[{"external_id":{"arxiv":["2402.02530"]},"_id":"51204","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","language":[{"iso":"eng"}],"publication":"Duke Math. Journal ","type":"journal_article","abstract":[{"lang":"eng","text":"Given a real semisimple connected Lie group $G$ and a discrete torsion-free\r\nsubgroup $\\Gamma < G$ we prove a precise connection between growth rates of the\r\ngroup $\\Gamma$, polyhedral bounds on the joint spectrum of the ring of\r\ninvariant differential operators, and the decay of matrix coefficients. In\r\nparticular, this allows us to completely characterize temperedness of\r\n$L^2(\\Gamma\\backslash G)$ in this general setting."}],"status":"public","date_updated":"2026-02-18T10:37:47Z","volume":"(to appear)","author":[{"last_name":"Lutsko","full_name":"Lutsko, Christopher","first_name":"Christopher"},{"id":"49178","full_name":"Weich, Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias"},{"first_name":"Lasse Lennart","orcid":"0000-0001-8893-2045","last_name":"Wolf","full_name":"Wolf, Lasse Lennart","id":"45027"}],"date_created":"2024-02-06T20:35:36Z","title":"Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces","year":"2026","citation":{"mla":"Lutsko, Christopher, et al. “Polyhedral Bounds on the Joint Spectrum and Temperedness of Locally  Symmetric Spaces.” <i>Duke Math. Journal </i>, vol. (to appear), 2026.","bibtex":"@article{Lutsko_Weich_Wolf_2026, title={Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces}, volume={(to appear)}, journal={Duke Math. Journal }, author={Lutsko, Christopher and Weich, Tobias and Wolf, Lasse Lennart}, year={2026} }","short":"C. Lutsko, T. Weich, L.L. Wolf, Duke Math. Journal  (to appear) (2026).","apa":"Lutsko, C., Weich, T., &#38; Wolf, L. L. (2026). Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces. <i>Duke Math. Journal </i>, <i>(to appear)</i>.","chicago":"Lutsko, Christopher, Tobias Weich, and Lasse Lennart Wolf. “Polyhedral Bounds on the Joint Spectrum and Temperedness of Locally  Symmetric Spaces.” <i>Duke Math. Journal </i> (to appear) (2026).","ieee":"C. Lutsko, T. Weich, and L. L. Wolf, “Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces,” <i>Duke Math. Journal </i>, vol. (to appear), 2026.","ama":"Lutsko C, Weich T, Wolf LL. Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces. <i>Duke Math Journal </i>. 2026;(to appear)."}},{"abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n                  <jats:p>We show how the Fourier transform for distributional sections of vector bundles over symmetric spaces of non‐compact type  can be used for questions of solvability of systems of invariant differential equations in analogy to Hörmander's proof of the Ehrenpreis–Malgrange theorem. We get complete solvability for the hyperbolic plane  and partial results for products  and the hyperbolic 3‐space .</jats:p>","lang":"eng"}],"status":"public","publication":"Mathematische Nachrichten","type":"journal_article","language":[{"iso":"eng"}],"_id":"64569","department":[{"_id":"548"}],"user_id":"109467","year":"2026","page":"456-479","intvolume":"       299","citation":{"chicago":"Olbrich, Martin, and Guendalina Palmirotta. “Solvability of Invariant Systems of Differential Equations on H2$\\mathbb {H}^2$ and Beyond.” <i>Mathematische Nachrichten</i> 299, no. 2 (2026): 456–79. <a href=\"https://doi.org/10.1002/mana.70100\">https://doi.org/10.1002/mana.70100</a>.","ieee":"M. Olbrich and G. Palmirotta, “Solvability of invariant systems of differential equations on H2$\\mathbb {H}^2$ and beyond,” <i>Mathematische Nachrichten</i>, vol. 299, no. 2, pp. 456–479, 2026, doi: <a href=\"https://doi.org/10.1002/mana.70100\">10.1002/mana.70100</a>.","ama":"Olbrich M, Palmirotta G. Solvability of invariant systems of differential equations on H2$\\mathbb {H}^2$ and beyond. <i>Mathematische Nachrichten</i>. 2026;299(2):456-479. doi:<a href=\"https://doi.org/10.1002/mana.70100\">10.1002/mana.70100</a>","short":"M. Olbrich, G. Palmirotta, Mathematische Nachrichten 299 (2026) 456–479.","bibtex":"@article{Olbrich_Palmirotta_2026, title={Solvability of invariant systems of differential equations on H2$\\mathbb {H}^2$ and beyond}, volume={299}, DOI={<a href=\"https://doi.org/10.1002/mana.70100\">10.1002/mana.70100</a>}, number={2}, journal={Mathematische Nachrichten}, publisher={Wiley}, author={Olbrich, Martin and Palmirotta, Guendalina}, year={2026}, pages={456–479} }","mla":"Olbrich, Martin, and Guendalina Palmirotta. “Solvability of Invariant Systems of Differential Equations on H2$\\mathbb {H}^2$ and Beyond.” <i>Mathematische Nachrichten</i>, vol. 299, no. 2, Wiley, 2026, pp. 456–79, doi:<a href=\"https://doi.org/10.1002/mana.70100\">10.1002/mana.70100</a>.","apa":"Olbrich, M., &#38; Palmirotta, G. (2026). Solvability of invariant systems of differential equations on H2$\\mathbb {H}^2$ and beyond. <i>Mathematische Nachrichten</i>, <i>299</i>(2), 456–479. <a href=\"https://doi.org/10.1002/mana.70100\">https://doi.org/10.1002/mana.70100</a>"},"publication_identifier":{"issn":["0025-584X","1522-2616"]},"publication_status":"published","issue":"2","title":"Solvability of invariant systems of differential equations on H2$\\mathbb {H}^2$ and beyond","doi":"10.1002/mana.70100","date_updated":"2026-02-20T20:01:56Z","publisher":"Wiley","volume":299,"author":[{"last_name":"Olbrich","full_name":"Olbrich, Martin","first_name":"Martin"},{"full_name":"Palmirotta, Guendalina","id":"109467","last_name":"Palmirotta","first_name":"Guendalina"}],"date_created":"2026-02-20T19:56:33Z"},{"department":[{"_id":"10"},{"_id":"548"}],"user_id":"109467","_id":"57580","project":[{"name":"TRR 358 - B02: TRR 358 - Spektraltheorie in höherem Rang und unendlichem Volumen (Teilprojekt B02)","_id":"356"}],"status":"public","type":"journal_article","doi":"10.1016/j.jde.2025.114065","main_file_link":[{"url":"https://doi.org/10.1016/j.jde.2025.114065","open_access":"1"}],"author":[{"last_name":"Palmirotta","full_name":"Palmirotta, Guendalina","id":"109467","first_name":"Guendalina"},{"first_name":"Yannick","last_name":"Sire","full_name":"Sire, Yannick"},{"first_name":"Jean-Philippe","full_name":"Anker, Jean-Philippe","last_name":"Anker"}],"oa":"1","date_updated":"2026-03-30T12:03:37Z","citation":{"short":"G. Palmirotta, Y. Sire, J.-P. Anker, Journal of Differential Equations (2026).","mla":"Palmirotta, Guendalina, et al. “The Schrödinger Equation with Fractional Laplacian on Hyperbolic Spaces and Homogeneous Trees.” <i>Journal of Differential Equations</i>, Elsevier, 2026, doi:<a href=\"https://doi.org/10.1016/j.jde.2025.114065\">10.1016/j.jde.2025.114065</a>.","bibtex":"@article{Palmirotta_Sire_Anker_2026, title={The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees}, DOI={<a href=\"https://doi.org/10.1016/j.jde.2025.114065\">10.1016/j.jde.2025.114065</a>}, journal={Journal of Differential Equations}, publisher={Elsevier}, author={Palmirotta, Guendalina and Sire, Yannick and Anker, Jean-Philippe}, year={2026} }","ama":"Palmirotta G, Sire Y, Anker J-P. The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees. <i>Journal of Differential Equations</i>. Published online 2026. doi:<a href=\"https://doi.org/10.1016/j.jde.2025.114065\">10.1016/j.jde.2025.114065</a>","apa":"Palmirotta, G., Sire, Y., &#38; Anker, J.-P. (2026). The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees. <i>Journal of Differential Equations</i>. <a href=\"https://doi.org/10.1016/j.jde.2025.114065\">https://doi.org/10.1016/j.jde.2025.114065</a>","chicago":"Palmirotta, Guendalina, Yannick Sire, and Jean-Philippe Anker. “The Schrödinger Equation with Fractional Laplacian on Hyperbolic Spaces and Homogeneous Trees.” <i>Journal of Differential Equations</i>, 2026. <a href=\"https://doi.org/10.1016/j.jde.2025.114065\">https://doi.org/10.1016/j.jde.2025.114065</a>.","ieee":"G. Palmirotta, Y. Sire, and J.-P. Anker, “The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees,” <i>Journal of Differential Equations</i>, 2026, doi: <a href=\"https://doi.org/10.1016/j.jde.2025.114065\">10.1016/j.jde.2025.114065</a>."},"related_material":{"link":[{"relation":"confirmation","url":"https://www.sciencedirect.com/science/article/pii/S0022039625010927?via%3Dihub"}]},"publication_status":"published","language":[{"iso":"eng"}],"keyword":["Schrödinger equation","Fractional Laplacian","Dispersive estimates","Strichartz estimates","Real hyperbolic spaces","Homogeneous trees"],"external_id":{"arxiv":["2412.00780"]},"abstract":[{"text":"We investigate dispersive and Strichartz estimates for the Schrödinger equation involving the fractional Laplacian in real hyperbolic spaces and their discrete analogues, homogeneous trees. Due to the Knapp phenomenon, the Strichartz estimates on Euclidean spaces for the fractional Laplacian exhibit loss of derivatives. A similar phenomenon appears on real hyperbolic spaces. However, such a loss disappears on homogeneous trees, due to the triviality of the estimates for small times.","lang":"eng"}],"publication":"Journal of Differential Equations","title":"The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees","date_created":"2024-12-04T16:21:38Z","publisher":"Elsevier","year":"2026"},{"citation":{"chicago":"Arends, Christian, and Guendalina Palmirotta. “Patterson-Sullivan Distributions of Finite Regular Graphs.” <i>ArXiv:2603.09779</i>, 2026.","ieee":"C. Arends and G. Palmirotta, “Patterson-Sullivan distributions of finite regular graphs,” <i>arXiv:2603.09779</i>. 2026.","ama":"Arends C, Palmirotta G. Patterson-Sullivan distributions of finite regular graphs. <i>arXiv:260309779</i>. Published online 2026.","bibtex":"@article{Arends_Palmirotta_2026, title={Patterson-Sullivan distributions of finite regular graphs}, journal={arXiv:2603.09779}, author={Arends, Christian and Palmirotta, Guendalina}, year={2026} }","mla":"Arends, Christian, and Guendalina Palmirotta. “Patterson-Sullivan Distributions of Finite Regular Graphs.” <i>ArXiv:2603.09779</i>, 2026.","short":"C. Arends, G. Palmirotta, ArXiv:2603.09779 (2026).","apa":"Arends, C., &#38; Palmirotta, G. (2026). Patterson-Sullivan distributions of finite regular graphs. In <i>arXiv:2603.09779</i>."},"page":"38","year":"2026","date_created":"2026-03-30T11:56:04Z","author":[{"last_name":"Arends","full_name":"Arends, Christian","first_name":"Christian"},{"id":"109467","full_name":"Palmirotta, Guendalina","last_name":"Palmirotta","first_name":"Guendalina"}],"oa":"1","date_updated":"2026-03-30T12:02:56Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2603.09779"}],"title":"Patterson-Sullivan distributions of finite regular graphs","type":"preprint","publication":"arXiv:2603.09779","status":"public","abstract":[{"lang":"eng","text":"On finite regular graphs, we construct Patterson-Sullivan distributions associated with eigenfunctions of the discrete Laplace operator via their boundary values on the phase space. These distributions are closely related to Wigner distributions defined via a pseudo-differential calculus on graphs, which appear naturally in the study of quantum chaos. Using a pairing formula, we prove that Patterson-Sullivan distributions are also related to invariant Ruelle distributions arising from the transfer operator of the geodesic flow on the shift space. Both relationships provide discrete analogues of results for compact hyperbolic surfaces obtained by Anantharaman-Zelditch and by Guillarmou-Hilgert-Weich."}],"user_id":"109467","department":[{"_id":"548"},{"_id":"10"},{"_id":"34"}],"project":[{"_id":"358","name":"TRR 358; TP B04:  Geodätische Flüsse und Weyl Kammer Flüsse auf affinen Gebäuden"}],"_id":"65232","external_id":{"arxiv":["2603.09779"]},"language":[{"iso":"eng"}]},{"ddc":["510"],"language":[{"iso":"eng"}],"publication":"Journal of Functional Analysis","file":[{"file_size":978990,"access_level":"open_access","file_name":"2103.02968.pdf","file_id":"32100","date_updated":"2022-06-22T09:56:39Z","creator":"weich","date_created":"2022-06-22T09:56:39Z","relation":"main_file","content_type":"application/pdf"}],"date_created":"2022-06-22T09:56:43Z","title":"Wave Front Sets of Nilpotent Lie Group Representations","issue":"1","year":"2025","_id":"32099","project":[{"grant_number":"491392403","name":"TRR 358 - B02: TRR 358 - Spektraltheorie in höherem Rang und unendlichem Volumen (Teilprojekt B02)","_id":"356"},{"name":"Mikrolokale Methoden für hyperbolische Dynamiken","_id":"355","grant_number":"422642921"}],"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","file_date_updated":"2022-06-22T09:56:39Z","type":"journal_article","status":"public","date_updated":"2024-09-25T08:18:44Z","oa":"1","volume":288,"author":[{"orcid":"0000-0002-9648-6919","last_name":"Weich","id":"49178","full_name":"Weich, Tobias","first_name":"Tobias"},{"first_name":"Julia","last_name":"Budde","full_name":"Budde, Julia"}],"doi":" https://doi.org/10.1016/j.jfa.2024.110684","has_accepted_license":"1","intvolume":"       288","citation":{"ama":"Weich T, Budde J. Wave Front Sets of Nilpotent Lie Group Representations. <i>Journal of Functional Analysis</i>. 2025;288(1). doi:<a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\"> https://doi.org/10.1016/j.jfa.2024.110684</a>","chicago":"Weich, Tobias, and Julia Budde. “Wave Front Sets of Nilpotent Lie Group Representations.” <i>Journal of Functional Analysis</i> 288, no. 1 (2025). <a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\">https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684</a>.","ieee":"T. Weich and J. Budde, “Wave Front Sets of Nilpotent Lie Group Representations,” <i>Journal of Functional Analysis</i>, vol. 288, no. 1, 2025, doi: <a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\"> https://doi.org/10.1016/j.jfa.2024.110684</a>.","mla":"Weich, Tobias, and Julia Budde. “Wave Front Sets of Nilpotent Lie Group Representations.” <i>Journal of Functional Analysis</i>, vol. 288, no. 1, 2025, doi:<a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\"> https://doi.org/10.1016/j.jfa.2024.110684</a>.","short":"T. Weich, J. Budde, Journal of Functional Analysis 288 (2025).","bibtex":"@article{Weich_Budde_2025, title={Wave Front Sets of Nilpotent Lie Group Representations}, volume={288}, DOI={<a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\"> https://doi.org/10.1016/j.jfa.2024.110684</a>}, number={1}, journal={Journal of Functional Analysis}, author={Weich, Tobias and Budde, Julia}, year={2025} }","apa":"Weich, T., &#38; Budde, J. (2025). Wave Front Sets of Nilpotent Lie Group Representations. <i>Journal of Functional Analysis</i>, <i>288</i>(1). <a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\">https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684</a>"}},{"year":"2025","citation":{"ama":"Delarue B, Monclair D, Sanders A. Locally homogeneous Axiom A flows I: projective Anosov subgroups and exponential mixing. <i>Geometric and Functional Analysis (GAFA)</i>. 2025;35:673–735. doi:<a href=\"https://doi.org/10.1007/s00039-025-00712-2\">10.1007/s00039-025-00712-2</a>","ieee":"B. Delarue, D. Monclair, and A. Sanders, “Locally homogeneous Axiom A flows I: projective Anosov subgroups and exponential mixing,” <i>Geometric and Functional Analysis (GAFA)</i>, vol. 35, pp. 673–735, 2025, doi: <a href=\"https://doi.org/10.1007/s00039-025-00712-2\">10.1007/s00039-025-00712-2</a>.","chicago":"Delarue, Benjamin, Daniel Monclair, and Andrew Sanders. “Locally Homogeneous Axiom A Flows I: Projective Anosov Subgroups and Exponential Mixing.” <i>Geometric and Functional Analysis (GAFA)</i> 35 (2025): 673–735. <a href=\"https://doi.org/10.1007/s00039-025-00712-2\">https://doi.org/10.1007/s00039-025-00712-2</a>.","short":"B. Delarue, D. Monclair, A. Sanders, Geometric and Functional Analysis (GAFA) 35 (2025) 673–735.","bibtex":"@article{Delarue_Monclair_Sanders_2025, title={Locally homogeneous Axiom A flows I: projective Anosov subgroups and exponential mixing}, volume={35}, DOI={<a href=\"https://doi.org/10.1007/s00039-025-00712-2\">10.1007/s00039-025-00712-2</a>}, journal={Geometric and Functional Analysis (GAFA)}, author={Delarue, Benjamin and Monclair, Daniel and Sanders, Andrew}, year={2025}, pages={673–735} }","mla":"Delarue, Benjamin, et al. “Locally Homogeneous Axiom A Flows I: Projective Anosov Subgroups and Exponential Mixing.” <i>Geometric and Functional Analysis (GAFA)</i>, vol. 35, 2025, pp. 673–735, doi:<a href=\"https://doi.org/10.1007/s00039-025-00712-2\">10.1007/s00039-025-00712-2</a>.","apa":"Delarue, B., Monclair, D., &#38; Sanders, A. (2025). Locally homogeneous Axiom A flows I: projective Anosov subgroups and exponential mixing. <i>Geometric and Functional Analysis (GAFA)</i>, <i>35</i>, 673–735. <a href=\"https://doi.org/10.1007/s00039-025-00712-2\">https://doi.org/10.1007/s00039-025-00712-2</a>"},"page":"673–735","intvolume":"        35","publication_status":"published","title":"Locally homogeneous Axiom A flows I: projective Anosov subgroups and exponential mixing","doi":"10.1007/s00039-025-00712-2","date_updated":"2026-01-09T09:25:45Z","author":[{"first_name":"Benjamin","id":"70575","full_name":"Delarue, Benjamin","last_name":"Delarue"},{"first_name":"Daniel","last_name":"Monclair","full_name":"Monclair, Daniel"},{"last_name":"Sanders","full_name":"Sanders, Andrew","first_name":"Andrew"}],"date_created":"2024-04-11T12:31:34Z","volume":35,"abstract":[{"text":"By constructing a non-empty domain of discontinuity in a suitable homogeneous\r\nspace, we prove that every torsion-free projective Anosov subgroup is the\r\nmonodromy group of a locally homogeneous contact Axiom A dynamical system with\r\na unique basic hyperbolic set on which the flow is conjugate to the refraction\r\nflow of Sambarino. Under the assumption of irreducibility, we utilize the work\r\nof Stoyanov to establish spectral estimates for the associated complex Ruelle\r\ntransfer operators, and by way of corollary: exponential mixing, exponentially\r\ndecaying error term in the prime orbit theorem, and a spectral gap for the\r\nRuelle zeta function. With no irreducibility assumption, results of\r\nDyatlov-Guillarmou imply the global meromorphic continuation of zeta functions\r\nwith smooth weights, as well as the existence of a discrete spectrum of\r\nRuelle-Pollicott resonances and (co)-resonant states. We apply our results to\r\nspace-like geodesic flows for the convex cocompact pseudo-Riemannian manifolds\r\nof Danciger-Gu\\'eritaud-Kassel, and the Benoist-Hilbert geodesic flow for\r\nstrictly convex real projective manifolds.","lang":"eng"}],"status":"public","type":"journal_article","publication":"Geometric and Functional Analysis (GAFA)","article_type":"original","language":[{"iso":"eng"}],"_id":"53414","user_id":"70575","department":[{"_id":"548"}]},{"article_type":"original","language":[{"iso":"eng"}],"_id":"53412","user_id":"70575","department":[{"_id":"548"}],"abstract":[{"lang":"eng","text":"Let $M$ be a symplectic manifold carrying a Hamiltonian $S^1$-action with\r\nmomentum map $J:M \\rightarrow \\mathbb{R}$ and consider the corresponding\r\nsymplectic quotient $\\mathcal{M}_0:=J^{-1}(0)/S^1$. We extend Sjamaar's complex\r\nof differential forms on $\\mathcal{M}_0$, whose cohomology is isomorphic to the\r\nsingular cohomology $H(\\mathcal{M}_0;\\mathbb{R})$ of $\\mathcal{M}_0$ with real\r\ncoefficients, to a complex of differential forms on $\\mathcal{M}_0$ associated\r\nwith a partial desingularization $\\widetilde{\\mathcal{M}}_0$, which we call\r\nresolution differential forms. The cohomology of that complex turns out to be\r\nisomorphic to the de Rham cohomology $H(\\widetilde{ \\mathcal{M}}_0)$ of\r\n$\\widetilde{\\mathcal{M}}_0$. Based on this, we derive a long exact sequence\r\ninvolving both $H(\\mathcal{M}_0;\\mathbb{R})$ and $H(\\widetilde{\r\n\\mathcal{M}}_0)$ and give conditions for its splitting. We then define a Kirwan\r\nmap $\\mathcal{K}:H_{S^1}(M) \\rightarrow H(\\widetilde{\\mathcal{M}}_0)$ from the\r\nequivariant cohomology $H_{S^1}(M)$ of $M$ to $H(\\widetilde{\\mathcal{M}}_0)$\r\nand show that its image contains the image of $H(\\mathcal{M}_0;\\mathbb{R})$ in\r\n$H(\\widetilde{\\mathcal{M}}_0)$ under the natural inclusion. Combining both\r\nresults in the case that all fixed point components of $M$ have vanishing odd\r\ncohomology we obtain a surjection $\\check \\kappa:H^\\textrm{ev}_{S^1}(M)\r\n\\rightarrow H^\\textrm{ev}(\\mathcal{M}_0;\\mathbb{R})$ in even degrees, while\r\nalready simple examples show that a similar surjection in odd degrees does not\r\nexist in general. As an interesting class of examples we study abelian polygon\r\nspaces."}],"status":"public","type":"journal_article","publication":"Transformation Groups","title":"Singular cohomology of symplectic quotients by circle actions and Kirwan  surjectivity","doi":"10.1007/s00031-025-09924-0","date_updated":"2026-01-09T09:27:08Z","date_created":"2024-04-11T12:30:59Z","author":[{"first_name":"Benjamin","last_name":"Delarue","full_name":"Delarue, Benjamin","id":"70575"},{"full_name":"Ramacher, Pablo","last_name":"Ramacher","first_name":"Pablo"},{"first_name":"Maximilian","full_name":"Schmitt, Maximilian","last_name":"Schmitt"}],"year":"2025","citation":{"short":"B. Delarue, P. Ramacher, M. Schmitt, Transformation Groups (2025).","mla":"Delarue, Benjamin, et al. “Singular Cohomology of Symplectic Quotients by Circle Actions and Kirwan  Surjectivity.” <i>Transformation Groups</i>, 2025, doi:<a href=\"https://doi.org/10.1007/s00031-025-09924-0\">10.1007/s00031-025-09924-0</a>.","bibtex":"@article{Delarue_Ramacher_Schmitt_2025, title={Singular cohomology of symplectic quotients by circle actions and Kirwan  surjectivity}, DOI={<a href=\"https://doi.org/10.1007/s00031-025-09924-0\">10.1007/s00031-025-09924-0</a>}, journal={Transformation Groups}, author={Delarue, Benjamin and Ramacher, Pablo and Schmitt, Maximilian}, year={2025} }","apa":"Delarue, B., Ramacher, P., &#38; Schmitt, M. (2025). Singular cohomology of symplectic quotients by circle actions and Kirwan  surjectivity. <i>Transformation Groups</i>. <a href=\"https://doi.org/10.1007/s00031-025-09924-0\">https://doi.org/10.1007/s00031-025-09924-0</a>","chicago":"Delarue, Benjamin, Pablo Ramacher, and Maximilian Schmitt. “Singular Cohomology of Symplectic Quotients by Circle Actions and Kirwan  Surjectivity.” <i>Transformation Groups</i>, 2025. <a href=\"https://doi.org/10.1007/s00031-025-09924-0\">https://doi.org/10.1007/s00031-025-09924-0</a>.","ieee":"B. Delarue, P. Ramacher, and M. Schmitt, “Singular cohomology of symplectic quotients by circle actions and Kirwan  surjectivity,” <i>Transformation Groups</i>, 2025, doi: <a href=\"https://doi.org/10.1007/s00031-025-09924-0\">10.1007/s00031-025-09924-0</a>.","ama":"Delarue B, Ramacher P, Schmitt M. Singular cohomology of symplectic quotients by circle actions and Kirwan  surjectivity. <i>Transformation Groups</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1007/s00031-025-09924-0\">10.1007/s00031-025-09924-0</a>"},"publication_status":"epub_ahead"},{"_id":"53413","user_id":"220","department":[{"_id":"548"}],"article_type":"original","language":[{"iso":"eng"}],"type":"journal_article","publication":"Journal of Lie Theory","abstract":[{"lang":"eng","text":"For negatively curved symmetric spaces it is known that the poles of the\r\nscattering matrices defined via the standard intertwining operators for the\r\nspherical principal representations of the isometry group are either given as\r\npoles of the intertwining operators or as quantum resonances, i.e. poles of the\r\nmeromorphically continued resolvents of the Laplace-Beltrami operator. We\r\nextend this result to classical locally symmetric spaces of negative curvature\r\nwith convex-cocompact fundamental group using results of Bunke and Olbrich. The\r\nmethod of proof forces us to exclude the spectral parameters corresponding to\r\nsingular Poisson transforms."}],"status":"public","date_updated":"2026-03-31T09:07:17Z","author":[{"first_name":"Benjamin","last_name":"Delarue","id":"70575","full_name":"Delarue, Benjamin"},{"first_name":"Joachim","id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert"}],"date_created":"2024-04-11T12:31:18Z","volume":35,"title":"Quantum resonances and scattering poles of classical rank one locally  symmetric spaces","publication_status":"inpress","publication_identifier":{"issn":["0949-5932"]},"issue":"(4)","year":"2025","citation":{"bibtex":"@article{Delarue_Hilgert, title={Quantum resonances and scattering poles of classical rank one locally  symmetric spaces}, volume={35}, number={(4)}, journal={Journal of Lie Theory}, author={Delarue, Benjamin and Hilgert, Joachim}, pages={787--804} }","short":"B. Delarue, J. Hilgert, Journal of Lie Theory 35 (n.d.) 787--804.","mla":"Delarue, Benjamin, and Joachim Hilgert. “Quantum Resonances and Scattering Poles of Classical Rank One Locally  Symmetric Spaces.” <i>Journal of Lie Theory</i>, vol. 35, no. (4), pp. 787--804.","apa":"Delarue, B., &#38; Hilgert, J. (n.d.). Quantum resonances and scattering poles of classical rank one locally  symmetric spaces. <i>Journal of Lie Theory</i>, <i>35</i>((4)), 787--804.","ama":"Delarue B, Hilgert J. Quantum resonances and scattering poles of classical rank one locally  symmetric spaces. <i>Journal of Lie Theory</i>. 35((4)):787--804.","ieee":"B. Delarue and J. Hilgert, “Quantum resonances and scattering poles of classical rank one locally  symmetric spaces,” <i>Journal of Lie Theory</i>, vol. 35, no. (4), pp. 787--804.","chicago":"Delarue, Benjamin, and Joachim Hilgert. “Quantum Resonances and Scattering Poles of Classical Rank One Locally  Symmetric Spaces.” <i>Journal of Lie Theory</i> 35, no. (4) (n.d.): 787--804."},"intvolume":"        35","page":"787--804"},{"status":"public","abstract":[{"text":"Let $X=X_1\\times X_2$ be a product of two rank one symmetric spaces of\r\nnon-compact type and $\\Gamma$ a torsion-free discrete subgroup in $G_1\\times\r\nG_2$. We show that the spectrum of $\\Gamma \\backslash X$ is related to the\r\nasymptotic growth of $\\Gamma$ in the two direction defined by the two factors.\r\nWe obtain that $L^2(\\Gamma \\backslash G)$ is tempered for large class of\r\n$\\Gamma$.","lang":"eng"}],"publication":"Geom Dedicata","type":"journal_article","language":[{"iso":"eng"}],"article_number":"76","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"45027","_id":"51207","external_id":{"arxiv":["2304.09573"]},"intvolume":"       218","citation":{"ieee":"T. Weich and L. L. Wolf, “Temperedness of locally symmetric spaces: The product case,” <i>Geom Dedicata</i>, vol. 218, Art. no. 76, 2024, doi: <a href=\"https://doi.org/10.1007/s10711-024-00904-4\">https://doi.org/10.1007/s10711-024-00904-4</a>.","chicago":"Weich, Tobias, and Lasse Lennart Wolf. “Temperedness of Locally Symmetric Spaces: The Product Case.” <i>Geom Dedicata</i> 218 (2024). <a href=\"https://doi.org/10.1007/s10711-024-00904-4\">https://doi.org/10.1007/s10711-024-00904-4</a>.","ama":"Weich T, Wolf LL. Temperedness of locally symmetric spaces: The product case. <i>Geom Dedicata</i>. 2024;218. doi:<a href=\"https://doi.org/10.1007/s10711-024-00904-4\">https://doi.org/10.1007/s10711-024-00904-4</a>","bibtex":"@article{Weich_Wolf_2024, title={Temperedness of locally symmetric spaces: The product case}, volume={218}, DOI={<a href=\"https://doi.org/10.1007/s10711-024-00904-4\">https://doi.org/10.1007/s10711-024-00904-4</a>}, number={76}, journal={Geom Dedicata}, author={Weich, Tobias and Wolf, Lasse Lennart}, year={2024} }","short":"T. Weich, L.L. Wolf, Geom Dedicata 218 (2024).","mla":"Weich, Tobias, and Lasse Lennart Wolf. “Temperedness of Locally Symmetric Spaces: The Product Case.” <i>Geom Dedicata</i>, vol. 218, 76, 2024, doi:<a href=\"https://doi.org/10.1007/s10711-024-00904-4\">https://doi.org/10.1007/s10711-024-00904-4</a>.","apa":"Weich, T., &#38; Wolf, L. L. (2024). Temperedness of locally symmetric spaces: The product case. <i>Geom Dedicata</i>, <i>218</i>, Article 76. <a href=\"https://doi.org/10.1007/s10711-024-00904-4\">https://doi.org/10.1007/s10711-024-00904-4</a>"},"year":"2024","doi":"https://doi.org/10.1007/s10711-024-00904-4","title":"Temperedness of locally symmetric spaces: The product case","volume":218,"date_created":"2024-02-06T21:00:55Z","author":[{"last_name":"Weich","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","id":"49178","first_name":"Tobias"},{"first_name":"Lasse Lennart","id":"45027","full_name":"Wolf, Lasse Lennart","last_name":"Wolf","orcid":"0000-0001-8893-2045"}],"date_updated":"2024-05-07T11:44:34Z"},{"title":"Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik","doi":"10.1007/978-3-662-67357-7","publisher":"Springer Berlin Heidelberg","date_updated":"2024-08-08T08:05:30Z","date_created":"2024-07-12T08:36:42Z","author":[{"orcid":"0000-0002-6964-7123","last_name":"Hoffmann","id":"32202","full_name":"Hoffmann, Max","first_name":"Max"},{"first_name":"Joachim","last_name":"Hilgert","id":"220","full_name":"Hilgert, Joachim"},{"first_name":"Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","id":"49178","full_name":"Weich, Tobias"}],"year":"2024","place":"Berlin, Heidelberg","citation":{"chicago":"Hoffmann, Max, Joachim Hilgert, and Tobias Weich. <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Berlin, Heidelberg: Springer Berlin Heidelberg, 2024. <a href=\"https://doi.org/10.1007/978-3-662-67357-7\">https://doi.org/10.1007/978-3-662-67357-7</a>.","ieee":"M. Hoffmann, J. Hilgert, and T. Weich, <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Berlin, Heidelberg: Springer Berlin Heidelberg, 2024.","ama":"Hoffmann M, Hilgert J, Weich T. <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Springer Berlin Heidelberg; 2024. doi:<a href=\"https://doi.org/10.1007/978-3-662-67357-7\">10.1007/978-3-662-67357-7</a>","short":"M. Hoffmann, J. Hilgert, T. Weich, Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik, Springer Berlin Heidelberg, Berlin, Heidelberg, 2024.","bibtex":"@book{Hoffmann_Hilgert_Weich_2024, place={Berlin, Heidelberg}, title={Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik}, DOI={<a href=\"https://doi.org/10.1007/978-3-662-67357-7\">10.1007/978-3-662-67357-7</a>}, publisher={Springer Berlin Heidelberg}, author={Hoffmann, Max and Hilgert, Joachim and Weich, Tobias}, year={2024} }","mla":"Hoffmann, Max, et al. <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Springer Berlin Heidelberg, 2024, doi:<a href=\"https://doi.org/10.1007/978-3-662-67357-7\">10.1007/978-3-662-67357-7</a>.","apa":"Hoffmann, M., Hilgert, J., &#38; Weich, T. (2024). <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-662-67357-7\">https://doi.org/10.1007/978-3-662-67357-7</a>"},"publication_identifier":{"isbn":["9783662673560","9783662673577"]},"publication_status":"published","language":[{"iso":"ger"}],"_id":"55193","department":[{"_id":"97"},{"_id":"643"},{"_id":"548"}],"user_id":"220","status":"public","type":"book"},{"title":"Ruelle-Taylor resonances of Anosov actions","date_created":"2022-06-22T09:56:51Z","year":"2024","issue":"8","language":[{"iso":"eng"}],"ddc":["510"],"file":[{"file_size":796410,"file_name":"2007.14275.pdf","file_id":"32102","access_level":"open_access","date_updated":"2022-06-22T09:56:47Z","creator":"weich","date_created":"2022-06-22T09:56:47Z","relation":"main_file","content_type":"application/pdf"}],"publication":"J. Europ. Math. Soc.","doi":"https://doi.org/10.4171/JEMS/1428","author":[{"last_name":"Weich","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","id":"49178","first_name":"Tobias"},{"first_name":"Yannick","last_name":"Guedes Bonthonneau","full_name":"Guedes Bonthonneau, Yannick"},{"first_name":"Colin","full_name":"Guillarmou, Colin","last_name":"Guillarmou"},{"first_name":"Joachim","id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert"}],"volume":27,"oa":"1","date_updated":"2026-02-18T10:33:34Z","citation":{"apa":"Weich, T., Guedes Bonthonneau, Y., Guillarmou, C., &#38; Hilgert, J. (2024). Ruelle-Taylor resonances of Anosov actions. <i>J. Europ. Math. Soc.</i>, <i>27</i>(8), 3085–3147. <a href=\"https://doi.org/10.4171/JEMS/1428\">https://doi.org/10.4171/JEMS/1428</a>","mla":"Weich, Tobias, et al. “Ruelle-Taylor Resonances of Anosov Actions.” <i>J. Europ. Math. Soc.</i>, vol. 27, no. 8, 2024, pp. 3085–3147, doi:<a href=\"https://doi.org/10.4171/JEMS/1428\">https://doi.org/10.4171/JEMS/1428</a>.","short":"T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, J. Europ. Math. Soc. 27 (2024) 3085–3147.","bibtex":"@article{Weich_Guedes Bonthonneau_Guillarmou_Hilgert_2024, title={Ruelle-Taylor resonances of Anosov actions}, volume={27}, DOI={<a href=\"https://doi.org/10.4171/JEMS/1428\">https://doi.org/10.4171/JEMS/1428</a>}, number={8}, journal={J. Europ. Math. Soc.}, author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin and Hilgert, Joachim}, year={2024}, pages={3085–3147} }","ieee":"T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, and J. Hilgert, “Ruelle-Taylor resonances of Anosov actions,” <i>J. Europ. Math. Soc.</i>, vol. 27, no. 8, pp. 3085–3147, 2024, doi: <a href=\"https://doi.org/10.4171/JEMS/1428\">https://doi.org/10.4171/JEMS/1428</a>.","chicago":"Weich, Tobias, Yannick Guedes Bonthonneau, Colin Guillarmou, and Joachim Hilgert. “Ruelle-Taylor Resonances of Anosov Actions.” <i>J. Europ. Math. Soc.</i> 27, no. 8 (2024): 3085–3147. <a href=\"https://doi.org/10.4171/JEMS/1428\">https://doi.org/10.4171/JEMS/1428</a>.","ama":"Weich T, Guedes Bonthonneau Y, Guillarmou C, Hilgert J. Ruelle-Taylor resonances of Anosov actions. <i>J Europ Math Soc</i>. 2024;27(8):3085–3147. doi:<a href=\"https://doi.org/10.4171/JEMS/1428\">https://doi.org/10.4171/JEMS/1428</a>"},"page":"3085–3147","intvolume":"        27","publication_status":"published","has_accepted_license":"1","file_date_updated":"2022-06-22T09:56:47Z","user_id":"49178","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"_id":"32101","status":"public","type":"journal_article"},{"user_id":"109467","department":[{"_id":"10"},{"_id":"548"}],"project":[{"grant_number":"491392403","name":"TRR 358 - B02: TRR 358 - Spektraltheorie in höherem Rang und unendlichem Volumen (Teilprojekt B02)","_id":"356"}],"_id":"57582","external_id":{"arxiv":["2411.19782"]},"language":[{"iso":"eng"}],"type":"preprint","publication":"arXiv:2411.19782","status":"public","abstract":[{"text":"We prove that the Patterson-Sullivan and Wigner distributions on the unit\r\nsphere bundle of a convex-cocompact hyperbolic surface are asymptotically\r\nidentical. This generalizes results in the compact case by\r\nAnantharaman-Zelditch and Hansen-Hilgert-Schr\\\"oder.","lang":"eng"}],"author":[{"full_name":"Delarue, Benjamin","last_name":"Delarue","first_name":"Benjamin"},{"first_name":"Guendalina","full_name":"Palmirotta, Guendalina","last_name":"Palmirotta"}],"date_created":"2024-12-04T16:28:05Z","date_updated":"2024-12-04T16:33:27Z","title":"Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces","citation":{"bibtex":"@article{Delarue_Palmirotta_2024, title={Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces}, journal={arXiv:2411.19782}, author={Delarue, Benjamin and Palmirotta, Guendalina}, year={2024} }","short":"B. Delarue, G. Palmirotta, ArXiv:2411.19782 (2024).","mla":"Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner Distributions of Convex-Cocompact  Hyperbolic Surfaces.” <i>ArXiv:2411.19782</i>, 2024.","apa":"Delarue, B., &#38; Palmirotta, G. (2024). Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces. In <i>arXiv:2411.19782</i>.","ama":"Delarue B, Palmirotta G. Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces. <i>arXiv:241119782</i>. Published online 2024.","chicago":"Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner Distributions of Convex-Cocompact  Hyperbolic Surfaces.” <i>ArXiv:2411.19782</i>, 2024.","ieee":"B. Delarue and G. Palmirotta, “Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces,” <i>arXiv:2411.19782</i>. 2024."},"year":"2024"},{"date_updated":"2025-01-02T15:39:43Z","oa":"1","volume":128,"author":[{"last_name":"Weich","orcid":"0000-0002-9648-6919","id":"49178","full_name":"Weich, Tobias","first_name":"Tobias"},{"first_name":"Yannick","last_name":"Guedes Bonthonneau","full_name":"Guedes Bonthonneau, Yannick"},{"first_name":"Colin","last_name":"Guillarmou","full_name":"Guillarmou, Colin"}],"doi":" DOI: 10.4310/jdg/1729092452","has_accepted_license":"1","page":"959-1026","intvolume":"       128","citation":{"chicago":"Weich, Tobias, Yannick Guedes Bonthonneau, and Colin Guillarmou. “SRB Measures of Anosov Actions.” <i>Journal of Differential Geometry</i> 128 (2024): 959–1026. <a href=\"https://doi.org/ DOI: 10.4310/jdg/1729092452\">https://doi.org/ DOI: 10.4310/jdg/1729092452</a>.","ieee":"T. Weich, Y. Guedes Bonthonneau, and C. Guillarmou, “SRB Measures of Anosov Actions,” <i>Journal of Differential Geometry</i>, vol. 128, pp. 959–1026, 2024, doi: <a href=\"https://doi.org/ DOI: 10.4310/jdg/1729092452\"> DOI: 10.4310/jdg/1729092452</a>.","ama":"Weich T, Guedes Bonthonneau Y, Guillarmou C. SRB Measures of Anosov Actions. <i>Journal of Differential Geometry</i>. 2024;128:959-1026. doi:<a href=\"https://doi.org/ DOI: 10.4310/jdg/1729092452\"> DOI: 10.4310/jdg/1729092452</a>","apa":"Weich, T., Guedes Bonthonneau, Y., &#38; Guillarmou, C. (2024). SRB Measures of Anosov Actions. <i>Journal of Differential Geometry</i>, <i>128</i>, 959–1026. <a href=\"https://doi.org/ DOI: 10.4310/jdg/1729092452\">https://doi.org/ DOI: 10.4310/jdg/1729092452</a>","bibtex":"@article{Weich_Guedes Bonthonneau_Guillarmou_2024, title={SRB Measures of Anosov Actions}, volume={128}, DOI={<a href=\"https://doi.org/ DOI: 10.4310/jdg/1729092452\"> DOI: 10.4310/jdg/1729092452</a>}, journal={Journal of Differential Geometry}, author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin}, year={2024}, pages={959–1026} }","mla":"Weich, Tobias, et al. “SRB Measures of Anosov Actions.” <i>Journal of Differential Geometry</i>, vol. 128, 2024, pp. 959–1026, doi:<a href=\"https://doi.org/ DOI: 10.4310/jdg/1729092452\"> DOI: 10.4310/jdg/1729092452</a>.","short":"T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, Journal of Differential Geometry 128 (2024) 959–1026."},"_id":"32097","project":[{"grant_number":"491392403","_id":"358","name":"TRR 358 - Geodätische Flüsse und Weyl Kammer Flüsse auf affinen Gebäuden (Teilprojekt B04)"},{"grant_number":"422642921","_id":"355","name":"Mikrolokale Methoden für hyperbolische Dynamiken"}],"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","file_date_updated":"2022-06-22T09:56:08Z","type":"journal_article","status":"public","date_created":"2022-06-22T09:56:23Z","title":"SRB Measures of Anosov Actions","year":"2024","external_id":{"arxiv":["https://arxiv.org/abs/2103.12127"]},"ddc":["510"],"language":[{"iso":"eng"}],"publication":"Journal of Differential Geometry","file":[{"file_size":745870,"access_level":"open_access","file_name":"2103.12127.pdf","file_id":"32098","date_updated":"2022-06-22T09:56:08Z","date_created":"2022-06-22T09:56:08Z","creator":"weich","relation":"main_file","content_type":"application/pdf"}]},{"citation":{"ieee":"B. Delarue and G. Palmirotta, “Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces,” <i>arXiv:2411.19782</i>. 2024.","chicago":"Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner Distributions of Convex-Cocompact  Hyperbolic Surfaces.” <i>ArXiv:2411.19782</i>, 2024.","ama":"Delarue B, Palmirotta G. Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces. <i>arXiv:241119782</i>. Published online 2024.","short":"B. Delarue, G. Palmirotta, ArXiv:2411.19782 (2024).","mla":"Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner Distributions of Convex-Cocompact  Hyperbolic Surfaces.” <i>ArXiv:2411.19782</i>, 2024.","bibtex":"@article{Delarue_Palmirotta_2024, title={Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces}, journal={arXiv:2411.19782}, author={Delarue, Benjamin and Palmirotta, Guendalina}, year={2024} }","apa":"Delarue, B., &#38; Palmirotta, G. (2024). Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces. In <i>arXiv:2411.19782</i>."},"year":"2024","author":[{"id":"70575","full_name":"Delarue, Benjamin","last_name":"Delarue","first_name":"Benjamin"},{"last_name":"Palmirotta","full_name":"Palmirotta, Guendalina","id":"109467","first_name":"Guendalina"}],"date_created":"2025-02-28T10:32:30Z","date_updated":"2026-03-30T12:01:12Z","title":"Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces","publication":"arXiv:2411.19782","type":"preprint","status":"public","abstract":[{"lang":"eng","text":"We prove that the Patterson-Sullivan and Wigner distributions on the unit\r\nsphere bundle of a convex-cocompact hyperbolic surface are asymptotically\r\nidentical. This generalizes results in the compact case by\r\nAnantharaman-Zelditch and Hansen-Hilgert-Schr\\\"oder."}],"department":[{"_id":"548"}],"user_id":"109467","external_id":{"arxiv":["2411.19782"]},"_id":"58873","project":[{"_id":"356","name":"TRR 358; TP B02: Spektraltheorie in höherem Rang und unendlichem Volumen"}],"language":[{"iso":"eng"}]},{"user_id":"49178","department":[{"_id":"10"},{"_id":"548"},{"_id":"623"}],"external_id":{"arxiv":["2205.03167"]},"_id":"31189","language":[{"iso":"eng"}],"type":"journal_article","publication":"Communications in Mathematical Physics","status":"public","abstract":[{"text":"Given a geometrically finite hyperbolic surface of infinite volume it is a\r\nclassical result of Patterson that the positive Laplace-Beltrami operator has\r\nno $L^2$-eigenvalues $\\geq 1/4$. In this article we prove a generalization of\r\nthis result for the joint $L^2$-eigenvalues of the algebra of commuting\r\ndifferential operators on Riemannian locally symmetric spaces $\\Gamma\\backslash\r\nG/K$ of higher rank. We derive dynamical assumptions on the $\\Gamma$-action on\r\nthe geodesic and the Satake compactifications which imply the absence of the\r\ncorresponding principal eigenvalues. A large class of examples fulfilling these\r\nassumptions are the non-compact quotients by Anosov subgroups.","lang":"eng"}],"date_created":"2022-05-11T10:38:11Z","author":[{"first_name":"Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","id":"49178","full_name":"Weich, Tobias"},{"full_name":"Wolf, Lasse Lennart","id":"45027","last_name":"Wolf","first_name":"Lasse Lennart"}],"volume":403,"date_updated":"2024-02-06T20:52:40Z","doi":"https://doi.org/10.1007/s00220-023-04819-1","title":"Absence of principal eigenvalues for higher rank locally symmetric  spaces","publication_identifier":{"unknown":["1275-1295"]},"citation":{"mla":"Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for Higher Rank Locally Symmetric  Spaces.” <i>Communications in Mathematical Physics</i>, vol. 403, 2023, doi:<a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>.","bibtex":"@article{Weich_Wolf_2023, title={Absence of principal eigenvalues for higher rank locally symmetric  spaces}, volume={403}, DOI={<a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>}, journal={Communications in Mathematical Physics}, author={Weich, Tobias and Wolf, Lasse Lennart}, year={2023} }","short":"T. Weich, L.L. Wolf, Communications in Mathematical Physics 403 (2023).","apa":"Weich, T., &#38; Wolf, L. L. (2023). Absence of principal eigenvalues for higher rank locally symmetric  spaces. <i>Communications in Mathematical Physics</i>, <i>403</i>. <a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>","ama":"Weich T, Wolf LL. Absence of principal eigenvalues for higher rank locally symmetric  spaces. <i>Communications in Mathematical Physics</i>. 2023;403. doi:<a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>","chicago":"Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for Higher Rank Locally Symmetric  Spaces.” <i>Communications in Mathematical Physics</i> 403 (2023). <a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>.","ieee":"T. Weich and L. L. Wolf, “Absence of principal eigenvalues for higher rank locally symmetric  spaces,” <i>Communications in Mathematical Physics</i>, vol. 403, 2023, doi: <a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>."},"intvolume":"       403","year":"2023"},{"publication":"arXiv:2308.13463","type":"preprint","abstract":[{"lang":"eng","text":"We present a numerical algorithm for the computation of invariant Ruelle\r\ndistributions on convex co-compact hyperbolic surfaces. This is achieved by\r\nexploiting the connection between invariant Ruelle distributions and residues\r\nof meromorphically continued weighted zeta functions established by the authors\r\ntogether with Barkhofen (2021). To make this applicable for numerics we express\r\nthe weighted zeta as the logarithmic derivative of a suitable parameter\r\ndependent Fredholm determinant similar to Borthwick (2014). As an additional\r\ndifficulty our transfer operator has to include a contracting direction which\r\nwe account for with techniques developed by Rugh (1992). We achieve a further\r\nimprovement in convergence speed for our algorithm in the case of surfaces with\r\nadditional symmetries by proving and applying a symmetry reduction of weighted\r\nzeta functions."}],"status":"public","_id":"51206","external_id":{"arxiv":["2308.13463"]},"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","language":[{"iso":"eng"}],"year":"2023","citation":{"ieee":"P. Schütte and T. Weich, “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions,” <i>arXiv:2308.13463</i>. 2023.","chicago":"Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions.” <i>ArXiv:2308.13463</i>, 2023.","ama":"Schütte P, Weich T. Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions. <i>arXiv:230813463</i>. Published online 2023.","apa":"Schütte, P., &#38; Weich, T. (2023). Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions. In <i>arXiv:2308.13463</i>.","mla":"Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions.” <i>ArXiv:2308.13463</i>, 2023.","bibtex":"@article{Schütte_Weich_2023, title={Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions}, journal={arXiv:2308.13463}, author={Schütte, Philipp and Weich, Tobias}, year={2023} }","short":"P. Schütte, T. Weich, ArXiv:2308.13463 (2023)."},"date_updated":"2024-02-11T19:56:01Z","date_created":"2024-02-06T20:58:35Z","author":[{"first_name":"Philipp","id":"50168","full_name":"Schütte, Philipp","last_name":"Schütte"},{"first_name":"Tobias","full_name":"Weich, Tobias","id":"49178","orcid":"0000-0002-9648-6919","last_name":"Weich"}],"title":"Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions"},{"date_updated":"2024-02-19T06:30:26Z","author":[{"full_name":"Arends, Christian","id":"43994","last_name":"Arends","first_name":"Christian"},{"id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim"}],"volume":10,"doi":"10.5802/jep.220","publication_status":"published","publication_identifier":{"issn":["2429-7100"],"eissn":["2270-518X"]},"citation":{"apa":"Arends, C., &#38; Hilgert, J. (2023). Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters. <i>Journal de l’École Polytechnique — Mathématiques</i>, <i>10</i>, 335–403. <a href=\"https://doi.org/10.5802/jep.220\">https://doi.org/10.5802/jep.220</a>","bibtex":"@article{Arends_Hilgert_2023, title={Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters}, volume={10}, DOI={<a href=\"https://doi.org/10.5802/jep.220\">10.5802/jep.220</a>}, journal={Journal de l’École polytechnique — Mathématiques}, author={Arends, Christian and Hilgert, Joachim}, year={2023}, pages={335–403} }","short":"C. Arends, J. Hilgert, Journal de l’École Polytechnique — Mathématiques 10 (2023) 335–403.","mla":"Arends, Christian, and Joachim Hilgert. “Spectral Correspondences for Rank One Locally Symmetric Spaces: The Case of Exceptional Parameters.” <i>Journal de l’École Polytechnique — Mathématiques</i>, vol. 10, 2023, pp. 335–403, doi:<a href=\"https://doi.org/10.5802/jep.220\">10.5802/jep.220</a>.","ama":"Arends C, Hilgert J. Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters. <i>Journal de l’École polytechnique — Mathématiques</i>. 2023;10:335-403. doi:<a href=\"https://doi.org/10.5802/jep.220\">10.5802/jep.220</a>","chicago":"Arends, Christian, and Joachim Hilgert. “Spectral Correspondences for Rank One Locally Symmetric Spaces: The Case of Exceptional Parameters.” <i>Journal de l’École Polytechnique — Mathématiques</i> 10 (2023): 335–403. <a href=\"https://doi.org/10.5802/jep.220\">https://doi.org/10.5802/jep.220</a>.","ieee":"C. Arends and J. Hilgert, “Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters,” <i>Journal de l’École polytechnique — Mathématiques</i>, vol. 10, pp. 335–403, 2023, doi: <a href=\"https://doi.org/10.5802/jep.220\">10.5802/jep.220</a>."},"page":"335-403","intvolume":"        10","_id":"31210","user_id":"49063","department":[{"_id":"10"},{"_id":"548"},{"_id":"91"}],"type":"journal_article","status":"public","date_created":"2022-05-11T12:27:00Z","title":"Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters","year":"2023","external_id":{"arxiv":["2112.11073"]},"keyword":["Ruelle resonances","Poisson transforms","locally symmetric spaces","principal series representations"],"language":[{"iso":"eng"}],"publication":"Journal de l’École polytechnique — Mathématiques","abstract":[{"text":"In this paper we complete the program of relating the Laplace spectrum for\r\nrank one compact locally symmetric spaces with the first band Ruelle-Pollicott\r\nresonances of the geodesic flow on its sphere bundle. This program was started\r\nby Flaminio and Forni for hyperbolic surfaces, continued by Dyatlov, Faure and\r\nGuillarmou for real hyperbolic spaces and by Guillarmou, Hilgert and Weich for\r\ngeneral rank one spaces. Except for the case of hyperbolic surfaces a countable\r\nset of exceptional spectral parameters always left untreated since the\r\ncorresponding Poisson transforms are neither injective nor surjective. We use\r\nvector valued Poisson transforms to treat also the exceptional spectral\r\nparameters. For surfaces the exceptional spectral parameters lead to discrete\r\nseries representations of $\\mathrm{SL}(2,\\mathbb R)$. In higher dimensions the\r\nsituation is more complicated, but can be described completely.","lang":"eng"}]},{"language":[{"iso":"eng"}],"department":[{"_id":"10"},{"_id":"548"}],"user_id":"45027","_id":"53404","external_id":{"arxiv":["2311.11770"]},"status":"public","abstract":[{"lang":"eng","text":"In this short note we observe, on locally symmetric spaces of higher rank, a\r\nconnection between the growth indicator function introduced by Quint and the\r\nmodified critical exponent of the Poincar\\'e series equipped with the\r\npolyhedral distance. As a consequence, we provide a different characterization\r\nof the bottom of the $L^2$-spectrum of the Laplace-Beltrami operator in terms\r\nof the growth indicator function. Moreover, we explore the relationship between\r\nthese three objects and the temperedness."}],"publication":"arXiv:2311.11770","type":"preprint","title":"$L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces","date_created":"2024-04-10T13:45:59Z","author":[{"last_name":"Wolf","full_name":"Wolf, Lasse L.","first_name":"Lasse L."},{"full_name":"Zhang, Hong-Wei","last_name":"Zhang","first_name":"Hong-Wei"}],"date_updated":"2024-04-10T13:48:17Z","citation":{"ama":"Wolf LL, Zhang H-W. $L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces. <i>arXiv:231111770</i>. Published online 2023.","chicago":"Wolf, Lasse L., and Hong-Wei Zhang. “$L^2$-Spectrum, Growth Indicator Function and Critical Exponent on  Locally Symmetric Spaces.” <i>ArXiv:2311.11770</i>, 2023.","ieee":"L. L. Wolf and H.-W. Zhang, “$L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces,” <i>arXiv:2311.11770</i>. 2023.","bibtex":"@article{Wolf_Zhang_2023, title={$L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces}, journal={arXiv:2311.11770}, author={Wolf, Lasse L. and Zhang, Hong-Wei}, year={2023} }","mla":"Wolf, Lasse L., and Hong-Wei Zhang. “$L^2$-Spectrum, Growth Indicator Function and Critical Exponent on  Locally Symmetric Spaces.” <i>ArXiv:2311.11770</i>, 2023.","short":"L.L. Wolf, H.-W. Zhang, ArXiv:2311.11770 (2023).","apa":"Wolf, L. L., &#38; Zhang, H.-W. (2023). $L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces. In <i>arXiv:2311.11770</i>."},"year":"2023"},{"issue":"2","publication_identifier":{"issn":["1424-0637","1424-0661"]},"publication_status":"published","page":"1607-1656","intvolume":"        25","citation":{"mla":"Delarue, Benjamin, et al. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” <i>Annales Henri Poincaré</i>, vol. 25, no. 2, Springer Science and Business Media LLC, 2023, pp. 1607–56, doi:<a href=\"https://doi.org/10.1007/s00023-023-01379-x\">10.1007/s00023-023-01379-x</a>.","bibtex":"@article{Delarue_Schütte_Weich_2023, title={Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models}, volume={25}, DOI={<a href=\"https://doi.org/10.1007/s00023-023-01379-x\">10.1007/s00023-023-01379-x</a>}, number={2}, journal={Annales Henri Poincaré}, publisher={Springer Science and Business Media LLC}, author={Delarue, Benjamin and Schütte, Philipp and Weich, Tobias}, year={2023}, pages={1607–1656} }","short":"B. Delarue, P. Schütte, T. Weich, Annales Henri Poincaré 25 (2023) 1607–1656.","apa":"Delarue, B., Schütte, P., &#38; Weich, T. (2023). Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models. <i>Annales Henri Poincaré</i>, <i>25</i>(2), 1607–1656. <a href=\"https://doi.org/10.1007/s00023-023-01379-x\">https://doi.org/10.1007/s00023-023-01379-x</a>","ama":"Delarue B, Schütte P, Weich T. Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models. <i>Annales Henri Poincaré</i>. 2023;25(2):1607-1656. doi:<a href=\"https://doi.org/10.1007/s00023-023-01379-x\">10.1007/s00023-023-01379-x</a>","ieee":"B. Delarue, P. Schütte, and T. Weich, “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models,” <i>Annales Henri Poincaré</i>, vol. 25, no. 2, pp. 1607–1656, 2023, doi: <a href=\"https://doi.org/10.1007/s00023-023-01379-x\">10.1007/s00023-023-01379-x</a>.","chicago":"Delarue, Benjamin, Philipp Schütte, and Tobias Weich. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” <i>Annales Henri Poincaré</i> 25, no. 2 (2023): 1607–56. <a href=\"https://doi.org/10.1007/s00023-023-01379-x\">https://doi.org/10.1007/s00023-023-01379-x</a>."},"year":"2023","volume":25,"date_created":"2024-04-11T12:30:14Z","author":[{"first_name":"Benjamin","full_name":"Delarue, Benjamin","id":"70575","last_name":"Delarue"},{"full_name":"Schütte, Philipp","id":"50168","last_name":"Schütte","first_name":"Philipp"},{"last_name":"Weich","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","id":"49178","first_name":"Tobias"}],"date_updated":"2024-04-11T12:37:34Z","publisher":"Springer Science and Business Media LLC","doi":"10.1007/s00023-023-01379-x","title":"Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models","publication":"Annales Henri Poincaré","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"<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>"}],"department":[{"_id":"548"}],"user_id":"70575","_id":"53410","language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"]},{"status":"public","abstract":[{"text":"We compute a Riemann-Roch formula for the invariant Riemann-Roch number of a\r\nquantizable Hamiltonian $S^1$-manifold $(M,\\omega,\\mathcal{J})$ in terms of the\r\ngeometry of its symplectic quotient, allowing $0$ to be a singular value of the\r\nmoment map $\\mathcal{J}:M\\to\\mathbb{R}$. The formula involves a new explicit\r\nlocal invariant of the singularities. Our approach relies on a complete\r\nsingular stationary phase expansion of the associated Witten integral.","lang":"eng"}],"publication":"arXiv:2302.09894","type":"preprint","language":[{"iso":"eng"}],"department":[{"_id":"548"}],"user_id":"70575","external_id":{"arxiv":["2302.09894"]},"_id":"53411","citation":{"apa":"Delarue, B., Ioos, L., &#38; Ramacher, P. (2023). A Riemann-Roch formula for singular reductions by circle actions. In <i>arXiv:2302.09894</i>.","short":"B. Delarue, L. Ioos, P. Ramacher, ArXiv:2302.09894 (2023).","mla":"Delarue, Benjamin, et al. “A Riemann-Roch Formula for Singular Reductions by Circle Actions.” <i>ArXiv:2302.09894</i>, 2023.","bibtex":"@article{Delarue_Ioos_Ramacher_2023, title={A Riemann-Roch formula for singular reductions by circle actions}, journal={arXiv:2302.09894}, author={Delarue, Benjamin and Ioos, Louis and Ramacher, Pablo}, year={2023} }","chicago":"Delarue, Benjamin, Louis Ioos, and Pablo Ramacher. “A Riemann-Roch Formula for Singular Reductions by Circle Actions.” <i>ArXiv:2302.09894</i>, 2023.","ieee":"B. Delarue, L. Ioos, and P. Ramacher, “A Riemann-Roch formula for singular reductions by circle actions,” <i>arXiv:2302.09894</i>. 2023.","ama":"Delarue B, Ioos L, Ramacher P. A Riemann-Roch formula for singular reductions by circle actions. <i>arXiv:230209894</i>. Published online 2023."},"year":"2023","title":"A Riemann-Roch formula for singular reductions by circle actions","date_created":"2024-04-11T12:30:42Z","author":[{"full_name":"Delarue, Benjamin","id":"70575","last_name":"Delarue","first_name":"Benjamin"},{"last_name":"Ioos","full_name":"Ioos, Louis","first_name":"Louis"},{"first_name":"Pablo","full_name":"Ramacher, Pablo","last_name":"Ramacher"}],"date_updated":"2024-04-11T12:37:09Z"}]