@article{51204,
  abstract     = {{Given a real semisimple connected Lie group $G$ and a discrete torsion-free
subgroup $\Gamma < G$ we prove a precise connection between growth rates of the
group $\Gamma$, polyhedral bounds on the joint spectrum of the ring of
invariant differential operators, and the decay of matrix coefficients. In
particular, this allows us to completely characterize temperedness of
$L^2(\Gamma\backslash G)$ in this general setting.}},
  author       = {{Lutsko, Christopher and Weich, Tobias and Wolf, Lasse Lennart}},
  journal      = {{Duke Math. Journal }},
  title        = {{{Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces}}},
  volume       = {{(to appear)}},
  year         = {{2026}},
}

@unpublished{65255,
  abstract     = {{In this paper we generalize the geodesic flow on (finite) homogeneous graphs to a multiparameter flow on compact quotients of Euclidean buildings. Then we study the joint spectra of the associated transfer operators acting on suitable Lipschitz spaces. The main result says that outside an arbitrarily small neighborhood of zero in the set of spectral parameters the Taylor spectrum of the commuting family of transfer operators is contained in the joint point spectrum.}},
  author       = {{Hilgert, Joachim and Kahl, Daniel and Weich, Tobias}},
  booktitle    = {{arXiv:2603.26949}},
  title        = {{{Spectral theory for transfer operators on compact quotients of Euclidean buildings}}},
  year         = {{2026}},
}

@article{32099,
  author       = {{Weich, Tobias and Budde, Julia}},
  journal      = {{Journal of Functional Analysis}},
  number       = {{1}},
  title        = {{{Wave Front Sets of Nilpotent Lie Group Representations}}},
  doi          = {{ https://doi.org/10.1016/j.jfa.2024.110684}},
  volume       = {{288}},
  year         = {{2025}},
}

@article{51207,
  abstract     = {{Let $X=X_1\times X_2$ be a product of two rank one symmetric spaces of
non-compact type and $\Gamma$ a torsion-free discrete subgroup in $G_1\times
G_2$. We show that the spectrum of $\Gamma \backslash X$ is related to the
asymptotic growth of $\Gamma$ in the two direction defined by the two factors.
We obtain that $L^2(\Gamma \backslash G)$ is tempered for large class of
$\Gamma$.}},
  author       = {{Weich, Tobias and Wolf, Lasse Lennart}},
  journal      = {{Geom Dedicata}},
  title        = {{{Temperedness of locally symmetric spaces: The product case}}},
  doi          = {{https://doi.org/10.1007/s10711-024-00904-4}},
  volume       = {{218}},
  year         = {{2024}},
}

@book{55193,
  author       = {{Hoffmann, Max and Hilgert, Joachim and Weich, Tobias}},
  isbn         = {{9783662673560}},
  publisher    = {{Springer Berlin Heidelberg}},
  title        = {{{Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik}}},
  doi          = {{10.1007/978-3-662-67357-7}},
  year         = {{2024}},
}

@article{32101,
  author       = {{Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin and Hilgert, Joachim}},
  journal      = {{J. Europ. Math. Soc.}},
  number       = {{8}},
  pages        = {{3085–3147}},
  title        = {{{Ruelle-Taylor resonances of Anosov actions}}},
  doi          = {{https://doi.org/10.4171/JEMS/1428}},
  volume       = {{27}},
  year         = {{2024}},
}

@article{32097,
  author       = {{Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin}},
  journal      = {{Journal of Differential Geometry}},
  pages        = {{959--1026}},
  title        = {{{SRB Measures of Anosov Actions}}},
  doi          = {{ DOI: 10.4310/jdg/1729092452}},
  volume       = {{128}},
  year         = {{2024}},
}

@article{58103,
  author       = {{Bux, K.-U. and Hilgert, Joachim and Weich, Tobias}},
  issn         = {{0019-3577}},
  journal      = {{Indagationes Mathematicae}},
  number       = {{1}},
  pages        = {{188--217}},
  publisher    = {{Elsevier BV}},
  title        = {{{Spectral correspondences for finite graphs without dead ends}}},
  doi          = {{10.1016/j.indag.2024.05.001}},
  volume       = {{36}},
  year         = {{2024}},
}

@article{52876,
  author       = {{Arends, Christian and Wolf, Lasse Lennart and Meinecke, Jasmin and Barkhofen, Sonja and Weich, Tobias and Bartley, Tim}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  keywords     = {{General Physics and Astronomy}},
  number       = {{1}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Decomposing large unitaries into multimode devices of arbitrary size}}},
  doi          = {{10.1103/physrevresearch.6.l012043}},
  volume       = {{6}},
  year         = {{2024}},
}

@article{31189,
  abstract     = {{Given a geometrically finite hyperbolic surface of infinite volume it is a
classical result of Patterson that the positive Laplace-Beltrami operator has
no $L^2$-eigenvalues $\geq 1/4$. In this article we prove a generalization of
this result for the joint $L^2$-eigenvalues of the algebra of commuting
differential operators on Riemannian locally symmetric spaces $\Gamma\backslash
G/K$ of higher rank. We derive dynamical assumptions on the $\Gamma$-action on
the geodesic and the Satake compactifications which imply the absence of the
corresponding principal eigenvalues. A large class of examples fulfilling these
assumptions are the non-compact quotients by Anosov subgroups.}},
  author       = {{Weich, Tobias and Wolf, Lasse Lennart}},
  journal      = {{Communications in Mathematical Physics}},
  title        = {{{Absence of principal eigenvalues for higher rank locally symmetric  spaces}}},
  doi          = {{https://doi.org/10.1007/s00220-023-04819-1}},
  volume       = {{403}},
  year         = {{2023}},
}

@unpublished{51206,
  abstract     = {{We present a numerical algorithm for the computation of invariant Ruelle
distributions on convex co-compact hyperbolic surfaces. This is achieved by
exploiting the connection between invariant Ruelle distributions and residues
of meromorphically continued weighted zeta functions established by the authors
together with Barkhofen (2021). To make this applicable for numerics we express
the weighted zeta as the logarithmic derivative of a suitable parameter
dependent Fredholm determinant similar to Borthwick (2014). As an additional
difficulty our transfer operator has to include a contracting direction which
we account for with techniques developed by Rugh (1992). We achieve a further
improvement in convergence speed for our algorithm in the case of surfaces with
additional symmetries by proving and applying a symmetry reduction of weighted
zeta functions.}},
  author       = {{Schütte, Philipp and Weich, Tobias}},
  booktitle    = {{arXiv:2308.13463}},
  title        = {{{Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions}}},
  year         = {{2023}},
}

@article{53410,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing, the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146, 2016) can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.</jats:p>}},
  author       = {{Delarue, Benjamin and Schütte, Philipp and Weich, Tobias}},
  issn         = {{1424-0637}},
  journal      = {{Annales Henri Poincaré}},
  keywords     = {{Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics}},
  number       = {{2}},
  pages        = {{1607--1656}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models}}},
  doi          = {{10.1007/s00023-023-01379-x}},
  volume       = {{25}},
  year         = {{2023}},
}

@article{31190,
  abstract     = {{For a compact Riemannian locally symmetric space $\Gamma\backslash G/K$ of
arbitrary rank we determine the location of certain Ruelle-Taylor resonances
for the Weyl chamber action. We provide a Weyl-lower bound on an appropriate
counting function for the Ruelle-Taylor resonances and establish a spectral gap
which is uniform in $\Gamma$ if $G/K$ is irreducible of higher rank. This is
achieved by proving a quantum-classical correspondence, i.e. a
1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant
states and joint eigenfunctions of the algebra of invariant differential
operators on $G/K$.}},
  author       = {{Hilgert, Joachim and Weich, Tobias and Wolf, Lasse Lennart}},
  journal      = {{Analysis & PDE}},
  number       = {{10}},
  pages        = {{2241–2265}},
  publisher    = {{MSP}},
  title        = {{{Higher rank quantum-classical correspondence}}},
  doi          = {{https://doi.org/10.2140/apde.2023.16.2241}},
  volume       = {{16}},
  year         = {{2023}},
}

@article{31059,
  abstract     = {{In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving equality between residues of weighted zetas and invariant Ruelle distributions. We combine this equality with results of Guillarmou, Hilgert and Weich (2021) in order to relate the residues to Patterson-Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems.}},
  author       = {{Schütte, Philipp and Weich, Tobias and Barkhofen, Sonja}},
  journal      = {{Communications in Mathematical Physics}},
  pages        = {{655--678}},
  title        = {{{Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems}}},
  doi          = {{https://doi.org/10.1007/s00220-022-04538-z}},
  volume       = {{398}},
  year         = {{2023}},
}

@article{35306,
  author       = {{Guedes Bonthonneau, Yannick and Weich, Tobias}},
  issn         = {{1435-9855}},
  journal      = {{Journal of the European Mathematical Society}},
  keywords     = {{Applied Mathematics, General Mathematics}},
  number       = {{3}},
  pages        = {{851--923}},
  publisher    = {{European Mathematical Society - EMS - Publishing House GmbH}},
  title        = {{{Ruelle–Pollicott resonances for manifolds with hyperbolic cusps}}},
  doi          = {{10.4171/jems/1103}},
  volume       = {{24}},
  year         = {{2022}},
}

@article{31057,
  abstract     = {{In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. Then we derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich yields a high frequency interpretation of invariant Ruelle distributions as quantum mechanical matrix coefficients in constant negative curvature. We finish by presenting numerical calculations of phase space distributions in the more physical setting of 3-disk scattering systems.}},
  author       = {{Barkhofen, Sonja and Schütte, Philipp and Weich, Tobias}},
  journal      = {{Journal of Physics A: Mathematical and Theoretical}},
  number       = {{24}},
  publisher    = {{IOP Publishing Ltd}},
  title        = {{{Semiclassical formulae For Wigner distributions}}},
  doi          = {{10.1088/1751-8121/ac6d2b}},
  volume       = {{55}},
  year         = {{2022}},
}

@article{35322,
  author       = {{Bux, Kai-Uwe and Hilgert, Joachim and Weich, Tobias}},
  issn         = {{1664-039X}},
  journal      = {{Journal of Spectral Theory}},
  keywords     = {{Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics}},
  number       = {{2}},
  pages        = {{659--681}},
  publisher    = {{European Mathematical Society - EMS - Publishing House GmbH}},
  title        = {{{Poisson transforms for trees of bounded degree}}},
  doi          = {{10.4171/jst/414}},
  volume       = {{12}},
  year         = {{2022}},
}

@article{51385,
  author       = {{Hilgert, Joachim and Weich, Tobias and Bux, K.-U.}},
  journal      = {{J. of Spectral Theory}},
  pages        = {{659--681}},
  title        = {{{Poisson transforms for trees of bounded degree}}},
  volume       = {{12}},
  year         = {{2022}},
}

@unpublished{31058,
  abstract     = {{We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.}},
  author       = {{Schütte, Philipp and Weich, Tobias and Delarue, Benjamin}},
  title        = {{{Resonances and weighted zeta functions for obstacle scattering via smooth models}}},
  year         = {{2021}},
}

@article{31263,
  author       = {{Guillarmou, Colin and Hilgert, Joachim and Weich, Tobias}},
  issn         = {{2644-9463}},
  journal      = {{Annales Henri Lebesgue}},
  pages        = {{81--119}},
  publisher    = {{Cellule MathDoc/CEDRAM}},
  title        = {{{High frequency limits for invariant Ruelle densities}}},
  doi          = {{10.5802/ahl.67}},
  volume       = {{4}},
  year         = {{2021}},
}