@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{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}},
}

@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}},
}

@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}},
}

@article{36271,
  author       = {{Brennecken, Dominik and Hilgert, Joachim and Ciardo, Lorenzo}},
  journal      = {{Journal of Lie Theory}},
  number       = {{2}},
  pages        = {{459----468}},
  publisher    = {{Heldermann Verlag}},
  title        = {{{Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R)}}},
  doi          = {{10.48550/arXiv.2008.07479}},
  volume       = {{31}},
  year         = {{2021}},
}

@misc{51556,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{171–173}},
  title        = {{{Philip Ording: 99 Variations on a Proof. Princeton University Press 2019}}},
  doi          = {{10.1007/s00591-021-00295-7}},
  volume       = {{68}},
  year         = {{2021}},
}

@misc{51555,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{175–177}},
  title        = {{{Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020}}},
  doi          = {{10.1007/s00591-021-00296-6}},
  volume       = {{68}},
  year         = {{2021}},
}

@article{35702,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Mathematics Learning Support Centres are becoming more and more common in higher education both internationally and in Germany. Whereas it is clear that their quality largely depends on a functioning interaction in consultations, little is known about how such consultations proceed in detail. On the basis of models from the literature and recorded support sessions (N = 36), we constructed a process model that divides consultations into four ideal–typical phases. In the individual consultations, forward or backward leaps occur, but overall the model seems to describe the data well. A high intercoder reliability shows that it can be applied consistently on real data by different researchers. An analysis of the consultations between students and tutors shows that both mainly work on past attempts or thoughts of the students to solve the exercise or problems and on concrete strategies to solve a problem within the session. In contrast, very little time is dedicated to summarizing and reflecting the solution. The data allows for a more in-depth discussion of what constitutes quality in advising processes and how it might be further explored. Practically, the model may structure support sessions and help in focussing on different goals in different phases.</jats:p>}},
  author       = {{Schürmann, Mirko and Panse, Anja and Shaikh, Zain and Biehler, Rolf and Schaper, Niclas and Liebendörfer, Michael and Hilgert, Joachim}},
  issn         = {{2198-9745}},
  journal      = {{International Journal of Research in Undergraduate Mathematics Education}},
  keywords     = {{Education, Mathematics (miscellaneous)}},
  number       = {{1}},
  pages        = {{94--120}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Consultation Phases in Mathematics Learning and Support Centres}}},
  doi          = {{10.1007/s40753-021-00154-9}},
  volume       = {{8}},
  year         = {{2021}},
}

@book{51493,
  author       = {{Hilgert, Joachim and Hilgert, Ingrid}},
  publisher    = {{Springer Spektrum}},
  title        = {{{Mathematik - Ein Reiseführer 2. Auflage}}},
  year         = {{2021}},
}

@article{51386,
  author       = {{Hilgert, Joachim and Barnum, H.}},
  journal      = {{J. of Lie Theory}},
  pages        = {{315--344}},
  title        = {{{Spectral Properties of Convex Bodies}}},
  volume       = {{30}},
  year         = {{2020}},
}

@misc{51559,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{301–305}},
  title        = {{{Titu Andreescu und Vlad Crisan: Mathematical Induction – A powerful and elegant method of proof. XYZ Press 2017 und Florian André Dalwigk: Vollständige Induktion – Beispiele und Aufgaben bis zum Umfallen. Springer Spektrum 2019}}},
  doi          = {{10.1007/s00591-020-00282-4}},
  volume       = {{67}},
  year         = {{2020}},
}

@misc{51557,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{307–309}},
  title        = {{{Fabio Toscano: The Secret Formula – How a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation. Princeton University Press 2020}}},
  doi          = {{10.1007/s00591-020-00283-3}},
  volume       = {{67}},
  year         = {{2020}},
}

@misc{51561,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{123–124}},
  title        = {{{Robert Bosch: OPT ART – From Mathematical Optimization to Visual Design. Princeton University Press 2019}}},
  doi          = {{10.1007/s00591-020-00272-6}},
  volume       = {{67}},
  year         = {{2020}},
}

@misc{51560,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{297–299}},
  title        = {{{David M. Bressoud: Calculus Reordered -- A History of the Big Ideas. Princeton University Press 2019}}},
  doi          = {{10.1007/s00591-020-00280-6}},
  volume       = {{67}},
  year         = {{2020}},
}