---
OA_place: publisher
OA_type: hybrid
_id: '18483'
abstract:
- lang: eng
  text: In this paper we prove a perturbative version of a remarkable Bialy–Mironov
    (Ann. Math. 196(1):389–413, 2022) result. They prove non perturbative Birkhoff
    conjecture for centrally-symmetric convex domains, namely, a centrally-symmetric
    convex domain with integrable billiard is ellipse. We combine techniques from
    Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) with a local result by Kaloshin–Sorrentino
    (Ann. Math. 188(1):315–380, 2018) and show that a domain close enough to a centrally
    symmetric one with integrable billiard is ellipse. To combine these results we
    derive a slight extension of Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) by
    proving that a notion of rational integrability is equivalent to the C0-integrability
    condition used in their paper.
acknowledgement: We are grateful to the anonymous referee for their careful reading
  and valuable remarks and comments which helped to improve significantly the paper.
  Open access funding provided by Institute of Science and Technology (IST Austria).
  V.K. and C.E.K. gratefully acknowledge support from the European Research Council
  (ERC) through the Advanced Grant “SPERIG” (#885 707).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
- first_name: Edmond
  full_name: Koudjinan, Edmond
  id: 52DF3E68-AEFA-11EA-95A4-124A3DDC885E
  last_name: Koudjinan
  orcid: 0000-0003-2640-4049
- first_name: Ke
  full_name: Zhang, Ke
  last_name: Zhang
citation:
  ama: Kaloshin V, Koudjinan E, Zhang K. Birkhoff conjecture for nearly centrally
    symmetric domains. <i>Geometric and Functional Analysis</i>. 2024;34:1973-2007.
    doi:<a href="https://doi.org/10.1007/s00039-024-00695-6">10.1007/s00039-024-00695-6</a>
  apa: Kaloshin, V., Koudjinan, E., &#38; Zhang, K. (2024). Birkhoff conjecture for
    nearly centrally symmetric domains. <i>Geometric and Functional Analysis</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s00039-024-00695-6">https://doi.org/10.1007/s00039-024-00695-6</a>
  chicago: Kaloshin, Vadim, Edmond Koudjinan, and Ke Zhang. “Birkhoff Conjecture for
    Nearly Centrally Symmetric Domains.” <i>Geometric and Functional Analysis</i>.
    Springer Nature, 2024. <a href="https://doi.org/10.1007/s00039-024-00695-6">https://doi.org/10.1007/s00039-024-00695-6</a>.
  ieee: V. Kaloshin, E. Koudjinan, and K. Zhang, “Birkhoff conjecture for nearly centrally
    symmetric domains,” <i>Geometric and Functional Analysis</i>, vol. 34. Springer
    Nature, pp. 1973–2007, 2024.
  ista: Kaloshin V, Koudjinan E, Zhang K. 2024. Birkhoff conjecture for nearly centrally
    symmetric domains. Geometric and Functional Analysis. 34, 1973–2007.
  mla: Kaloshin, Vadim, et al. “Birkhoff Conjecture for Nearly Centrally Symmetric
    Domains.” <i>Geometric and Functional Analysis</i>, vol. 34, Springer Nature,
    2024, pp. 1973–2007, doi:<a href="https://doi.org/10.1007/s00039-024-00695-6">10.1007/s00039-024-00695-6</a>.
  short: V. Kaloshin, E. Koudjinan, K. Zhang, Geometric and Functional Analysis 34
    (2024) 1973–2007.
corr_author: '1'
date_created: 2024-10-27T23:01:45Z
date_published: 2024-12-01T00:00:00Z
date_updated: 2025-09-08T14:27:45Z
day: '01'
ddc:
- '510'
department:
- _id: VaKa
doi: 10.1007/s00039-024-00695-6
ec_funded: 1
external_id:
  arxiv:
  - '2306.12301'
  isi:
  - '001329804200001'
file:
- access_level: open_access
  checksum: e7fcd9f78beb40408c7d858ac0625e27
  content_type: application/pdf
  creator: dernst
  date_created: 2025-01-13T09:14:24Z
  date_updated: 2025-01-13T09:14:24Z
  file_id: '18833'
  file_name: 2024_GeometricFunctionalAnalysis_Kaloshin.pdf
  file_size: 2260980
  relation: main_file
  success: 1
file_date_updated: 2025-01-13T09:14:24Z
has_accepted_license: '1'
intvolume: '        34'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '12'
oa: 1
oa_version: Published Version
page: 1973-2007
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
  call_identifier: H2020
  grant_number: '885707'
  name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Geometric and Functional Analysis
publication_identifier:
  eissn:
  - 1420-8970
  issn:
  - 1016-443X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Birkhoff conjecture for nearly centrally symmetric domains
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: 34
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '20616'
abstract:
- lang: eng
  text: We establish two WDVV-style relations for the disk invariants of real symplectic
    fourfolds by implementing Georgieva’s suggestion to lift homology relations from
    the Deligne–Mumford moduli spaces of stable real curves. This is accomplished
    by lifting judiciously chosen cobordisms realizing these relations. The resulting
    lifted relations lead to the recursions for Welschinger invariants announced by
    Solomon in 2007 and have the same structure as his WDVV-style relations, but differ
    by signs from the latter. Our topological approach provides a general framework
    for lifting relations via morphisms between not necessarily orientable spaces.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Xujia
  full_name: Chen, Xujia
  id: 968ad14a-fd86-11ee-a420-ea29715511a3
  last_name: Chen
citation:
  ama: Chen X. Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for
    Welschinger invariants. <i>Geometric and Functional Analysis</i>. 2022;32(3):490-567.
    doi:<a href="https://doi.org/10.1007/s00039-022-00596-6">10.1007/s00039-022-00596-6</a>
  apa: Chen, X. (2022). Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations
    for Welschinger invariants. <i>Geometric and Functional Analysis</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s00039-022-00596-6">https://doi.org/10.1007/s00039-022-00596-6</a>
  chicago: Chen, Xujia. “Steenrod Pseudocycles, Lifted Cobordisms, and Solomon’s Relations
    for Welschinger Invariants.” <i>Geometric and Functional Analysis</i>. Springer
    Nature, 2022. <a href="https://doi.org/10.1007/s00039-022-00596-6">https://doi.org/10.1007/s00039-022-00596-6</a>.
  ieee: X. Chen, “Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations
    for Welschinger invariants,” <i>Geometric and Functional Analysis</i>, vol. 32,
    no. 3. Springer Nature, pp. 490–567, 2022.
  ista: Chen X. 2022. Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations
    for Welschinger invariants. Geometric and Functional Analysis. 32(3), 490–567.
  mla: Chen, Xujia. “Steenrod Pseudocycles, Lifted Cobordisms, and Solomon’s Relations
    for Welschinger Invariants.” <i>Geometric and Functional Analysis</i>, vol. 32,
    no. 3, Springer Nature, 2022, pp. 490–567, doi:<a href="https://doi.org/10.1007/s00039-022-00596-6">10.1007/s00039-022-00596-6</a>.
  short: X. Chen, Geometric and Functional Analysis 32 (2022) 490–567.
date_created: 2025-11-10T08:40:40Z
date_published: 2022-04-15T00:00:00Z
date_updated: 2025-11-10T15:18:07Z
day: '15'
doi: 10.1007/s00039-022-00596-6
extern: '1'
external_id:
  arxiv:
  - '1809.08919'
intvolume: '        32'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1809.08919
month: '04'
oa: 1
oa_version: Preprint
page: 490-567
publication: Geometric and Functional Analysis
publication_identifier:
  eissn:
  - 1420-8970
  issn:
  - 1016-443X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger
  invariants
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 32
year: '2022'
...
---
OA_place: repository
OA_type: green
_id: '22055'
abstract:
- lang: eng
  text: We present a general method for obtaining conservation laws for integrable
    PDE at negative regularity and exhibit its application to KdV, NLS, and mKdV.
    Our method works uniformly for these problems posed both on the line and on the
    circle.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
- first_name: Xiaoyi
  full_name: Zhang, Xiaoyi
  last_name: Zhang
citation:
  ama: Killip R, Vişan M, Zhang X. Low regularity conservation laws for integrable
    PDE. <i>Geometric and Functional Analysis</i>. 2018;28(4):1062-1090. doi:<a href="https://doi.org/10.1007/s00039-018-0444-0">10.1007/s00039-018-0444-0</a>
  apa: Killip, R., Vişan, M., &#38; Zhang, X. (2018). Low regularity conservation
    laws for integrable PDE. <i>Geometric and Functional Analysis</i>. Springer Nature.
    <a href="https://doi.org/10.1007/s00039-018-0444-0">https://doi.org/10.1007/s00039-018-0444-0</a>
  chicago: Killip, Rowan, Monica Vişan, and Xiaoyi Zhang. “Low Regularity Conservation
    Laws for Integrable PDE.” <i>Geometric and Functional Analysis</i>. Springer Nature,
    2018. <a href="https://doi.org/10.1007/s00039-018-0444-0">https://doi.org/10.1007/s00039-018-0444-0</a>.
  ieee: R. Killip, M. Vişan, and X. Zhang, “Low regularity conservation laws for integrable
    PDE,” <i>Geometric and Functional Analysis</i>, vol. 28, no. 4. Springer Nature,
    pp. 1062–1090, 2018.
  ista: Killip R, Vişan M, Zhang X. 2018. Low regularity conservation laws for integrable
    PDE. Geometric and Functional Analysis. 28(4), 1062–1090.
  mla: Killip, Rowan, et al. “Low Regularity Conservation Laws for Integrable PDE.”
    <i>Geometric and Functional Analysis</i>, vol. 28, no. 4, Springer Nature, 2018,
    pp. 1062–90, doi:<a href="https://doi.org/10.1007/s00039-018-0444-0">10.1007/s00039-018-0444-0</a>.
  short: R. Killip, M. Vişan, X. Zhang, Geometric and Functional Analysis 28 (2018)
    1062–1090.
das_tickbox: '1'
date_created: 2026-06-19T07:56:48Z
date_published: 2018-07-01T00:00:00Z
date_updated: 2026-06-29T09:55:53Z
day: '01'
doi: 10.1007/s00039-018-0444-0
extern: '1'
external_id:
  arxiv:
  - '1708.05362'
intvolume: '        28'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1708.05362
month: '07'
oa: 1
oa_version: Preprint
page: 1062-1090
publication: Geometric and Functional Analysis
publication_identifier:
  eissn:
  - 1420-8970
  issn:
  - 1016-443X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Low regularity conservation laws for integrable PDE
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2018'
...
---
OA_place: repository
OA_type: green
_id: '259'
abstract:
- lang: eng
  text: "The Hasse principle and weak approximation is established for\r\nnon-singular
    cubic hypersurfaces X over the function field Fq(t), provided that\r\nchar(Fq)
    > 3 and X has dimension at least 6."
acknowledgement: "EP/J018260/1\tEngineering and Physical Sciences Research Council
  EPSRC"
article_processing_charge: No
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: Pankaj
  full_name: Vishe, Pankaj
  last_name: Vishe
citation:
  ama: Browning TD, Vishe P. Rational points on cubic hypersurfaces over F_q(t) .
    <i>Geometric and Functional Analysis</i>. 2015;25(3):671-732. doi:<a href="https://doi.org/10.1007/s00039-015-0328-5">10.1007/s00039-015-0328-5</a>
  apa: Browning, T. D., &#38; Vishe, P. (2015). Rational points on cubic hypersurfaces
    over F_q(t) . <i>Geometric and Functional Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s00039-015-0328-5">https://doi.org/10.1007/s00039-015-0328-5</a>
  chicago: Browning, Timothy D, and Pankaj Vishe. “Rational Points on Cubic Hypersurfaces
    over F_q(T) .” <i>Geometric and Functional Analysis</i>. Springer Nature, 2015.
    <a href="https://doi.org/10.1007/s00039-015-0328-5">https://doi.org/10.1007/s00039-015-0328-5</a>.
  ieee: T. D. Browning and P. Vishe, “Rational points on cubic hypersurfaces over
    F_q(t) ,” <i>Geometric and Functional Analysis</i>, vol. 25, no. 3. Springer Nature,
    pp. 671–732, 2015.
  ista: Browning TD, Vishe P. 2015. Rational points on cubic hypersurfaces over F_q(t)
    . Geometric and Functional Analysis. 25(3), 671–732.
  mla: Browning, Timothy D., and Pankaj Vishe. “Rational Points on Cubic Hypersurfaces
    over F_q(T) .” <i>Geometric and Functional Analysis</i>, vol. 25, no. 3, Springer
    Nature, 2015, pp. 671–732, doi:<a href="https://doi.org/10.1007/s00039-015-0328-5">10.1007/s00039-015-0328-5</a>.
  short: T.D. Browning, P. Vishe, Geometric and Functional Analysis 25 (2015) 671–732.
date_created: 2018-12-11T11:45:29Z
date_published: 2015-06-11T00:00:00Z
date_updated: 2026-05-19T09:46:04Z
day: '11'
doi: 10.1007/s00039-015-0328-5
extern: '1'
external_id:
  arxiv:
  - '1502.00772'
intvolume: '        25'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.1502.00772'
month: '06'
oa: 1
oa_version: Preprint
page: 671 - 732
publication: Geometric and Functional Analysis
publication_identifier:
  eissn:
  - 1420-8970
  issn:
  - 1016-443X
publication_status: published
publisher: Springer Nature
publist_id: '7643'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Rational points on cubic hypersurfaces over F_q(t) '
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 25
year: '2015'
...