---
_id: '59860'
abstract:
- lang: eng
  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."
author:
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Colin
  full_name: Guillarmou, Colin
  last_name: Guillarmou
- first_name: Daniel
  full_name: Monclair, Daniel
  last_name: Monclair
citation:
  ama: Delarue B, Guillarmou C, Monclair D. Spectra of Lorentzian quasi-Fuchsian manifolds.
    <i>arXiv:250421762</i>. Published online 2025.
  apa: Delarue, B., Guillarmou, C., &#38; Monclair, D. (2025). Spectra of Lorentzian
    quasi-Fuchsian manifolds. In <i>arXiv:2504.21762</i>.
  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} }'
  chicago: Delarue, Benjamin, Colin Guillarmou, and Daniel Monclair. “Spectra of Lorentzian
    Quasi-Fuchsian Manifolds.” <i>ArXiv:2504.21762</i>, 2025.
  ieee: B. Delarue, C. Guillarmou, and D. Monclair, “Spectra of Lorentzian quasi-Fuchsian
    manifolds,” <i>arXiv:2504.21762</i>. 2025.
  mla: Delarue, Benjamin, et al. “Spectra of Lorentzian Quasi-Fuchsian Manifolds.”
    <i>ArXiv:2504.21762</i>, 2025.
  short: B. Delarue, C. Guillarmou, D. Monclair, ArXiv:2504.21762 (2025).
date_created: 2025-05-12T08:17:23Z
date_updated: 2025-05-12T08:18:06Z
external_id:
  arxiv:
  - '2504.21762'
language:
- iso: eng
publication: arXiv:2504.21762
status: public
title: Spectra of Lorentzian quasi-Fuchsian manifolds
type: preprint
user_id: '70575'
year: '2025'
...
---
_id: '58872'
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 $G$."
author:
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Daniel
  full_name: Monclair, Daniel
  last_name: Monclair
- first_name: Andrew
  full_name: Sanders, Andrew
  last_name: Sanders
citation:
  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.'
  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>.'
  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}
    }'
  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.'
  mla: 'Delarue, Benjamin, et al. “Locally Homogeneous Axiom A Flows II: Geometric
    Structures for Anosov  Subgroups.” <i>ArXiv:2502.20195</i>, 2025.'
  short: B. Delarue, D. Monclair, A. Sanders, ArXiv:2502.20195 (2025).
date_created: 2025-02-28T10:31:36Z
date_updated: 2025-02-28T10:33:03Z
external_id:
  arxiv:
  - '2502.20195'
language:
- iso: eng
publication: arXiv:2502.20195
status: public
title: 'Locally homogeneous Axiom A flows II: geometric structures for Anosov  subgroups'
type: preprint
user_id: '70575'
year: '2025'
...
---
_id: '53414'
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."
article_type: original
author:
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Daniel
  full_name: Monclair, Daniel
  last_name: Monclair
- first_name: Andrew
  full_name: Sanders, Andrew
  last_name: Sanders
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>'
  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>'
  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} }'
  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>.'
  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>.'
  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.
date_created: 2024-04-11T12:31:34Z
date_updated: 2026-01-09T09:25:45Z
department:
- _id: '548'
doi: 10.1007/s00039-025-00712-2
intvolume: '        35'
language:
- iso: eng
page: 673–735
publication: Geometric and Functional Analysis (GAFA)
publication_status: published
status: public
title: 'Locally homogeneous Axiom A flows I: projective Anosov subgroups and exponential
  mixing'
type: journal_article
user_id: '70575'
volume: 35
year: '2025'
...
---
_id: '53412'
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."
article_type: original
author:
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Pablo
  full_name: Ramacher, Pablo
  last_name: Ramacher
- first_name: Maximilian
  full_name: Schmitt, Maximilian
  last_name: Schmitt
citation:
  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>
  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>
  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} }'
  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>.'
  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>.
  short: B. Delarue, P. Ramacher, M. Schmitt, Transformation Groups (2025).
date_created: 2024-04-11T12:30:59Z
date_updated: 2026-01-09T09:27:08Z
department:
- _id: '548'
doi: 10.1007/s00031-025-09924-0
language:
- iso: eng
publication: Transformation Groups
publication_status: epub_ahead
status: public
title: Singular cohomology of symplectic quotients by circle actions and Kirwan  surjectivity
type: journal_article
user_id: '70575'
year: '2025'
...
---
_id: '53413'
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."
article_type: original
author:
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  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}
    }'
  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.
  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.
date_created: 2024-04-11T12:31:18Z
date_updated: 2026-03-31T09:07:17Z
department:
- _id: '548'
intvolume: '        35'
issue: (4)
language:
- iso: eng
page: 787--804
publication: Journal of Lie Theory
publication_identifier:
  issn:
  - 0949-5932
publication_status: inpress
status: public
title: Quantum resonances and scattering poles of classical rank one locally  symmetric
  spaces
type: journal_article
user_id: '220'
volume: 35
year: '2025'
...
---
_id: '58873'
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."
author:
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Guendalina
  full_name: Palmirotta, Guendalina
  id: '109467'
  last_name: Palmirotta
citation:
  ama: Delarue B, Palmirotta G. Patterson-Sullivan and Wigner distributions of convex-cocompact 
    hyperbolic surfaces. <i>arXiv:241119782</i>. Published online 2024.
  apa: Delarue, B., &#38; Palmirotta, G. (2024). Patterson-Sullivan and Wigner distributions
    of convex-cocompact  hyperbolic surfaces. In <i>arXiv:2411.19782</i>.
  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} }'
  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.
  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).
date_created: 2025-02-28T10:32:30Z
date_updated: 2026-03-30T12:01:12Z
department:
- _id: '548'
external_id:
  arxiv:
  - '2411.19782'
language:
- iso: eng
project:
- _id: '356'
  name: 'TRR 358; TP B02: Spektraltheorie in höherem Rang und unendlichem Volumen'
publication: arXiv:2411.19782
status: public
title: Patterson-Sullivan and Wigner distributions of convex-cocompact  hyperbolic
  surfaces
type: preprint
user_id: '109467'
year: '2024'
...
---
_id: '53410'
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>
author:
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Philipp
  full_name: Schütte, Philipp
  id: '50168'
  last_name: Schütte
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  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>
  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} }'
  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>.'
  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>.'
  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>.
  short: B. Delarue, P. Schütte, T. Weich, Annales Henri Poincaré 25 (2023) 1607–1656.
date_created: 2024-04-11T12:30:14Z
date_updated: 2024-04-11T12:37:34Z
department:
- _id: '548'
doi: 10.1007/s00023-023-01379-x
intvolume: '        25'
issue: '2'
keyword:
- Mathematical Physics
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 1607-1656
publication: Annales Henri Poincaré
publication_identifier:
  issn:
  - 1424-0637
  - 1424-0661
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models
type: journal_article
user_id: '70575'
volume: 25
year: '2023'
...
---
_id: '53411'
abstract:
- lang: eng
  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."
author:
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Louis
  full_name: Ioos, Louis
  last_name: Ioos
- first_name: Pablo
  full_name: Ramacher, Pablo
  last_name: Ramacher
citation:
  ama: Delarue B, Ioos L, Ramacher P. A Riemann-Roch formula for singular reductions
    by circle actions. <i>arXiv:230209894</i>. Published online 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>.
  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.
  mla: Delarue, Benjamin, et al. “A Riemann-Roch Formula for Singular Reductions by
    Circle Actions.” <i>ArXiv:2302.09894</i>, 2023.
  short: B. Delarue, L. Ioos, P. Ramacher, ArXiv:2302.09894 (2023).
date_created: 2024-04-11T12:30:42Z
date_updated: 2024-04-11T12:37:09Z
department:
- _id: '548'
external_id:
  arxiv:
  - '2302.09894'
language:
- iso: eng
publication: arXiv:2302.09894
status: public
title: A Riemann-Roch formula for singular reductions by circle actions
type: preprint
user_id: '70575'
year: '2023'
...
---
_id: '31982'
abstract:
- lang: eng
  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>"
author:
- first_name: Mihajlo
  full_name: Cekić, Mihajlo
  last_name: Cekić
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Semyon
  full_name: Dyatlov, Semyon
  last_name: Dyatlov
- first_name: Gabriel P.
  full_name: Paternain, Gabriel P.
  last_name: Paternain
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>
  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} }'
  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>.'
  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>.
  short: M. Cekić, B. Delarue, S. Dyatlov, G.P. Paternain, Inventiones Mathematicae
    229 (2022) 303–394.
date_created: 2022-06-20T08:24:17Z
date_updated: 2022-06-21T11:55:15Z
department:
- _id: '548'
doi: 10.1007/s00222-022-01108-x
intvolume: '       229'
issue: '1'
keyword:
- General Mathematics
language:
- iso: eng
page: 303-394
publication: Inventiones mathematicae
publication_identifier:
  issn:
  - 0020-9910
  - 1432-1297
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
type: journal_article
user_id: '70575'
volume: 229
year: '2022'
...
---
_id: '32016'
article_type: original
author:
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Pablo
  full_name: Ramacher, Pablo
  last_name: Ramacher
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>
  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>
  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} }'
  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>.'
  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>.'
  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>.
  short: B. Delarue, P. Ramacher, Journal of Symplectic Geometry 19 (2021) 1281–1337.
date_created: 2022-06-20T08:46:56Z
date_updated: 2022-06-21T11:54:50Z
department:
- _id: '548'
doi: 10.4310/JSG.2021.v19.n6.a1
intvolume: '        19'
issue: '6'
language:
- iso: eng
page: 1281 - 1337
publication: Journal of Symplectic Geometry
publication_identifier:
  unknown:
  - 1540-2347
  - 1527-5256
publication_status: published
status: public
title: Asymptotic expansion of generalized Witten integrals for Hamiltonian circle
  actions
type: journal_article
user_id: '70575'
volume: 19
year: '2021'
...