkhofen, Communications in Mathematical Physics 398 (2023) 655–678.
Temperedness of locally symmetric spaces: The product case
T. Weich, L.L. Wolf, ArXiv:2304.09573 (2023).
Higher rank quantum-classical correspondence
J. Hilgert, T. Weich, L.L. Wolf, Analysis & PDE 16 (2023) 2241–2265.
Spectral correspondences for finite graphs without dead ends
K.-U. Bux, J. Hilgert, T. Weich, ArXiv:2307.10876 (2023).
Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters
C. Arends, J. Hilgert, Journal de l’École Polytechnique — Mathématiques 10 (2023) 335–403.
The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
M. Cekić, B. Delarue, S. Dyatlov, G.P. Paternain, Inventiones Mathematicae 229 (2022) 303–394.
Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature
M. Kolb, T. Weich, L.L. Wolf, Annales Henri Poincaré 23 (2022) 1283–1296.
Ruelle–Pollicott resonances for manifolds with hyperbolic cusps
Y. Guedes Bonthonneau, T. Weich, Journal of the European Mathematical Society 24 (2022) 851–923.
Semiclassical formulae For Wigner distributions
S. Barkhofen, P. Schütte, T. Weich, Journal of Physics A: Mathematical and Theoretical 55 (2022).
Poisson transforms for trees of bounded degree
K.-U. Bux, J. Hilgert, T. Weich, Journal of Spectral Theory 12 (2022) 659–681.
Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions
B. Delarue, P. Ramacher, Journal of Symplectic Geometry 19 (2021) 1281–1337.
Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces
B. Küster, T. Weich, International Mathematics Research Notices 2021 (2021) 8225–8296.
Wave Front Sets of Nilpotent Lie Group Representations
T. Weich, J. Budde, ArXiv:2103.02968v1 (2021).
High frequency limits for invariant Ruelle densities
C. Guillarmou, J. Hilgert, T. Weich, Annales Henri Lebesgue 4 (2021) 81–119.
Pollicott-Ruelle Resonant States and Betti Numbers
B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941.
Improved fractal Weyl bounds for hyperbolic manifolds. With an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich
S. Dyatlov, D. Borthwick, T. Weich, Journal of the European Mathematical Society 21 (2019) 1595–1639.
Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces
M. Kolb, T. Weich, L.L. Wolf, ArXiv:1909.06183 (2019).
Numerically Investigating Residues of Weighted Zeta Functions on Schottky Surfaces
P. Schütte, Numerically Investigating Residues of Weighted Zeta Functions on Schottky Surfaces, 2019.
Identifying and Realizing Symmetries in Quantum Walks - Symmetry Classes and Quantum Walks
P. Schütte, Identifying and Realizing Symmetries in Quantum Walks - Symmetry Classes and Quantum Walks, 2017.
Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps
F. Faure, T. Weich, Communications in Mathematical Physics 356 (2017) 755–822.
Wave front sets of reductive Lie group representations III
B. Harris, T. Weich, Advances in Mathematics 313 (2017) 176–236.
Classical and quantum resonances for hyperbolic surfaces
C. Guillarmou, J. Hilgert, T. Weich, Mathematische Annalen 370 (2017) 1231–1275.
Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps
J.F. ARNOLDI, F. FAURE, T. Weich, Ergodic Theory and Dynamical Systems 37 (2015) 1–58.
Resonance Chains and Geometric Limits on Schottky Surfaces
T. Weich, Communications in Mathematical Physics 337 (2015) 727–765.
Formation and interaction of resonance chains in the open three-disk system
T. Weich, S. Barkhofen, U. Kuhl, C. Poli, H. Schomerus, New Journal of Physics 16 (2014).
Experimental Observation of the Spectral Gap in Microwave n-Disk Systems
S. Barkhofen, T. Weich, A. Potzuweit, H.-J. Stöckmann, U. Kuhl, M. Zworski, Physical Review Letters 110 (2013).
Weyl asymptotics: From closed to open systems
A. Potzuweit, T. Weich, S. Barkhofen, U. Kuhl, H.-J. Stöckmann, M. Zworski, Physical Review E 86 (2012).
Alle Publikationen anzeigen