---
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
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'
...
---
_id: '8422'
abstract:
- lang: eng
  text: 'The Birkhoff conjecture says that the boundary of a strictly convex integrable
    billiard table is necessarily an ellipse. In this article, we consider a stronger
    notion of integrability, namely integrability close to the boundary, and prove
    a local version of this conjecture: a small perturbation of an ellipse of small
    eccentricity which preserves integrability near the boundary, is itself an ellipse.
    This extends the result in Avila et al. (Ann Math 184:527–558, ADK16), where integrability
    was assumed on a larger set. In particular, it shows that (local) integrability
    near the boundary implies global integrability. One of the crucial ideas in the
    proof consists in analyzing Taylor expansion of the corresponding action-angle
    coordinates with respect to the eccentricity parameter, deriving and studying
    higher order conditions for the preservation of integrable rational caustics.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Guan
  full_name: Huang, Guan
  last_name: Huang
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
- first_name: Alfonso
  full_name: Sorrentino, Alfonso
  last_name: Sorrentino
citation:
  ama: Huang G, Kaloshin V, Sorrentino A. Nearly circular domains which are integrable
    close to the boundary are ellipses. <i>Geometric and Functional Analysis</i>.
    2018;28(2):334-392. doi:<a href="https://doi.org/10.1007/s00039-018-0440-4">10.1007/s00039-018-0440-4</a>
  apa: Huang, G., Kaloshin, V., &#38; Sorrentino, A. (2018). Nearly circular domains
    which are integrable close to the boundary are ellipses. <i>Geometric and Functional
    Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s00039-018-0440-4">https://doi.org/10.1007/s00039-018-0440-4</a>
  chicago: Huang, Guan, Vadim Kaloshin, and Alfonso Sorrentino. “Nearly Circular Domains
    Which Are Integrable Close to the Boundary Are Ellipses.” <i>Geometric and Functional
    Analysis</i>. Springer Nature, 2018. <a href="https://doi.org/10.1007/s00039-018-0440-4">https://doi.org/10.1007/s00039-018-0440-4</a>.
  ieee: G. Huang, V. Kaloshin, and A. Sorrentino, “Nearly circular domains which are
    integrable close to the boundary are ellipses,” <i>Geometric and Functional Analysis</i>,
    vol. 28, no. 2. Springer Nature, pp. 334–392, 2018.
  ista: Huang G, Kaloshin V, Sorrentino A. 2018. Nearly circular domains which are
    integrable close to the boundary are ellipses. Geometric and Functional Analysis.
    28(2), 334–392.
  mla: Huang, Guan, et al. “Nearly Circular Domains Which Are Integrable Close to
    the Boundary Are Ellipses.” <i>Geometric and Functional Analysis</i>, vol. 28,
    no. 2, Springer Nature, 2018, pp. 334–92, doi:<a href="https://doi.org/10.1007/s00039-018-0440-4">10.1007/s00039-018-0440-4</a>.
  short: G. Huang, V. Kaloshin, A. Sorrentino, Geometric and Functional Analysis 28
    (2018) 334–392.
date_created: 2020-09-17T10:42:30Z
date_published: 2018-03-18T00:00:00Z
date_updated: 2021-01-12T08:19:11Z
day: '18'
doi: 10.1007/s00039-018-0440-4
extern: '1'
external_id:
  arxiv:
  - '1705.10601'
intvolume: '        28'
issue: '2'
keyword:
- Geometry and Topology
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1705.10601
month: '03'
oa: 1
oa_version: Preprint
page: 334-392
publication: Geometric and Functional Analysis
publication_identifier:
  issn:
  - 1016-443X
  - 1420-8970
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Nearly circular domains which are integrable close to the boundary are ellipses
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'
...
---
_id: '8524'
abstract:
- lang: eng
  text: 'A number α∈R is diophantine if it is not well approximable by rationals,
    i.e. for some C,ε>0 and any relatively prime p,q∈Z we have |αq−p|>Cq−1−ε. It is
    well-known and is easy to prove that almost every α in R is diophantine. In this
    paper we address a noncommutative version of the diophantine properties. Consider
    a pair A,B∈SO(3) and for each n∈Z+ take all possible words in A, A -1, B, and
    B - 1 of length n, i.e. for a multiindex I=(i1,i1,…,im,jm) define |I|=∑mk=1(|ik|+|jk|)=n
    and \( W_n(A,B ) = \{W_{\cal I}(A,B) = A^{i_1} B^{j_1} \dots A^{i_m} B^{j_m}\}_{|{\cal
    I|}=n \).¶Gamburd—Jakobson—Sarnak [GJS] raised the problem: prove that for Haar
    almost every pair A,B∈SO(3) the closest distance of words of length n to the identity,
    i.e. sA,B(n)=min|I|=n∥WI(A,B)−E∥, is bounded from below by an exponential function
    in n. This is the analog of the diophantine property for elements of SO(3). In
    this paper we prove that s A,B (n) is bounded from below by an exponential function
    in n 2. We also exhibit obstructions to a “simple” proof of the exponential estimate
    in n.'
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
- first_name: I.
  full_name: Rodnianski, I.
  last_name: Rodnianski
citation:
  ama: Kaloshin V, Rodnianski I. Diophantine properties of elements of SO(3). <i>Geometric
    And Functional Analysis</i>. 2001;11(5):953-970. doi:<a href="https://doi.org/10.1007/s00039-001-8222-8">10.1007/s00039-001-8222-8</a>
  apa: Kaloshin, V., &#38; Rodnianski, I. (2001). Diophantine properties of elements
    of SO(3). <i>Geometric And Functional Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s00039-001-8222-8">https://doi.org/10.1007/s00039-001-8222-8</a>
  chicago: Kaloshin, Vadim, and I. Rodnianski. “Diophantine Properties of Elements
    of SO(3).” <i>Geometric And Functional Analysis</i>. Springer Nature, 2001. <a
    href="https://doi.org/10.1007/s00039-001-8222-8">https://doi.org/10.1007/s00039-001-8222-8</a>.
  ieee: V. Kaloshin and I. Rodnianski, “Diophantine properties of elements of SO(3),”
    <i>Geometric And Functional Analysis</i>, vol. 11, no. 5. Springer Nature, pp.
    953–970, 2001.
  ista: Kaloshin V, Rodnianski I. 2001. Diophantine properties of elements of SO(3).
    Geometric And Functional Analysis. 11(5), 953–970.
  mla: Kaloshin, Vadim, and I. Rodnianski. “Diophantine Properties of Elements of
    SO(3).” <i>Geometric And Functional Analysis</i>, vol. 11, no. 5, Springer Nature,
    2001, pp. 953–70, doi:<a href="https://doi.org/10.1007/s00039-001-8222-8">10.1007/s00039-001-8222-8</a>.
  short: V. Kaloshin, I. Rodnianski, Geometric And Functional Analysis 11 (2001) 953–970.
date_created: 2020-09-18T10:50:11Z
date_published: 2001-12-01T00:00:00Z
date_updated: 2021-01-12T08:19:52Z
day: '01'
doi: 10.1007/s00039-001-8222-8
extern: '1'
intvolume: '        11'
issue: '5'
language:
- iso: eng
month: '12'
oa_version: None
page: 953-970
publication: Geometric And Functional Analysis
publication_identifier:
  issn:
  - 1016-443X
  - 1420-8970
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Diophantine properties of elements of SO(3)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2001'
...
---
_id: '2726'
abstract:
- lang: eng
  text: We investigate whether the eigenfunctions of the two-dimensional magnetic
    Schrödinger operator have a Gaussian decay of type exp(-Cx2) at infinity (the
    magnetic field is rotationally symmetric). We establish this decay if the energy
    (E) of the eigenfunction is below the bottom of the essential spectrum (B), and
    if the angular Fourier components of the external potential decay exponentially
    (real analyticity in the angle variable). We also demonstrate that almost the
    same decay is necessary. The behavior of C in the strong field limit and in the
    small (B - E) limit is also studied.
acknowledgement: Partial support from the Hungarian National Foundation for Scientific
  Research, grant no. 1902.
article_processing_charge: No
article_type: original
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
citation:
  ama: Erdös L. Gaussian decay of the magnetic eigenfunctions. <i>Geometric and Functional
    Analysis</i>. 1996;6(2):231-248. doi:<a href="https://doi.org/10.1007/BF02247886">10.1007/BF02247886</a>
  apa: Erdös, L. (1996). Gaussian decay of the magnetic eigenfunctions. <i>Geometric
    and Functional Analysis</i>. Birkhäuser. <a href="https://doi.org/10.1007/BF02247886">https://doi.org/10.1007/BF02247886</a>
  chicago: Erdös, László. “Gaussian Decay of the Magnetic Eigenfunctions.” <i>Geometric
    and Functional Analysis</i>. Birkhäuser, 1996. <a href="https://doi.org/10.1007/BF02247886">https://doi.org/10.1007/BF02247886</a>.
  ieee: L. Erdös, “Gaussian decay of the magnetic eigenfunctions,” <i>Geometric and
    Functional Analysis</i>, vol. 6, no. 2. Birkhäuser, pp. 231–248, 1996.
  ista: Erdös L. 1996. Gaussian decay of the magnetic eigenfunctions. Geometric and
    Functional Analysis. 6(2), 231–248.
  mla: Erdös, László. “Gaussian Decay of the Magnetic Eigenfunctions.” <i>Geometric
    and Functional Analysis</i>, vol. 6, no. 2, Birkhäuser, 1996, pp. 231–48, doi:<a
    href="https://doi.org/10.1007/BF02247886">10.1007/BF02247886</a>.
  short: L. Erdös, Geometric and Functional Analysis 6 (1996) 231–248.
date_created: 2018-12-11T11:59:17Z
date_published: 1996-03-01T00:00:00Z
date_updated: 2022-08-11T10:05:58Z
day: '01'
doi: 10.1007/BF02247886
extern: '1'
intvolume: '         6'
issue: '2'
language:
- iso: eng
month: '03'
oa_version: None
page: 231 - 248
publication: Geometric and Functional Analysis
publication_identifier:
  issn:
  - 1016-443X
publication_status: published
publisher: Birkhäuser
publist_id: '4166'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Gaussian decay of the magnetic eigenfunctions
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 6
year: '1996'
...