[{"year":"2025","citation":{"bibtex":"@article{Delarue_Guillarmou_Monclair_2025, title={Spectra of Lorentzian quasi-Fuchsian manifolds}, journal={arXiv:2504.21762}, author={Delarue, Benjamin and Guillarmou, Colin and Monclair, Daniel}, year={2025} }","short":"B. Delarue, C. Guillarmou, D. Monclair, ArXiv:2504.21762 (2025).","mla":"Delarue, Benjamin, et al. “Spectra of Lorentzian Quasi-Fuchsian Manifolds.” <i>ArXiv:2504.21762</i>, 2025.","apa":"Delarue, B., Guillarmou, C., &#38; Monclair, D. (2025). Spectra of Lorentzian quasi-Fuchsian manifolds. In <i>arXiv:2504.21762</i>.","ama":"Delarue B, Guillarmou C, Monclair D. Spectra of Lorentzian quasi-Fuchsian manifolds. <i>arXiv:250421762</i>. Published online 2025.","ieee":"B. Delarue, C. Guillarmou, and D. Monclair, “Spectra of Lorentzian quasi-Fuchsian manifolds,” <i>arXiv:2504.21762</i>. 2025.","chicago":"Delarue, Benjamin, Colin Guillarmou, and Daniel Monclair. “Spectra of Lorentzian Quasi-Fuchsian Manifolds.” <i>ArXiv:2504.21762</i>, 2025."},"date_updated":"2025-05-12T08:18:06Z","author":[{"last_name":"Delarue","id":"70575","full_name":"Delarue, Benjamin","first_name":"Benjamin"},{"full_name":"Guillarmou, Colin","last_name":"Guillarmou","first_name":"Colin"},{"last_name":"Monclair","full_name":"Monclair, Daniel","first_name":"Daniel"}],"date_created":"2025-05-12T08:17:23Z","title":"Spectra of Lorentzian quasi-Fuchsian manifolds","publication":"arXiv:2504.21762","type":"preprint","abstract":[{"text":"A three-dimensional quasi-Fuchsian Lorentzian manifold $M$ is a globally\r\nhyperbolic spacetime diffeomorphic to $\\Sigma\\times (-1,1)$ for a closed\r\norientable surface $\\Sigma$ of genus $\\geq 2$. It is the quotient\r\n$M=\\Gamma\\backslash \\Omega_\\Gamma$ of an open set $\\Omega_\\Gamma\\subset {\\rm\r\nAdS}_3$ by a discrete group $\\Gamma$ of isometries of ${\\rm AdS}_3$ which is a\r\nparticular example of an Anosov representation of $\\pi_1(\\Sigma)$. We first\r\nshow that the spacelike geodesic flow of $M$ is Axiom A, has a discrete Ruelle\r\nresonance spectrum with associated (co-)resonant states, and that the\r\nPoincar\\'e series for $\\Gamma$ extend meromorphically to $\\mathbb{C}$. This is\r\nthen used to prove that there is a natural notion of resolvent of the\r\npseudo-Riemannian Laplacian $\\Box$ of $M$, which is meromorphic on $\\mathbb{C}$\r\nwith poles of finite rank, defining a notion of quantum resonances and quantum\r\nresonant states related to the Ruelle resonances and (co-)resonant states by a\r\nquantum-classical correspondence. This initiates the spectral study of convex\r\nco-compact pseudo-Riemannian locally symmetric spaces.","lang":"eng"}],"status":"public","_id":"59860","external_id":{"arxiv":["2504.21762"]},"user_id":"70575","language":[{"iso":"eng"}]},{"author":[{"full_name":"Delarue, Benjamin","id":"70575","last_name":"Delarue","first_name":"Benjamin"},{"first_name":"Daniel","last_name":"Monclair","full_name":"Monclair, Daniel"},{"first_name":"Andrew","last_name":"Sanders","full_name":"Sanders, Andrew"}],"date_created":"2025-02-28T10:31:36Z","date_updated":"2025-02-28T10:33:03Z","title":"Locally homogeneous Axiom A flows II: geometric structures for Anosov  subgroups","citation":{"bibtex":"@article{Delarue_Monclair_Sanders_2025, title={Locally homogeneous Axiom A flows II: geometric structures for Anosov  subgroups}, journal={arXiv:2502.20195}, author={Delarue, Benjamin and Monclair, Daniel and Sanders, Andrew}, year={2025} }","short":"B. Delarue, D. Monclair, A. Sanders, ArXiv:2502.20195 (2025).","mla":"Delarue, Benjamin, et al. “Locally Homogeneous Axiom A Flows II: Geometric Structures for Anosov  Subgroups.” <i>ArXiv:2502.20195</i>, 2025.","apa":"Delarue, B., Monclair, D., &#38; Sanders, A. (2025). Locally homogeneous Axiom A flows II: geometric structures for Anosov  subgroups. In <i>arXiv:2502.20195</i>.","chicago":"Delarue, Benjamin, Daniel Monclair, and Andrew Sanders. “Locally Homogeneous Axiom A Flows II: Geometric Structures for Anosov  Subgroups.” <i>ArXiv:2502.20195</i>, 2025.","ieee":"B. Delarue, D. Monclair, and A. Sanders, “Locally homogeneous Axiom A flows II: geometric structures for Anosov  subgroups,” <i>arXiv:2502.20195</i>. 2025.","ama":"Delarue B, Monclair D, Sanders A. Locally homogeneous Axiom A flows II: geometric structures for Anosov  subgroups. <i>arXiv:250220195</i>. Published online 2025."},"year":"2025","user_id":"70575","external_id":{"arxiv":["2502.20195"]},"_id":"58872","language":[{"iso":"eng"}],"publication":"arXiv:2502.20195","type":"preprint","status":"public","abstract":[{"lang":"eng","text":"Given a non-compact semisimple real Lie group $G$ and an Anosov subgroup\r\n$\\Gamma$, we utilize the correspondence between $\\mathbb R$-valued additive\r\ncharacters on Levi subgroups $L$ of $G$ and $\\mathbb R$-affine homogeneous line\r\nbundles over $G/L$ to systematically construct families of non-empty domains of\r\nproper discontinuity for the $\\Gamma$-action. If $\\Gamma$ is torsion-free, the\r\nanalytic dynamical systems on the quotients are Axiom A, and assemble into a\r\nsingle partially hyperbolic multiflow. Each Axiom A system admits global\r\nanalytic stable/unstable foliations with non-wandering set a single basic set\r\non which the flow is conjugate to Sambarino's refraction flow, establishing\r\nthat all refraction flows arise in this fashion. Furthermore, the $\\mathbb\r\nR$-valued additive character is regular if and only if the associated Axiom A\r\nsystem admits a compatible pseudo-Riemannian metric and contact structure,\r\nwhich we relate to the Poisson structure on the dual of the Lie algebra of $G$."}]},{"language":[{"iso":"eng"}],"article_type":"original","department":[{"_id":"548"}],"user_id":"70575","_id":"53414","status":"public","abstract":[{"lang":"eng","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."}],"publication":"Geometric and Functional Analysis (GAFA)","type":"journal_article","doi":"10.1007/s00039-025-00712-2","title":"Locally homogeneous Axiom A flows I: projective Anosov subgroups and exponential mixing","volume":35,"date_created":"2024-04-11T12:31:34Z","author":[{"last_name":"Delarue","id":"70575","full_name":"Delarue, Benjamin","first_name":"Benjamin"},{"first_name":"Daniel","full_name":"Monclair, Daniel","last_name":"Monclair"},{"last_name":"Sanders","full_name":"Sanders, Andrew","first_name":"Andrew"}],"date_updated":"2026-01-09T09:25:45Z","intvolume":"        35","page":"673–735","citation":{"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>.","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} }","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>","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>.","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>"},"year":"2025","publication_status":"published"},{"type":"journal_article","publication":"Transformation Groups","status":"public","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."}],"user_id":"70575","department":[{"_id":"548"}],"_id":"53412","language":[{"iso":"eng"}],"article_type":"original","publication_status":"epub_ahead","citation":{"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>","short":"B. Delarue, P. Ramacher, M. Schmitt, Transformation Groups (2025).","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} }","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>.","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>.","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>.","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>"},"year":"2025","date_created":"2024-04-11T12:30:59Z","author":[{"first_name":"Benjamin","id":"70575","full_name":"Delarue, Benjamin","last_name":"Delarue"},{"full_name":"Ramacher, Pablo","last_name":"Ramacher","first_name":"Pablo"},{"last_name":"Schmitt","full_name":"Schmitt, Maximilian","first_name":"Maximilian"}],"date_updated":"2026-01-09T09:27:08Z","doi":"10.1007/s00031-025-09924-0","title":"Singular cohomology of symplectic quotients by circle actions and Kirwan  surjectivity"},{"language":[{"iso":"eng"}],"article_type":"original","user_id":"220","department":[{"_id":"548"}],"_id":"53413","status":"public","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."}],"type":"journal_article","publication":"Journal of Lie Theory","title":"Quantum resonances and scattering poles of classical rank one locally  symmetric spaces","date_created":"2024-04-11T12:31:18Z","author":[{"first_name":"Benjamin","id":"70575","full_name":"Delarue, Benjamin","last_name":"Delarue"},{"first_name":"Joachim","last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220"}],"volume":35,"date_updated":"2026-03-31T09:07:17Z","citation":{"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.","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.","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.","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.","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} }","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.","short":"B. Delarue, J. Hilgert, Journal of Lie Theory 35 (n.d.) 787--804."},"intvolume":"        35","page":"787--804","year":"2025","issue":"(4)","publication_status":"inpress","publication_identifier":{"issn":["0949-5932"]}},{"type":"preprint","publication":"arXiv:2411.19782","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"}],"status":"public","project":[{"name":"TRR 358; TP B02: Spektraltheorie in höherem Rang und unendlichem Volumen","_id":"356"}],"_id":"58873","external_id":{"arxiv":["2411.19782"]},"user_id":"109467","department":[{"_id":"548"}],"language":[{"iso":"eng"}],"year":"2024","citation":{"apa":"Delarue, B., &#38; Palmirotta, G. (2024). Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces. In <i>arXiv:2411.19782</i>.","mla":"Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner Distributions of Convex-Cocompact  Hyperbolic Surfaces.” <i>ArXiv:2411.19782</i>, 2024.","short":"B. Delarue, G. Palmirotta, ArXiv:2411.19782 (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} }","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."},"date_updated":"2026-03-30T12:01:12Z","date_created":"2025-02-28T10:32:30Z","author":[{"full_name":"Delarue, Benjamin","id":"70575","last_name":"Delarue","first_name":"Benjamin"},{"last_name":"Palmirotta","id":"109467","full_name":"Palmirotta, Guendalina","first_name":"Guendalina"}],"title":"Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic surfaces"},{"year":"2023","citation":{"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>.","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>","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>","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."},"page":"1607-1656","intvolume":"        25","publication_status":"published","publication_identifier":{"issn":["1424-0637","1424-0661"]},"issue":"2","title":"Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models","doi":"10.1007/s00023-023-01379-x","publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-11T12:37:34Z","author":[{"first_name":"Benjamin","last_name":"Delarue","id":"70575","full_name":"Delarue, Benjamin"},{"id":"50168","full_name":"Schütte, Philipp","last_name":"Schütte","first_name":"Philipp"},{"first_name":"Tobias","id":"49178","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich"}],"date_created":"2024-04-11T12:30:14Z","volume":25,"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>"}],"status":"public","type":"journal_article","publication":"Annales Henri Poincaré","keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"_id":"53410","user_id":"70575","department":[{"_id":"548"}]},{"title":"A Riemann-Roch formula for singular reductions by circle actions","date_created":"2024-04-11T12:30:42Z","author":[{"first_name":"Benjamin","last_name":"Delarue","id":"70575","full_name":"Delarue, Benjamin"},{"full_name":"Ioos, Louis","last_name":"Ioos","first_name":"Louis"},{"full_name":"Ramacher, Pablo","last_name":"Ramacher","first_name":"Pablo"}],"date_updated":"2024-04-11T12:37:09Z","citation":{"short":"B. Delarue, L. Ioos, P. Ramacher, ArXiv:2302.09894 (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} }","mla":"Delarue, Benjamin, et al. “A Riemann-Roch Formula for Singular Reductions by Circle Actions.” <i>ArXiv:2302.09894</i>, 2023.","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>.","ieee":"B. Delarue, L. Ioos, and P. Ramacher, “A Riemann-Roch formula for singular reductions by circle actions,” <i>arXiv:2302.09894</i>. 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.","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","language":[{"iso":"eng"}],"department":[{"_id":"548"}],"user_id":"70575","external_id":{"arxiv":["2302.09894"]},"_id":"53411","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"},{"date_updated":"2022-06-21T11:55:15Z","publisher":"Springer Science and Business Media LLC","volume":229,"date_created":"2022-06-20T08:24:17Z","author":[{"first_name":"Mihajlo","full_name":"Cekić, Mihajlo","last_name":"Cekić"},{"first_name":"Benjamin","last_name":"Delarue","full_name":"Delarue, Benjamin","id":"70575"},{"first_name":"Semyon","full_name":"Dyatlov, Semyon","last_name":"Dyatlov"},{"last_name":"Paternain","full_name":"Paternain, Gabriel P.","first_name":"Gabriel P."}],"title":"The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds","doi":"10.1007/s00222-022-01108-x","publication_identifier":{"issn":["0020-9910","1432-1297"]},"publication_status":"published","issue":"1","year":"2022","intvolume":"       229","page":"303-394","citation":{"ama":"Cekić M, Delarue B, Dyatlov S, Paternain GP. The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds. <i>Inventiones mathematicae</i>. 2022;229(1):303-394. doi:<a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>","chicago":"Cekić, Mihajlo, Benjamin Delarue, Semyon Dyatlov, and Gabriel P. Paternain. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” <i>Inventiones Mathematicae</i> 229, no. 1 (2022): 303–94. <a href=\"https://doi.org/10.1007/s00222-022-01108-x\">https://doi.org/10.1007/s00222-022-01108-x</a>.","ieee":"M. Cekić, B. Delarue, S. Dyatlov, and G. P. Paternain, “The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds,” <i>Inventiones mathematicae</i>, vol. 229, no. 1, pp. 303–394, 2022, doi: <a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>.","apa":"Cekić, M., Delarue, B., Dyatlov, S., &#38; Paternain, G. P. (2022). The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds. <i>Inventiones Mathematicae</i>, <i>229</i>(1), 303–394. <a href=\"https://doi.org/10.1007/s00222-022-01108-x\">https://doi.org/10.1007/s00222-022-01108-x</a>","bibtex":"@article{Cekić_Delarue_Dyatlov_Paternain_2022, title={The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds}, volume={229}, DOI={<a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>}, number={1}, journal={Inventiones mathematicae}, publisher={Springer Science and Business Media LLC}, author={Cekić, Mihajlo and Delarue, Benjamin and Dyatlov, Semyon and Paternain, Gabriel P.}, year={2022}, pages={303–394} }","short":"M. Cekić, B. Delarue, S. Dyatlov, G.P. Paternain, Inventiones Mathematicae 229 (2022) 303–394.","mla":"Cekić, Mihajlo, et al. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” <i>Inventiones Mathematicae</i>, vol. 229, no. 1, Springer Science and Business Media LLC, 2022, pp. 303–94, doi:<a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>."},"_id":"31982","department":[{"_id":"548"}],"user_id":"70575","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"publication":"Inventiones mathematicae","type":"journal_article","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>We show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Sigma $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>Σ</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula> with Betti number <jats:inline-formula><jats:alternatives><jats:tex-math>$$b_1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msub>\r\n                    <mml:mi>b</mml:mi>\r\n                    <mml:mn>1</mml:mn>\r\n                  </mml:msub>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, the order of vanishing of the Ruelle zeta function at zero equals <jats:inline-formula><jats:alternatives><jats:tex-math>$$4-b_1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mn>4</mml:mn>\r\n                    <mml:mo>-</mml:mo>\r\n                    <mml:msub>\r\n                      <mml:mi>b</mml:mi>\r\n                      <mml:mn>1</mml:mn>\r\n                    </mml:msub>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, while in the hyperbolic case it is equal to <jats:inline-formula><jats:alternatives><jats:tex-math>$$4-2b_1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mn>4</mml:mn>\r\n                    <mml:mo>-</mml:mo>\r\n                    <mml:mn>2</mml:mn>\r\n                    <mml:msub>\r\n                      <mml:mi>b</mml:mi>\r\n                      <mml:mn>1</mml:mn>\r\n                    </mml:msub>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>. This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott–Ruelle resonant differential forms at 0 in the hyperbolic case and using first variation for the perturbation. To show that the first variation is generically nonzero we introduce a new identity relating pushforwards of products of resonant and coresonant 2-forms on the sphere bundle <jats:inline-formula><jats:alternatives><jats:tex-math>$$S\\Sigma $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>S</mml:mi>\r\n                    <mml:mi>Σ</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> with harmonic 1-forms on <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Sigma $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>Σ</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula>.</jats:p>","lang":"eng"}],"status":"public"},{"date_updated":"2022-06-21T11:54:50Z","volume":19,"date_created":"2022-06-20T08:46:56Z","author":[{"first_name":"Benjamin","last_name":"Delarue","id":"70575","full_name":"Delarue, Benjamin"},{"first_name":"Pablo","full_name":"Ramacher, Pablo","last_name":"Ramacher"}],"title":"Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions","doi":"10.4310/JSG.2021.v19.n6.a1","publication_identifier":{"unknown":["1540-2347","1527-5256"]},"publication_status":"published","issue":"6","year":"2021","intvolume":"        19","page":"1281 - 1337","citation":{"ama":"Delarue B, Ramacher P. Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions. <i>Journal of Symplectic Geometry</i>. 2021;19(6):1281-1337. doi:<a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">10.4310/JSG.2021.v19.n6.a1</a>","ieee":"B. Delarue and P. Ramacher, “Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions,” <i>Journal of Symplectic Geometry</i>, vol. 19, no. 6, pp. 1281–1337, 2021, doi: <a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">10.4310/JSG.2021.v19.n6.a1</a>.","chicago":"Delarue, Benjamin, and Pablo Ramacher. “Asymptotic Expansion of Generalized Witten Integrals for Hamiltonian Circle Actions.” <i>Journal of Symplectic Geometry</i> 19, no. 6 (2021): 1281–1337. <a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">https://doi.org/10.4310/JSG.2021.v19.n6.a1</a>.","apa":"Delarue, B., &#38; Ramacher, P. (2021). Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions. <i>Journal of Symplectic Geometry</i>, <i>19</i>(6), 1281–1337. <a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">https://doi.org/10.4310/JSG.2021.v19.n6.a1</a>","short":"B. Delarue, P. Ramacher, Journal of Symplectic Geometry 19 (2021) 1281–1337.","bibtex":"@article{Delarue_Ramacher_2021, title={Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions}, volume={19}, DOI={<a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">10.4310/JSG.2021.v19.n6.a1</a>}, number={6}, journal={Journal of Symplectic Geometry}, author={Delarue, Benjamin and Ramacher, Pablo}, year={2021}, pages={1281–1337} }","mla":"Delarue, Benjamin, and Pablo Ramacher. “Asymptotic Expansion of Generalized Witten Integrals for Hamiltonian Circle Actions.” <i>Journal of Symplectic Geometry</i>, vol. 19, no. 6, 2021, pp. 1281–337, doi:<a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">10.4310/JSG.2021.v19.n6.a1</a>."},"_id":"32016","department":[{"_id":"548"}],"user_id":"70575","article_type":"original","language":[{"iso":"eng"}],"publication":"Journal of Symplectic Geometry","type":"journal_article","status":"public"}]