---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '21343'
abstract:
- lang: eng
  text: "The large sieve is used to estimate the density of quadratic polynomials
    Q ∈ Z[x],\r\nsuch that there exists an odd degree polynomial defined over Z which
    has resultant ±1 with Q.\r\nGiven a monic polynomial R ∈ Z[x] of odd degree, this
    is used to show that for almost all\r\nquadratic polynomials Q ∈ Z[x], there exists
    a prime p such that Q and R share a common\r\nroot in Fp. Using recent work of
    Landesman, an application to the average size of the odd part\r\nof the class
    group of quadratic number fields is also given"
- lang: fre
  text: ' Le grand crible est utilisé pour estimer la densité des polynômes quadratiques
    Q ∈ Z[x] tels qu’il existe un polynôme de degré impair défini sur Z dont le résultant
    avec Q est égal à ±1. Étant donné un polynôme unitaire R ∈ Z[x] de degré impair,
    on s’en sert pour montrer que, pour presque tous les polynômes quadratiques Q
    ∈ Z[x], il existe un nombre premier p tel que Q et R aient une racine commune
    dans Fp. En utilisant des travaux récents de Landesman, on obtient également une
    application concernant la taille moyenne de la partie impaire du groupe de classe
    des corps quadratiques.'
acknowledgement: While working on this paper, the first author was supported by a
  FWF grant (DOI 10.55776/P36278).
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Timothy D
  full_name: Browning, Timothy D
  id: 35827D50-F248-11E8-B48F-1D18A9856A87
  last_name: Browning
  orcid: 0000-0002-8314-0177
- first_name: Yik Tung
  full_name: Chan, Yik Tung
  id: c4c0afc8-9262-11ed-9231-d8b0bc743af1
  last_name: Chan
  orcid: 0000-0001-8467-4106
citation:
  ama: Browning TD, Chan S. Solubility of a resultant equation and applications. <i>Journal
    de l’ecole polytechnique mathematiques</i>. 2025;12:1677-1691. doi:<a href="https://doi.org/10.5802/jep.320">10.5802/jep.320</a>
  apa: Browning, T. D., &#38; Chan, S. (2025). Solubility of a resultant equation
    and applications. <i>Journal de l’ecole Polytechnique Mathematiques</i>. Ecole
    polytechnique. <a href="https://doi.org/10.5802/jep.320">https://doi.org/10.5802/jep.320</a>
  chicago: Browning, Timothy D, and Stephanie Chan. “Solubility of a Resultant Equation
    and Applications.” <i>Journal de l’ecole Polytechnique Mathematiques</i>. Ecole
    polytechnique, 2025. <a href="https://doi.org/10.5802/jep.320">https://doi.org/10.5802/jep.320</a>.
  ieee: T. D. Browning and S. Chan, “Solubility of a resultant equation and applications,”
    <i>Journal de l’ecole polytechnique mathematiques</i>, vol. 12. Ecole polytechnique,
    pp. 1677–1691, 2025.
  ista: Browning TD, Chan S. 2025. Solubility of a resultant equation and applications.
    Journal de l’ecole polytechnique mathematiques. 12, 1677–1691.
  mla: Browning, Timothy D., and Stephanie Chan. “Solubility of a Resultant Equation
    and Applications.” <i>Journal de l’ecole Polytechnique Mathematiques</i>, vol.
    12, Ecole polytechnique, 2025, pp. 1677–91, doi:<a href="https://doi.org/10.5802/jep.320">10.5802/jep.320</a>.
  short: T.D. Browning, S. Chan, Journal de l’ecole Polytechnique Mathematiques 12
    (2025) 1677–1691.
corr_author: '1'
date_created: 2026-02-22T23:01:36Z
date_published: 2025-10-21T00:00:00Z
date_updated: 2026-02-24T07:57:53Z
day: '21'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.5802/jep.320
external_id:
  arxiv:
  - '2411.09264'
file:
- access_level: open_access
  checksum: 828577ea48ac6109d3e9dd1aeddd45c4
  content_type: application/pdf
  creator: dernst
  date_created: 2026-02-24T07:56:34Z
  date_updated: 2026-02-24T07:56:34Z
  file_id: '21356'
  file_name: 2025_JEP_Browning.pdf
  file_size: 1003689
  relation: main_file
  success: 1
file_date_updated: 2026-02-24T07:56:34Z
has_accepted_license: '1'
intvolume: '        12'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1677-1691
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
  grant_number: P36278
  name: Rational curves via function field analytic number theory
publication: Journal de l'ecole polytechnique mathematiques
publication_identifier:
  eissn:
  - 2270-518X
  issn:
  - 2429-7100
publication_status: published
publisher: Ecole polytechnique
quality_controlled: '1'
scopus_import: '1'
status: public
title: Solubility of a resultant equation and applications
tmp:
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  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12
year: '2025'
...
---
_id: '18158'
abstract:
- lang: eng
  text: "We study the geometry of Poisson point processes from the point of view of
    optimal transport and Ricci lower bounds. We construct a Riemannian structure
    on the space of point processes and the associated distance W that corresponds
    to the Benamou–Brenier variational formula. Our main tool is a non-local continuity
    equation formulated with the difference operator. The closure of the domain of
    the relative entropy is a complete geodesic space, when endowed with \r\nW. The
    geometry of this non-local infinite-dimensional space is analogous to that of
    spaces with positive Ricci curvature. Among others: (a) the Ornstein–Uhlenbeck
    semi-group is the gradient flow of the relative entropy; (b) the Poisson space
    has an entropic Ricci curvature bounded from below by 1; (c) W satisfies an HWI
    inequality."
- lang: fre
  text: "Nous étudions la géométrie des processus ponctuels de Poisson à travers le
    prisme du transport optimal et de la minoration de la courbure de Ricci. Nous
    construisons une structure\r\nriemannienne sur l’espace des processus ponctuels
    et la distance associée W qui concorde avec la formulation variationnelle de Benamou–Brenier.
    Notre analyse repose sur une équation de continuité non locale définie à l’aide
    de l’opérateur de différence. La fermeture du domaine de l’entropie relative,
    équipé de W, est un espace géodésique complet. La géométrie de cet espace non
    local et de dimension infinie est analogue à celle des espaces à courbure de Ricci
    strictement positive. Entre autres : (a) le semi-groupe d’Ornstein–Uhlenbeck est
    le flot du gradient de l’entropie relative ; (b) l’espace de Poisson a une courbure
    de Ricci entropique minorée par 1 ; (c) W satisfait une inégalité HWI."
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
  full_name: Dello Schiavo, Lorenzo
  id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
  last_name: Dello Schiavo
  orcid: 0000-0002-9881-6870
- first_name: Ronan
  full_name: Herry, Ronan
  last_name: Herry
- first_name: Kohei
  full_name: Suzuki, Kohei
  last_name: Suzuki
citation:
  ama: Dello Schiavo L, Herry R, Suzuki K. Wasserstein geometry and Ricci curvature
    bounds for Poisson spaces. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>.
    2024;11:957-1010. doi:<a href="https://doi.org/10.5802/jep.270">10.5802/jep.270</a>
  apa: Dello Schiavo, L., Herry, R., &#38; Suzuki, K. (2024). Wasserstein geometry
    and Ricci curvature bounds for Poisson spaces. <i>Journal de l’Ecole Polytechnique
    - Mathematiques</i>. Ecole Polytechnique. <a href="https://doi.org/10.5802/jep.270">https://doi.org/10.5802/jep.270</a>
  chicago: Dello Schiavo, Lorenzo, Ronan Herry, and Kohei Suzuki. “Wasserstein Geometry
    and Ricci Curvature Bounds for Poisson Spaces.” <i>Journal de l’Ecole Polytechnique
    - Mathematiques</i>. Ecole Polytechnique, 2024. <a href="https://doi.org/10.5802/jep.270">https://doi.org/10.5802/jep.270</a>.
  ieee: L. Dello Schiavo, R. Herry, and K. Suzuki, “Wasserstein geometry and Ricci
    curvature bounds for Poisson spaces,” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>,
    vol. 11. Ecole Polytechnique, pp. 957–1010, 2024.
  ista: Dello Schiavo L, Herry R, Suzuki K. 2024. Wasserstein geometry and Ricci curvature
    bounds for Poisson spaces. Journal de l’Ecole Polytechnique - Mathematiques. 11,
    957–1010.
  mla: Dello Schiavo, Lorenzo, et al. “Wasserstein Geometry and Ricci Curvature Bounds
    for Poisson Spaces.” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>,
    vol. 11, Ecole Polytechnique, 2024, pp. 957–1010, doi:<a href="https://doi.org/10.5802/jep.270">10.5802/jep.270</a>.
  short: L. Dello Schiavo, R. Herry, K. Suzuki, Journal de l’Ecole Polytechnique -
    Mathematiques 11 (2024) 957–1010.
corr_author: '1'
date_created: 2024-09-29T22:01:38Z
date_published: 2024-01-01T00:00:00Z
date_updated: 2025-09-08T09:50:50Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.5802/jep.270
external_id:
  arxiv:
  - '2303.00398'
  isi:
  - '001367254000003'
file:
- access_level: open_access
  checksum: 5a51da5fb5f7fcaada378d43444cced8
  content_type: application/pdf
  creator: dernst
  date_created: 2024-10-01T07:31:56Z
  date_updated: 2024-10-01T07:31:56Z
  file_id: '18164'
  file_name: 2024_JourEcolePolytechniqueMath_DelloSchiavo.pdf
  file_size: 1250553
  relation: main_file
  success: 1
file_date_updated: 2024-10-01T07:31:56Z
has_accepted_license: '1'
intvolume: '        11'
isi: 1
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 957-1010
publication: Journal de l'Ecole Polytechnique - Mathematiques
publication_identifier:
  eissn:
  - 2270-518X
  issn:
  - 2429-7100
publication_status: published
publisher: Ecole Polytechnique
quality_controlled: '1'
scopus_import: '1'
status: public
title: Wasserstein geometry and Ricci curvature bounds for Poisson spaces
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 11
year: '2024'
...
---
_id: '180'
abstract:
- lang: eng
  text: In this paper we define and study the classical Uniform Electron Gas (UEG),
    a system of infinitely many electrons whose density is constant everywhere in
    space. The UEG is defined differently from Jellium, which has a positive constant
    background but no constraint on the density. We prove that the UEG arises in Density
    Functional Theory in the limit of a slowly varying density, minimizing the indirect
    Coulomb energy. We also construct the quantum UEG and compare it to the classical
    UEG at low density.
acknowledgement: "This project has received funding from the European Research Council
  (ERC) under the European\r\nUnion’s Horizon 2020 research and innovation programme
  (grant agreement 694227 for R.S. and MDFT 725528 for M.L.). Financial support by
  the Austrian Science Fund (FWF), project No P 27533-N27 (R.S.) and by the US National
  Science Foundation, grant No PHY12-1265118 (E.H.L.) are gratefully acknowledged."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mathieu
  full_name: Lewi, Mathieu
  last_name: Lewi
- first_name: Élliott
  full_name: Lieb, Élliott
  last_name: Lieb
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Lewi M, Lieb É, Seiringer R. Statistical mechanics of the uniform electron
    gas. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. 2018;5:79-116. doi:<a
    href="https://doi.org/10.5802/jep.64">10.5802/jep.64</a>
  apa: Lewi, M., Lieb, É., &#38; Seiringer, R. (2018). Statistical mechanics of the
    uniform electron gas. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>.
    Ecole Polytechnique. <a href="https://doi.org/10.5802/jep.64">https://doi.org/10.5802/jep.64</a>
  chicago: Lewi, Mathieu, Élliott Lieb, and Robert Seiringer. “Statistical Mechanics
    of the Uniform Electron Gas.” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>.
    Ecole Polytechnique, 2018. <a href="https://doi.org/10.5802/jep.64">https://doi.org/10.5802/jep.64</a>.
  ieee: M. Lewi, É. Lieb, and R. Seiringer, “Statistical mechanics of the uniform
    electron gas,” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>, vol. 5.
    Ecole Polytechnique, pp. 79–116, 2018.
  ista: Lewi M, Lieb É, Seiringer R. 2018. Statistical mechanics of the uniform electron
    gas. Journal de l’Ecole Polytechnique - Mathematiques. 5, 79–116.
  mla: Lewi, Mathieu, et al. “Statistical Mechanics of the Uniform Electron Gas.”
    <i>Journal de l’Ecole Polytechnique - Mathematiques</i>, vol. 5, Ecole Polytechnique,
    2018, pp. 79–116, doi:<a href="https://doi.org/10.5802/jep.64">10.5802/jep.64</a>.
  short: M. Lewi, É. Lieb, R. Seiringer, Journal de l’Ecole Polytechnique - Mathematiques
    5 (2018) 79–116.
date_created: 2018-12-11T11:45:03Z
date_published: 2018-07-01T00:00:00Z
date_updated: 2025-04-14T07:26:59Z
day: '01'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.5802/jep.64
ec_funded: 1
external_id:
  arxiv:
  - '1705.10676'
file:
- access_level: open_access
  checksum: 1ba7cccdf3900f42c4f715ae75d6813c
  content_type: application/pdf
  creator: dernst
  date_created: 2018-12-17T16:38:18Z
  date_updated: 2020-07-14T12:45:16Z
  file_id: '5726'
  file_name: 2018_JournaldeLecoleMath_Lewi.pdf
  file_size: 843938
  relation: main_file
file_date_updated: 2020-07-14T12:45:16Z
has_accepted_license: '1'
intvolume: '         5'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nd/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: 79 - 116
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P27533_N27
  name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Journal de l'Ecole Polytechnique - Mathematiques
publication_identifier:
  eissn:
  - 2270-518X
  issn:
  - 2429-7100
publication_status: published
publisher: Ecole Polytechnique
publist_id: '7741'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Statistical mechanics of the uniform electron gas
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  short: CC BY-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 5
year: '2018'
...