Forschungsinteressen
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Spektralgeometrie: Insbesondere mittels des Studiums von Resonanzen (sowohl des Laplace-Beltrami Operators als auch des geodätischen Flusses).
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Mathematische Physik: Spektraltheorie chaotischer deterministischer Systeme (Ruelle-Pollicott Resonanzen) sowie komplexer (chaotischen) Quantensystemen.
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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
Vollständige Liste der Publikationen der AG Spektralanalysis
Wave Front Sets of Nilpotent Lie Group Representations
T. Weich, J. Budde, Journal of Functional Analysis 288 (2025).
Locally homogeneous Axiom A flows I: projective Anosov subgroups and exponential mixing
B. Delarue, D. Monclair, A. Sanders, ArXiv:2403.14257 (2024).
Quantum resonances and scattering poles of classical rank one locally symmetric spaces
B. Delarue, J. Hilgert, ArXiv:2403.14426 (2024).
Temperedness of locally symmetric spaces: The product case
T. Weich, L.L. Wolf, Geom Dedicata 218 (2024).
Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces
C. Lutsko, T. Weich, L.L. Wolf, ArXiv:2402.02530 (2024).
Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik
M. Hoffmann, J. Hilgert, T. Weich, Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik, Springer Berlin Heidelberg, Berlin, Heidelberg, 2024.
Ruelle-Taylor resonances of Anosov actions
T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, J. Europ. Math. Soc. (2024) 3085–3147.
The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees
G. Palmirotta, Y. Sire, J.-P. Anker, ArXiv:2412.00780 (2024).
Patterson-Sullivan and Wigner distributions of convex-cocompact hyperbolic surfaces
B. Delarue, G. Palmirotta, ArXiv:2411.19782 (2024).
SRB Measures of Anosov Actions
T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, Journal of Differential Geometry 128 (2024) 959–1026.
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.
Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions
P. Schütte, T. Weich, ArXiv:2308.13463 (2023).
Higher rank quantum-classical correspondence
J. Hilgert, T. Weich, L.L. Wolf, Analysis & PDE 16 (2023) 2241–2265.
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.
$L^2$-spectrum, growth indicator function and critical exponent on locally symmetric spaces
L.L. Wolf, H.-W. Zhang, ArXiv:2311.11770 (2023).
Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models
B. Delarue, P. Schütte, T. Weich, Annales Henri Poincaré 25 (2023) 1607–1656.
Singular cohomology of symplectic quotients by circle actions and Kirwan surjectivity
B. Delarue, P. Ramacher, M. Schmitt, ArXiv:2312.03634 (2023).
A Riemann-Roch formula for singular reductions by circle actions
B. Delarue, L. Ioos, P. Ramacher, ArXiv:2302.09894 (2023).
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.
Resonances and weighted zeta functions for obstacle scattering via smooth models
P. Schütte, T. Weich, B. Delarue, (2021).
Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces
B. Küster, T. Weich, International Mathematics Research Notices 2021 (2021) 8225–8296.
High frequency limits for invariant Ruelle densities
C. Guillarmou, J. Hilgert, T. Weich, Annales Henri Lebesgue 4 (2021) 81–119.
Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds
C. Guillarmou, B. Küster, Annales Henri Poincaré 22 (2021) 3565–3617.
Pollicott-Ruelle Resonant States and Betti Numbers
B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941.
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.
Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces
B. Küster, T. Weich, International Mathematics Research Notices 2021 (2019) 8225–8296.
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.
On the semiclassical functional calculus for h-dependent functions
B. Küster, Annals of Global Analysis and Geometry 52 (2017) 57–97.
Quantum ergodicity and symmetry reduction
B. Küster, P. Ramacher, Journal of Functional Analysis 273 (2017) 41–124.
Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions
D. Borthwick, T. Weich, Journal of Spectral Theory 6 (2016) 267–329.
On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows
T. Weich, Annales Henri Poincaré 18 (2016) 37–52.
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.
Equivariant spectral asymptotics forh-pseudodifferential operators
T. Weich, Journal of Mathematical Physics 55 (2014).
Discontinuity of the Fuglede-Kadison determinant on a group von Neumann algebra
B. Küster, Communications in Mathematics 22 (2014) 141–149.
Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum
S. Barkhofen, F. Faure, T. Weich, Nonlinearity 27 (2014) 1829–1858.
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).
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