@unpublished{65255,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{58402,
  author       = {{Baier, Thomas and Ferreira, Ana Cristina and Hilgert, Joachim and Mourão, José M. and Nunes, João P.}},
  issn         = {{1664-2368}},
  journal      = {{Analysis and Mathematical Physics}},
  number       = {{1}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Fibering polarizations and Mabuchi rays on symmetric spaces of compact type}}},
  doi          = {{10.1007/s13324-025-01012-6}},
  volume       = {{15}},
  year         = {{2025}},
}

@article{59344,
  abstract     = {{<jats:title>Abstract</jats:title>
          <jats:p>For a finite graph, we establish natural isomorphisms between eigenspaces of a Laplace operator acting on functions on the edges and eigenspaces of a transfer operator acting on functions on one-sided infinite non-backtracking paths. Interpreting the transfer operator as a classical dynamical system and the Laplace operator as its quantization, this result can be viewed as a <jats:italic>quantum-classical correspondence</jats:italic>. In contrast to previously established quantum-classical correspondences for the vertex Laplacian which exclude certain exceptional spectral parameters, our correspondence is valid for all parameters. This allows us to relate certain spectral quantities to topological properties of the graph such as the cyclomatic number and the 2-colorability. The quantum-classical correspondence for the edge Laplacian is induced by an edge Poisson transform on the universal covering of the graph which is a tree of bounded degree. In the special case of regular trees, we relate both the vertex and the edge Poisson transform to the representation theory of the automorphism group of the tree and study associated operator valued Hecke algebras.</jats:p>}},
  author       = {{Arends, Christian and Frahm, Jan and Hilgert, Joachim}},
  issn         = {{0926-2601}},
  journal      = {{Potential Analysis}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Edge Laplacians and Edge Poisson Transforms for Graphs}}},
  doi          = {{10.1007/s11118-024-10184-y}},
  year         = {{2025}},
}

@article{59343,
  abstract     = {{<jats:title>Abstract</jats:title>
          <jats:p>On a finite regular graph, (co)resonant states are eigendistributions of the transfer operator associated to the shift on one-sided infinite non-backtracking paths. We introduce two pairings of resonant and coresonant states, the <jats:italic>vertex pairing</jats:italic> which involves only the dependence on the initial/terminal vertex of the path, and the <jats:italic>geodesic pairing</jats:italic> which is given by integrating over all geodesics the evaluation of the coresonant state on the first half of the geodesic times the resonant state on the second half. The main result is that these two pairings coincide up to a constant which depends on the resonance, i.e. the corresponding eigenvalue of the transfer operator.</jats:p>}},
  author       = {{Arends, Christian and Frahm, Jan and Hilgert, Joachim}},
  issn         = {{0025-5831}},
  journal      = {{Mathematische Annalen}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A pairing formula for resonant states on finite regular graphs}}},
  doi          = {{10.1007/s00208-025-03140-7}},
  year         = {{2025}},
}

@misc{64736,
  booktitle    = {{J. Lie Theory}},
  editor       = {{Frahm, Jan and Glöckner, Helge and Hilgert, Joachim and Olafsson, Gestur}},
  number       = {{4}},
  title        = {{{Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday}}},
  volume       = {{35}},
  year         = {{2025}},
}

@inbook{58587,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Symmetry in Geometry and Analysis, Volume 2}},
  title        = {{{Quantum-Classical Correspondences for Locally Symmetric Spaces}}},
  doi          = {{https://doi.org/10.1007/978-981-97-7662-7}},
  year         = {{2025}},
}

@article{53413,
  abstract     = {{For negatively curved symmetric spaces it is known that the poles of the
scattering matrices defined via the standard intertwining operators for the
spherical principal representations of the isometry group are either given as
poles of the intertwining operators or as quantum resonances, i.e. poles of the
meromorphically continued resolvents of the Laplace-Beltrami operator. We
extend this result to classical locally symmetric spaces of negative curvature
with convex-cocompact fundamental group using results of Bunke and Olbrich. The
method of proof forces us to exclude the spectral parameters corresponding to
singular Poisson transforms.}},
  author       = {{Delarue, Benjamin and Hilgert, Joachim}},
  issn         = {{0949-5932}},
  journal      = {{Journal of Lie Theory}},
  number       = {{(4)}},
  pages        = {{787----804}},
  title        = {{{Quantum resonances and scattering poles of classical rank one locally  symmetric spaces}}},
  volume       = {{35}},
  year         = {{2025}},
}

@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}},
}

@book{60078,
  author       = {{Hilgert, Joachim}},
  isbn         = {{9783662694114}},
  issn         = {{2731-3824}},
  publisher    = {{Springer Berlin Heidelberg}},
  title        = {{{Mathematical Structures}}},
  doi          = {{10.1007/978-3-662-69412-1}},
  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{57498,
  author       = {{Baier, Thomas and Hilgert, Joachim and Kaya, Oguzhan and Mourão, José M. and Nunes, João P.}},
  issn         = {{0393-0440}},
  journal      = {{Journal of Geometry and Physics}},
  publisher    = {{Elsevier BV}},
  title        = {{{Quantization in fibering polarizations, Mabuchi rays and geometric Peter–Weyl theorem}}},
  doi          = {{10.1016/j.geomphys.2024.105355}},
  volume       = {{207}},
  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}},
}

@book{57590,
  author       = {{Hilgert, Joachim}},
  isbn         = {{9783662688922}},
  publisher    = {{Springer Berlin Heidelberg}},
  title        = {{{Mathematische Strukturen 2. Auflage}}},
  doi          = {{10.1007/978-3-662-68893-9}},
  year         = {{2024}},
}

@article{31210,
  abstract     = {{In this paper we complete the program of relating the Laplace spectrum for
rank one compact locally symmetric spaces with the first band Ruelle-Pollicott
resonances of the geodesic flow on its sphere bundle. This program was started
by Flaminio and Forni for hyperbolic surfaces, continued by Dyatlov, Faure and
Guillarmou for real hyperbolic spaces and by Guillarmou, Hilgert and Weich for
general rank one spaces. Except for the case of hyperbolic surfaces a countable
set of exceptional spectral parameters always left untreated since the
corresponding Poisson transforms are neither injective nor surjective. We use
vector valued Poisson transforms to treat also the exceptional spectral
parameters. For surfaces the exceptional spectral parameters lead to discrete
series representations of $\mathrm{SL}(2,\mathbb R)$. In higher dimensions the
situation is more complicated, but can be described completely.}},
  author       = {{Arends, Christian and Hilgert, Joachim}},
  issn         = {{2270-518X}},
  journal      = {{Journal de l’École polytechnique — Mathématiques}},
  keywords     = {{Ruelle resonances, Poisson transforms, locally symmetric spaces, principal series representations}},
  pages        = {{335--403}},
  title        = {{{Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters}}},
  doi          = {{10.5802/jep.220}},
  volume       = {{10}},
  year         = {{2023}},
}

@article{34793,
  author       = {{Glöckner, Helge and Hilgert, Joachim}},
  issn         = {{0022-0396}},
  journal      = {{Journal of Differential Equations}},
  keywords     = {{22E65, 28B05, 34A12, 34H05, 46E30, 46E40}},
  pages        = {{186–232}},
  title        = {{{Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}}},
  doi          = {{10.1016/j.jde.2022.10.001}},
  volume       = {{343}},
  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{51383,
  author       = {{Hilgert, Joachim and Arends, C.}},
  journal      = {{J. de l'École polytechnique — Mathématiques}},
  pages        = {{335--403}},
  title        = {{{Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters}}},
  volume       = {{10}},
  year         = {{2023}},
}

@article{51384,
  author       = {{Hilgert, Joachim and Glöckner, H.}},
  journal      = {{J. Diff. Equations}},
  pages        = {{186--232}},
  title        = {{{Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}}},
  volume       = {{343}},
  year         = {{2023}},
}

@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}},
}

@misc{51554,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{151–153}},
  title        = {{{Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021}}},
  doi          = {{10.1007/s00591-021-00314-7}},
  volume       = {{69}},
  year         = {{2022}},
}