[{"publisher":"Oxford University Press (OUP)","date_created":"2022-05-17T12:00:36Z","title":"Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces","issue":"11","year":"2021","external_id":{"arxiv":["1710.04625"]},"keyword":["General Mathematics"],"language":[{"iso":"eng"}],"publication":"International Mathematics Research Notices","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>For a compact Riemannian locally symmetric space $\\mathcal M$ of rank 1 and an associated vector bundle $\\mathbf V_{\\tau }$ over the unit cosphere bundle $S^{\\ast }\\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\\mathbf V_{\\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\\ast }\\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\\sigma )$ on compatible associated vector bundles $\\mathbf W_{\\sigma }$ over $\\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\\tau$ and $\\sigma$ defining the bundles $\\mathbf V_{\\tau }$ and $\\mathbf W_{\\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\\mathbf W_{\\sigma }$. Our methods of proof are based on representation theory and Lie theory.</jats:p>","lang":"eng"}],"date_updated":"2022-05-25T06:42:01Z","author":[{"last_name":"Küster","full_name":"Küster, Benjamin","first_name":"Benjamin"},{"first_name":"Tobias","last_name":"Weich","full_name":"Weich, Tobias"}],"volume":2021,"doi":"10.1093/imrn/rnz068","publication_status":"published","publication_identifier":{"issn":["1073-7928","1687-0247"]},"citation":{"ieee":"B. Küster and T. Weich, “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces,” <i>International Mathematics Research Notices</i>, vol. 2021, no. 11, pp. 8225–8296, 2021, doi: <a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>.","chicago":"Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces.” <i>International Mathematics Research Notices</i> 2021, no. 11 (2021): 8225–96. <a href=\"https://doi.org/10.1093/imrn/rnz068\">https://doi.org/10.1093/imrn/rnz068</a>.","ama":"Küster B, Weich T. Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces. <i>International Mathematics Research Notices</i>. 2021;2021(11):8225-8296. doi:<a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>","apa":"Küster, B., &#38; Weich, T. (2021). Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces. <i>International Mathematics Research Notices</i>, <i>2021</i>(11), 8225–8296. <a href=\"https://doi.org/10.1093/imrn/rnz068\">https://doi.org/10.1093/imrn/rnz068</a>","bibtex":"@article{Küster_Weich_2021, title={Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces}, volume={2021}, DOI={<a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>}, number={11}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Küster, Benjamin and Weich, Tobias}, year={2021}, pages={8225–8296} }","short":"B. Küster, T. Weich, International Mathematics Research Notices 2021 (2021) 8225–8296.","mla":"Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces.” <i>International Mathematics Research Notices</i>, vol. 2021, no. 11, Oxford University Press (OUP), 2021, pp. 8225–96, doi:<a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>."},"intvolume":"      2021","page":"8225-8296","_id":"31261","user_id":"49178","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"type":"journal_article","status":"public"},{"keyword":["Geometry and Topology","Analysis"],"language":[{"iso":"eng"}],"publication":"Differential Geometry and its Applications","publisher":"Elsevier BV","date_created":"2022-12-22T09:20:30Z","title":"Symmetries of analytic curves","year":"2021","_id":"34818","user_id":"30905","department":[{"_id":"93"}],"article_type":"original","article_number":"101687","extern":"1","type":"journal_article","status":"public","date_updated":"2023-01-09T18:07:26Z","author":[{"first_name":"Maximilian","full_name":"Hanusch, Maximilian","id":"30905","last_name":"Hanusch"}],"volume":74,"doi":"10.1016/j.difgeo.2020.101687","publication_status":"published","publication_identifier":{"issn":["0926-2245"]},"citation":{"ama":"Hanusch M. Symmetries of analytic curves. <i>Differential Geometry and its Applications</i>. 2021;74. doi:<a href=\"https://doi.org/10.1016/j.difgeo.2020.101687\">10.1016/j.difgeo.2020.101687</a>","ieee":"M. Hanusch, “Symmetries of analytic curves,” <i>Differential Geometry and its Applications</i>, vol. 74, Art. no. 101687, 2021, doi: <a href=\"https://doi.org/10.1016/j.difgeo.2020.101687\">10.1016/j.difgeo.2020.101687</a>.","chicago":"Hanusch, Maximilian. “Symmetries of Analytic Curves.” <i>Differential Geometry and Its Applications</i> 74 (2021). <a href=\"https://doi.org/10.1016/j.difgeo.2020.101687\">https://doi.org/10.1016/j.difgeo.2020.101687</a>.","apa":"Hanusch, M. (2021). Symmetries of analytic curves. <i>Differential Geometry and Its Applications</i>, <i>74</i>, Article 101687. <a href=\"https://doi.org/10.1016/j.difgeo.2020.101687\">https://doi.org/10.1016/j.difgeo.2020.101687</a>","mla":"Hanusch, Maximilian. “Symmetries of Analytic Curves.” <i>Differential Geometry and Its Applications</i>, vol. 74, 101687, Elsevier BV, 2021, doi:<a href=\"https://doi.org/10.1016/j.difgeo.2020.101687\">10.1016/j.difgeo.2020.101687</a>.","short":"M. Hanusch, Differential Geometry and Its Applications 74 (2021).","bibtex":"@article{Hanusch_2021, title={Symmetries of analytic curves}, volume={74}, DOI={<a href=\"https://doi.org/10.1016/j.difgeo.2020.101687\">10.1016/j.difgeo.2020.101687</a>}, number={101687}, journal={Differential Geometry and its Applications}, publisher={Elsevier BV}, author={Hanusch, Maximilian}, year={2021} }"},"intvolume":"        74"},{"publication_identifier":{"issn":["2644-9463"]},"publication_status":"published","intvolume":"         4","page":"81-119","citation":{"ieee":"C. Guillarmou, J. Hilgert, and T. Weich, “High frequency limits for invariant Ruelle densities,” <i>Annales Henri Lebesgue</i>, vol. 4, pp. 81–119, 2021, doi: <a href=\"https://doi.org/10.5802/ahl.67\">10.5802/ahl.67</a>.","chicago":"Guillarmou, Colin, Joachim Hilgert, and Tobias Weich. “High Frequency Limits for Invariant Ruelle Densities.” <i>Annales Henri Lebesgue</i> 4 (2021): 81–119. <a href=\"https://doi.org/10.5802/ahl.67\">https://doi.org/10.5802/ahl.67</a>.","ama":"Guillarmou C, Hilgert J, Weich T. High frequency limits for invariant Ruelle densities. <i>Annales Henri Lebesgue</i>. 2021;4:81-119. doi:<a href=\"https://doi.org/10.5802/ahl.67\">10.5802/ahl.67</a>","mla":"Guillarmou, Colin, et al. “High Frequency Limits for Invariant Ruelle Densities.” <i>Annales Henri Lebesgue</i>, vol. 4, Cellule MathDoc/CEDRAM, 2021, pp. 81–119, doi:<a href=\"https://doi.org/10.5802/ahl.67\">10.5802/ahl.67</a>.","short":"C. Guillarmou, J. Hilgert, T. Weich, Annales Henri Lebesgue 4 (2021) 81–119.","bibtex":"@article{Guillarmou_Hilgert_Weich_2021, title={High frequency limits for invariant Ruelle densities}, volume={4}, DOI={<a href=\"https://doi.org/10.5802/ahl.67\">10.5802/ahl.67</a>}, journal={Annales Henri Lebesgue}, publisher={Cellule MathDoc/CEDRAM}, author={Guillarmou, Colin and Hilgert, Joachim and Weich, Tobias}, year={2021}, pages={81–119} }","apa":"Guillarmou, C., Hilgert, J., &#38; Weich, T. (2021). High frequency limits for invariant Ruelle densities. <i>Annales Henri Lebesgue</i>, <i>4</i>, 81–119. <a href=\"https://doi.org/10.5802/ahl.67\">https://doi.org/10.5802/ahl.67</a>"},"volume":4,"author":[{"first_name":"Colin","last_name":"Guillarmou","full_name":"Guillarmou, Colin"},{"id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim"},{"first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","id":"49178"}],"date_updated":"2024-02-19T06:27:43Z","doi":"10.5802/ahl.67","type":"journal_article","status":"public","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"user_id":"49063","_id":"31263","year":"2021","date_created":"2022-05-17T12:05:17Z","publisher":"Cellule MathDoc/CEDRAM","title":"High frequency limits for invariant Ruelle densities","publication":"Annales Henri Lebesgue","external_id":{"arxiv":["1803.06717"]},"language":[{"iso":"eng"}]},{"publication_status":"published","issue":"2","year":"2021","citation":{"ieee":"D. Brennecken, J. Hilgert, and L. Ciardo, “Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R),” <i>Journal of Lie Theory</i>, vol. 31, no. 2, pp. 459--468, 2021, doi: <a href=\"https://doi.org/10.48550/arXiv.2008.07479\">10.48550/arXiv.2008.07479</a>.","chicago":"Brennecken, Dominik, Joachim Hilgert, and Lorenzo Ciardo. “Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R).” <i>Journal of Lie Theory</i> 31, no. 2 (2021): 459--468. <a href=\"https://doi.org/10.48550/arXiv.2008.07479\">https://doi.org/10.48550/arXiv.2008.07479</a>.","ama":"Brennecken D, Hilgert J, Ciardo L. Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R). <i>Journal of Lie Theory</i>. 2021;31(2):459--468. doi:<a href=\"https://doi.org/10.48550/arXiv.2008.07479\">10.48550/arXiv.2008.07479</a>","apa":"Brennecken, D., Hilgert, J., &#38; Ciardo, L. (2021). Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R). <i>Journal of Lie Theory</i>, <i>31</i>(2), 459--468. <a href=\"https://doi.org/10.48550/arXiv.2008.07479\">https://doi.org/10.48550/arXiv.2008.07479</a>","short":"D. Brennecken, J. Hilgert, L. Ciardo, Journal of Lie Theory 31 (2021) 459--468.","bibtex":"@article{Brennecken_Hilgert_Ciardo_2021, title={Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R)}, volume={31}, DOI={<a href=\"https://doi.org/10.48550/arXiv.2008.07479\">10.48550/arXiv.2008.07479</a>}, number={2}, journal={Journal of Lie Theory}, publisher={Heldermann Verlag}, author={Brennecken, Dominik and Hilgert, Joachim and Ciardo, Lorenzo}, year={2021}, pages={459--468} }","mla":"Brennecken, Dominik, et al. “Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R).” <i>Journal of Lie Theory</i>, vol. 31, no. 2, Heldermann Verlag, 2021, pp. 459--468, doi:<a href=\"https://doi.org/10.48550/arXiv.2008.07479\">10.48550/arXiv.2008.07479</a>."},"page":"459--468","intvolume":"        31","publisher":"Heldermann Verlag","date_updated":"2024-02-19T06:27:09Z","date_created":"2023-01-12T08:23:28Z","author":[{"first_name":"Dominik","id":"55911","full_name":"Brennecken, Dominik","last_name":"Brennecken"},{"first_name":"Joachim","id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert"},{"full_name":"Ciardo, Lorenzo","last_name":"Ciardo","first_name":"Lorenzo"}],"volume":31,"title":"Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R)","doi":"10.48550/arXiv.2008.07479","type":"journal_article","publication":"Journal of Lie Theory","status":"public","_id":"36271","user_id":"49063","department":[{"_id":"555"},{"_id":"91"}],"language":[{"iso":"eng"}]},{"department":[{"_id":"91"}],"user_id":"49063","_id":"51556","language":[{"iso":"eng"}],"publication":"Mathematische Semesterberichte","type":"review","status":"public","volume":68,"date_created":"2024-02-20T09:52:08Z","author":[{"id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim"}],"date_updated":"2024-02-20T10:03:43Z","doi":"10.1007/s00591-021-00295-7","title":"Philip Ording: 99 Variations on a Proof. Princeton University Press 2019","publication_status":"published","intvolume":"        68","page":"171–173","citation":{"ama":"Hilgert J. Philip Ording: 99 Variations on a Proof. Princeton University Press 2019. <i>Mathematische Semesterberichte</i>. 2021;68:171–173. doi:<a href=\"https://doi.org/10.1007/s00591-021-00295-7\">10.1007/s00591-021-00295-7</a>","ieee":"J. Hilgert, “Philip Ording: 99 Variations on a Proof. Princeton University Press 2019,” <i>Mathematische Semesterberichte</i>, vol. 68. pp. 171–173, 2021, doi: <a href=\"https://doi.org/10.1007/s00591-021-00295-7\">10.1007/s00591-021-00295-7</a>.","chicago":"Hilgert, Joachim. “Philip Ording: 99 Variations on a Proof. Princeton University Press 2019.” <i>Mathematische Semesterberichte</i>, 2021. <a href=\"https://doi.org/10.1007/s00591-021-00295-7\">https://doi.org/10.1007/s00591-021-00295-7</a>.","apa":"Hilgert, J. (2021). Philip Ording: 99 Variations on a Proof. Princeton University Press 2019. In <i>Mathematische Semesterberichte</i> (Vol. 68, pp. 171–173). <a href=\"https://doi.org/10.1007/s00591-021-00295-7\">https://doi.org/10.1007/s00591-021-00295-7</a>","mla":"Hilgert, Joachim. “Philip Ording: 99 Variations on a Proof. Princeton University Press 2019.” <i>Mathematische Semesterberichte</i>, vol. 68, 2021, pp. 171–173, doi:<a href=\"https://doi.org/10.1007/s00591-021-00295-7\">10.1007/s00591-021-00295-7</a>.","bibtex":"@article{Hilgert_2021, title={Philip Ording: 99 Variations on a Proof. Princeton University Press 2019}, volume={68}, DOI={<a href=\"https://doi.org/10.1007/s00591-021-00295-7\">10.1007/s00591-021-00295-7</a>}, journal={Mathematische Semesterberichte}, author={Hilgert, Joachim}, year={2021}, pages={171–173} }","short":"J. Hilgert, Mathematische Semesterberichte 68 (2021) 171–173."},"year":"2021"},{"doi":"10.1007/s00591-021-00296-6","title":"Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020","author":[{"last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220","first_name":"Joachim"}],"date_created":"2024-02-20T09:50:31Z","volume":68,"date_updated":"2024-02-20T10:14:56Z","citation":{"chicago":"Hilgert, Joachim. “Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020.” <i>Mathematische Semesterberichte</i>, 2021. <a href=\"https://doi.org/10.1007/s00591-021-00296-6\">https://doi.org/10.1007/s00591-021-00296-6</a>.","ieee":"J. Hilgert, “Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020,” <i>Mathematische Semesterberichte</i>, vol. 68. pp. 175–177, 2021, doi: <a href=\"https://doi.org/10.1007/s00591-021-00296-6\">10.1007/s00591-021-00296-6</a>.","ama":"Hilgert J. Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020. <i>Mathematische Semesterberichte</i>. 2021;68:175–177. doi:<a href=\"https://doi.org/10.1007/s00591-021-00296-6\">10.1007/s00591-021-00296-6</a>","bibtex":"@article{Hilgert_2021, title={Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020}, volume={68}, DOI={<a href=\"https://doi.org/10.1007/s00591-021-00296-6\">10.1007/s00591-021-00296-6</a>}, journal={Mathematische Semesterberichte}, author={Hilgert, Joachim}, year={2021}, pages={175–177} }","short":"J. Hilgert, Mathematische Semesterberichte 68 (2021) 175–177.","mla":"Hilgert, Joachim. “Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020.” <i>Mathematische Semesterberichte</i>, vol. 68, 2021, pp. 175–177, doi:<a href=\"https://doi.org/10.1007/s00591-021-00296-6\">10.1007/s00591-021-00296-6</a>.","apa":"Hilgert, J. (2021). Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020. In <i>Mathematische Semesterberichte</i> (Vol. 68, pp. 175–177). <a href=\"https://doi.org/10.1007/s00591-021-00296-6\">https://doi.org/10.1007/s00591-021-00296-6</a>"},"page":"175–177","intvolume":"        68","year":"2021","publication_status":"published","language":[{"iso":"ger"}],"user_id":"49063","department":[{"_id":"91"}],"_id":"51555","status":"public","type":"review","publication":"Mathematische Semesterberichte"},{"_id":"32006","department":[{"_id":"548"}],"user_id":"70575","type":"journal_article","status":"public","date_updated":"2024-04-11T12:39:23Z","volume":22,"author":[{"last_name":"Guillarmou","full_name":"Guillarmou, Colin","first_name":"Colin"},{"full_name":"Küster, Benjamin","last_name":"Küster","first_name":"Benjamin"}],"doi":"10.1007/s00023-021-01068-7","publication_identifier":{"issn":["1424-0637","1424-0661"]},"publication_status":"published","page":"3565-3617","intvolume":"        22","citation":{"bibtex":"@article{Guillarmou_Küster_2021, title={Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds}, volume={22}, DOI={<a href=\"https://doi.org/10.1007/s00023-021-01068-7\">10.1007/s00023-021-01068-7</a>}, number={11}, journal={Annales Henri Poincaré}, publisher={Springer Science and Business Media LLC}, author={Guillarmou, Colin and Küster, Benjamin}, year={2021}, pages={3565–3617} }","short":"C. Guillarmou, B. Küster, Annales Henri Poincaré 22 (2021) 3565–3617.","mla":"Guillarmou, Colin, and Benjamin Küster. “Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds.” <i>Annales Henri Poincaré</i>, vol. 22, no. 11, Springer Science and Business Media LLC, 2021, pp. 3565–617, doi:<a href=\"https://doi.org/10.1007/s00023-021-01068-7\">10.1007/s00023-021-01068-7</a>.","apa":"Guillarmou, C., &#38; Küster, B. (2021). Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds. <i>Annales Henri Poincaré</i>, <i>22</i>(11), 3565–3617. <a href=\"https://doi.org/10.1007/s00023-021-01068-7\">https://doi.org/10.1007/s00023-021-01068-7</a>","chicago":"Guillarmou, Colin, and Benjamin Küster. “Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds.” <i>Annales Henri Poincaré</i> 22, no. 11 (2021): 3565–3617. <a href=\"https://doi.org/10.1007/s00023-021-01068-7\">https://doi.org/10.1007/s00023-021-01068-7</a>.","ieee":"C. Guillarmou and B. Küster, “Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds,” <i>Annales Henri Poincaré</i>, vol. 22, no. 11, pp. 3565–3617, 2021, doi: <a href=\"https://doi.org/10.1007/s00023-021-01068-7\">10.1007/s00023-021-01068-7</a>.","ama":"Guillarmou C, Küster B. Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds. <i>Annales Henri Poincaré</i>. 2021;22(11):3565-3617. doi:<a href=\"https://doi.org/10.1007/s00023-021-01068-7\">10.1007/s00023-021-01068-7</a>"},"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"publication":"Annales Henri Poincaré","publisher":"Springer Science and Business Media LLC","date_created":"2022-06-20T08:37:52Z","title":"Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds","issue":"11","year":"2021"},{"_id":"35702","user_id":"37888","department":[{"_id":"363"},{"_id":"423"},{"_id":"91"},{"_id":"625"}],"keyword":["Education","Mathematics (miscellaneous)"],"language":[{"iso":"eng"}],"type":"journal_article","publication":"International Journal of Research in Undergraduate Mathematics Education","abstract":[{"text":"<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>","lang":"eng"}],"status":"public","publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-18T10:09:08Z","date_created":"2023-01-10T09:09:23Z","author":[{"full_name":"Schürmann, Mirko","id":"59707","orcid":"0000-0003-2646-085X","last_name":"Schürmann","first_name":"Mirko"},{"last_name":"Panse","full_name":"Panse, Anja","first_name":"Anja"},{"first_name":"Zain","full_name":"Shaikh, Zain","last_name":"Shaikh"},{"first_name":"Rolf","full_name":"Biehler, Rolf","id":"16274","last_name":"Biehler"},{"first_name":"Niclas","full_name":"Schaper, Niclas","last_name":"Schaper"},{"first_name":"Michael","last_name":"Liebendörfer","orcid":"0000-0001-9887-2074","full_name":"Liebendörfer, Michael","id":"30933"},{"first_name":"Joachim","id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert"}],"volume":8,"title":"Consultation Phases in Mathematics Learning and Support Centres","doi":"10.1007/s40753-021-00154-9","publication_status":"published","publication_identifier":{"issn":["2198-9745","2198-9753"]},"issue":"1","year":"2021","citation":{"short":"M. Schürmann, A. Panse, Z. Shaikh, R. Biehler, N. Schaper, M. Liebendörfer, J. Hilgert, International Journal of Research in Undergraduate Mathematics Education 8 (2021) 94–120.","bibtex":"@article{Schürmann_Panse_Shaikh_Biehler_Schaper_Liebendörfer_Hilgert_2021, title={Consultation Phases in Mathematics Learning and Support Centres}, volume={8}, DOI={<a href=\"https://doi.org/10.1007/s40753-021-00154-9\">10.1007/s40753-021-00154-9</a>}, number={1}, journal={International Journal of Research in Undergraduate Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Schürmann, Mirko and Panse, Anja and Shaikh, Zain and Biehler, Rolf and Schaper, Niclas and Liebendörfer, Michael and Hilgert, Joachim}, year={2021}, pages={94–120} }","mla":"Schürmann, Mirko, et al. “Consultation Phases in Mathematics Learning and Support Centres.” <i>International Journal of Research in Undergraduate Mathematics Education</i>, vol. 8, no. 1, Springer Science and Business Media LLC, 2021, pp. 94–120, doi:<a href=\"https://doi.org/10.1007/s40753-021-00154-9\">10.1007/s40753-021-00154-9</a>.","apa":"Schürmann, M., Panse, A., Shaikh, Z., Biehler, R., Schaper, N., Liebendörfer, M., &#38; Hilgert, J. 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Xiang, Advances in Nonlinear Analysis 10 (2021) 707–731.","mla":"Wang, Yulan, et al. “Global Solvability in a Threee-Dimensional Keller-Segel.Stokes System Involving Arbitrary Superlinear Logistic Degradation.” <i>Advances in Nonlinear Analysis</i>, vol. 10, 2021, pp. 707–31.","bibtex":"@article{Wang_Winkler_Xiang_2021, title={Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation}, volume={10}, journal={Advances in Nonlinear Analysis}, author={Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}, year={2021}, pages={707–731} }"},"intvolume":"        10","page":"707-731","year":"2021"},{"status":"public","publication":"Zeitschrift für angewandte Mathematik und Physik","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","General Physics and Astronomy","General Mathematics"],"article_number":"96","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"user_id":"23686","_id":"34673","intvolume":"        72","citation":{"ieee":"T. Black, M. Fuest, and J. Lankeit, “Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems,” <i>Zeitschrift für angewandte Mathematik und Physik</i>, vol. 72, no. 3, Art. no. 96, 2021, doi: <a href=\"https://doi.org/10.1007/s00033-021-01524-8\">10.1007/s00033-021-01524-8</a>.","chicago":"Black, Tobias, Mario Fuest, and Johannes Lankeit. “Relaxed Parameter Conditions for Chemotactic Collapse in Logistic-Type Parabolic–Elliptic Keller–Segel Systems.” <i>Zeitschrift Für Angewandte Mathematik Und Physik</i> 72, no. 3 (2021). <a href=\"https://doi.org/10.1007/s00033-021-01524-8\">https://doi.org/10.1007/s00033-021-01524-8</a>.","ama":"Black T, Fuest M, Lankeit J. Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems. <i>Zeitschrift für angewandte Mathematik und Physik</i>. 2021;72(3). doi:<a href=\"https://doi.org/10.1007/s00033-021-01524-8\">10.1007/s00033-021-01524-8</a>","mla":"Black, Tobias, et al. “Relaxed Parameter Conditions for Chemotactic Collapse in Logistic-Type Parabolic–Elliptic Keller–Segel Systems.” <i>Zeitschrift Für Angewandte Mathematik Und Physik</i>, vol. 72, no. 3, 96, Springer Science and Business Media LLC, 2021, doi:<a href=\"https://doi.org/10.1007/s00033-021-01524-8\">10.1007/s00033-021-01524-8</a>.","bibtex":"@article{Black_Fuest_Lankeit_2021, title={Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems}, volume={72}, DOI={<a href=\"https://doi.org/10.1007/s00033-021-01524-8\">10.1007/s00033-021-01524-8</a>}, number={396}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer Science and Business Media LLC}, author={Black, Tobias and Fuest, Mario and Lankeit, Johannes}, year={2021} }","short":"T. Black, M. Fuest, J. Lankeit, Zeitschrift Für Angewandte Mathematik Und Physik 72 (2021).","apa":"Black, T., Fuest, M., &#38; Lankeit, J. (2021). Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems. <i>Zeitschrift Für Angewandte Mathematik Und Physik</i>, <i>72</i>(3), Article 96. <a href=\"https://doi.org/10.1007/s00033-021-01524-8\">https://doi.org/10.1007/s00033-021-01524-8</a>"},"year":"2021","issue":"3","publication_identifier":{"issn":["0044-2275","1420-9039"]},"publication_status":"published","doi":"10.1007/s00033-021-01524-8","title":"Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems","volume":72,"date_created":"2022-12-21T09:48:36Z","author":[{"full_name":"Black, Tobias","id":"23686","last_name":"Black","orcid":"0000-0001-9963-0800","first_name":"Tobias"},{"full_name":"Fuest, Mario","last_name":"Fuest","first_name":"Mario"},{"first_name":"Johannes","full_name":"Lankeit, Johannes","last_name":"Lankeit"}],"publisher":"Springer Science and Business Media LLC","date_updated":"2023-07-10T11:39:23Z"}]