Re­search In­terests

  • Spectral geometry: study of resonances both of the Laplace-Beltrami operator and the geodesic flow

  • Mathematical physics: spectral theory of chaotic, deterministic classical systems (Pollicott-Ruelle resonances) as well as complex (chaotic) quantum systems

  • Harmonic analysis on Lie groups: in particular the study of wavefront sets of unitary representations

Se­lec­ted pub­lic­a­tions of the work­ing group

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.

Fun­ded re­search pro­jects

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Emmy-No­eth­er group

Microlocal methods for hyperbolic dynamics

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Col­lab­or­at­ive Re­search Centre TRR 358

We are involved with two projects in the joint Collaborative Research Centre "Integer Structures in Geometry and Representation Theory" of the Universities of Bielefeld and Paderborn.

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PhoQC

We are involved in the research project "PhoQC: Photonic Quantum Computing" funded by the state of NRW.

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SPP

Benjamin Dealrue leads the project "Resonances for non-compact locally symmetric space" within the DFG-funded priority programme "Geometry at Infinity".

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Com­plete list of pub­lic­a­tions of the work­ing group Spec­tral Ana­lys­is

Wave Front Sets of Nilpotent Lie Group Representations

T. Weich, J. Budde, Journal of Functional Analysis 288 (2025).

DOI PDF

SRB Measures of Anosov Actions

T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, Journal of Differential Geometry (to Appear) --  ArXiv:2103.12127 (2024).

PDF arXiv

Locally homogeneous Axiom A flows I: projective Anosov subgroups and exponential mixing

B. Delarue, D. Monclair, A. Sanders, ArXiv:2403.14257 (2024).

arXiv

Quantum resonances and scattering poles of classical rank one locally symmetric spaces

B. Delarue, J. Hilgert, ArXiv:2403.14426 (2024).

arXiv

Temperedness of locally symmetric spaces: The product case

T. Weich, L.L. Wolf, Geom Dedicata 218 (2024).

DOI arXiv

Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces

C. Lutsko, T. Weich, L.L. Wolf, ArXiv:2402.02530 (2024).

arXiv

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.

DOI

Ruelle-Taylor resonances of Anosov actions

T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, J. Europ. Math. Soc. (2024) 1–36.

PDF

The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees

G. Palmirotta, Y. Sire, J.-P. Anker, ArXiv:2412.00780 (2024).

arXiv

Patterson-Sullivan and Wigner distributions of convex-cocompact hyperbolic surfaces

B. Delarue, G. Palmirotta, ArXiv:2411.19782 (2024).

arXiv

Absence of principal eigenvalues for higher rank locally symmetric spaces

T. Weich, L.L. Wolf, Communications in Mathematical Physics 403 (2023).

DOI arXiv

Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems

P. Schütte, T. Weich, S. Barkhofen, Communications in Mathematical Physics 398 (2023) 655–678.

DOI arXiv

Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions

P. Schütte, T. Weich, ArXiv:2308.13463 (2023).

arXiv

Higher rank quantum-classical correspondence

J. Hilgert, T. Weich, L.L. Wolf, Analysis & PDE 16 (2023) 2241–2265.

arXiv

Spectral correspondences for finite graphs without dead ends

K.-U. Bux, J. Hilgert, T. Weich, ArXiv:2307.10876 (2023).

arXiv

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.

DOI arXiv

$L^2$-spectrum, growth indicator function and critical exponent on locally symmetric spaces

L.L. Wolf, H.-W. Zhang, ArXiv:2311.11770 (2023).

arXiv

Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models

B. Delarue, P. Schütte, T. Weich, Annales Henri Poincaré 25 (2023) 1607–1656.

DOI

Singular cohomology of symplectic quotients by circle actions and Kirwan surjectivity

B. Delarue, P. Ramacher, M. Schmitt, ArXiv:2312.03634 (2023).

arXiv

A Riemann-Roch formula for singular reductions by circle actions

B. Delarue, L. Ioos, P. Ramacher, ArXiv:2302.09894 (2023).

arXiv

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.

DOI

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.

DOI arXiv

Ruelle–Pollicott resonances for manifolds with hyperbolic cusps

Y. Guedes Bonthonneau, T. Weich, Journal of the European Mathematical Society 24 (2022) 851–923.

DOI

Semiclassical formulae For Wigner distributions

S. Barkhofen, P. Schütte, T. Weich, Journal of Physics A: Mathematical and Theoretical 55 (2022).

DOI arXiv

Poisson transforms for trees of bounded degree

K.-U. Bux, J. Hilgert, T. Weich, Journal of Spectral Theory 12 (2022) 659–681.

DOI

Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions

B. Delarue, P. Ramacher, Journal of Symplectic Geometry 19 (2021) 1281–1337.

DOI

Resonances and weighted zeta functions for obstacle scattering via smooth models

P. Schütte, T. Weich, B. Delarue, (2021).

arXiv

Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces

B. Küster, T. Weich, International Mathematics Research Notices 2021 (2021) 8225–8296.

DOI arXiv

High frequency limits for invariant Ruelle densities

C. Guillarmou, J. Hilgert, T. Weich, Annales Henri Lebesgue 4 (2021) 81–119.

DOI arXiv

Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds

C. Guillarmou, B. Küster, Annales Henri Poincaré 22 (2021) 3565–3617.

DOI

Pollicott-Ruelle Resonant States and Betti Numbers

B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941.

DOI

Pollicott-Ruelle Resonant States and Betti Numbers

B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941.

DOI

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.

DOI arXiv

Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces

M. Kolb, T. Weich, L.L. Wolf, ArXiv:1909.06183 (2019).

arXiv

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.

DOI

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.

DOI arXiv

Wave front sets of reductive Lie group representations III

B. Harris, T. Weich, Advances in Mathematics 313 (2017) 176–236.

DOI arXiv

Classical and quantum resonances for hyperbolic surfaces

C. Guillarmou, J. Hilgert, T. Weich, Mathematische Annalen 370 (2017) 1231–1275.

DOI arXiv

On the semiclassical functional calculus for h-dependent functions

B. Küster, Annals of Global Analysis and Geometry 52 (2017) 57–97.

DOI

Quantum ergodicity and symmetry reduction

B. Küster, P. Ramacher, Journal of Functional Analysis 273 (2017) 41–124.

DOI

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.

DOI arXiv

On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows

T. Weich, Annales Henri Poincaré 18 (2016) 37–52.

DOI arXiv

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.

DOI arXiv

Resonance Chains and Geometric Limits on Schottky Surfaces

T. Weich, Communications in Mathematical Physics 337 (2015) 727–765.

DOI arXiv

Equivariant spectral asymptotics for<i>h</i>-pseudodifferential operators

T. Weich, Journal of Mathematical Physics 55 (2014).

DOI arXiv

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.

DOI arXiv

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).

DOI arXiv

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).

DOI arXiv

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).

DOI arXiv

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