---
OA_place: publisher
OA_type: hybrid
_id: '18705'
abstract:
- lang: eng
  text: Given a non-singular diagonal cubic hypersurface X⊂Pn−1 over Fq(t) with char(Fq)≠3,
    we show that the number of rational points of height at most |P| is O(|P|3+ε)
    for n=6 and O(|P|2+ε) for n=4. In fact, if n=4 and char(Fq)>3 we prove that the
    number of rational points away from any rational line contained in X is bounded
    by O(|P|3/2+ε). From the result in 6 variables we deduce weak approximation for
    diagonal cubic hypersurfaces for n≥7 over Fq(t) when char(Fq)>3 and handle Waring's
    problem for cubes in 7 variables over Fq(t) when char(Fq)≠3. Our results answer
    a question of Davenport regarding the number of solutions of bounded height to
    x31+x32+x33=x34+x35+x36 with xi∈Fq[t].
acknowledgement: "Open Access funding enabled and organized by Projekt DEAL.\r\nThe
  authors would like to thank Tim Browning for suggesting this project. Further they
  are grateful for his and Damaris Schindler’s helpful comments. We would also like
  to thank Efthymios Sofos for bringing Davenport’s question to our attention and
  Keith Matthews for providing us with scanned copies of the original correspondence.
  Finally we would like to thank the reviewer for helpful comments."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Jakob
  full_name: Glas, Jakob
  id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb
  last_name: Glas
- first_name: Leonhard
  full_name: Hochfilzer, Leonhard
  last_name: Hochfilzer
citation:
  ama: Glas J, Hochfilzer L. On a question of Davenport and diagonal cubic forms over
    Fq(t). <i>Mathematische Annalen</i>. 2025;391:5485-5533. doi:<a href="https://doi.org/10.1007/s00208-024-03035-z">10.1007/s00208-024-03035-z</a>
  apa: Glas, J., &#38; Hochfilzer, L. (2025). On a question of Davenport and diagonal
    cubic forms over Fq(t). <i>Mathematische Annalen</i>. Springer Nature. <a href="https://doi.org/10.1007/s00208-024-03035-z">https://doi.org/10.1007/s00208-024-03035-z</a>
  chicago: Glas, Jakob, and Leonhard Hochfilzer. “On a Question of Davenport and Diagonal
    Cubic Forms over Fq(T).” <i>Mathematische Annalen</i>. Springer Nature, 2025.
    <a href="https://doi.org/10.1007/s00208-024-03035-z">https://doi.org/10.1007/s00208-024-03035-z</a>.
  ieee: J. Glas and L. Hochfilzer, “On a question of Davenport and diagonal cubic
    forms over Fq(t),” <i>Mathematische Annalen</i>, vol. 391. Springer Nature, pp.
    5485–5533, 2025.
  ista: Glas J, Hochfilzer L. 2025. On a question of Davenport and diagonal cubic
    forms over Fq(t). Mathematische Annalen. 391, 5485–5533.
  mla: Glas, Jakob, and Leonhard Hochfilzer. “On a Question of Davenport and Diagonal
    Cubic Forms over Fq(T).” <i>Mathematische Annalen</i>, vol. 391, Springer Nature,
    2025, pp. 5485–533, doi:<a href="https://doi.org/10.1007/s00208-024-03035-z">10.1007/s00208-024-03035-z</a>.
  short: J. Glas, L. Hochfilzer, Mathematische Annalen 391 (2025) 5485–5533.
corr_author: '1'
date_created: 2024-12-22T23:01:48Z
date_published: 2025-04-01T00:00:00Z
date_updated: 2025-05-19T14:04:46Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1007/s00208-024-03035-z
external_id:
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  - '2208.05422'
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month: '04'
oa: 1
oa_version: Published Version
page: 5485-5533
publication: Mathematische Annalen
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
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status: public
title: On a question of Davenport and diagonal cubic forms over Fq(t)
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 391
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...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20367'
abstract:
- lang: eng
  text: We prove upper and lower bounds on the number of pairs of commuting n x n
    matrices with integer entries in [-T, T], as T -> . Our work uses Fourier analysis
    and leads to an analysis of exponential sums involving matrices over finite fields.
    These are bounded by combining a stratification result of Fouvry and Katz with
    a new result about the flatness of the commutator Lie bracket.
acknowledgement: The authors are very grateful to Alina Ostafe, Matthew Satriano and
  Igor Shparlinski for drawing their attention to this problem and for useful comments,
  and to Michael Larsen and Peter Sarnak for their helpful correspondence. We also
  thank the referee for their valuable input. While working on this paper the first
  author was supported by a FWF grant (DOI 10.55776/P36278), the second author by
  a Sloan Research Fellowship, and the third author by the European Union’s Horizon
  2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
  No. 101034413. Open access funding provided by Institute of Science and Technology
  (IST Austria).
article_processing_charge: Yes (via OA deal)
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: Will
  full_name: Sawin, Will
  last_name: Sawin
- first_name: Victor
  full_name: Wang, Victor
  id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9
  last_name: Wang
  orcid: 0000-0002-0704-7026
citation:
  ama: Browning TD, Sawin W, Wang V. Pairs of commuting integer matrices. <i>Mathematische
    Annalen</i>. 2025;393:1863–1880. doi:<a href="https://doi.org/10.1007/s00208-025-03285-5">10.1007/s00208-025-03285-5</a>
  apa: Browning, T. D., Sawin, W., &#38; Wang, V. (2025). Pairs of commuting integer
    matrices. <i>Mathematische Annalen</i>. Springer Nature. <a href="https://doi.org/10.1007/s00208-025-03285-5">https://doi.org/10.1007/s00208-025-03285-5</a>
  chicago: Browning, Timothy D, Will Sawin, and Victor Wang. “Pairs of Commuting Integer
    Matrices.” <i>Mathematische Annalen</i>. Springer Nature, 2025. <a href="https://doi.org/10.1007/s00208-025-03285-5">https://doi.org/10.1007/s00208-025-03285-5</a>.
  ieee: T. D. Browning, W. Sawin, and V. Wang, “Pairs of commuting integer matrices,”
    <i>Mathematische Annalen</i>, vol. 393. Springer Nature, pp. 1863–1880, 2025.
  ista: Browning TD, Sawin W, Wang V. 2025. Pairs of commuting integer matrices. Mathematische
    Annalen. 393, 1863–1880.
  mla: Browning, Timothy D., et al. “Pairs of Commuting Integer Matrices.” <i>Mathematische
    Annalen</i>, vol. 393, Springer Nature, 2025, pp. 1863–1880, doi:<a href="https://doi.org/10.1007/s00208-025-03285-5">10.1007/s00208-025-03285-5</a>.
  short: T.D. Browning, W. Sawin, V. Wang, Mathematische Annalen 393 (2025) 1863–1880.
corr_author: '1'
date_created: 2025-09-21T22:01:31Z
date_published: 2025-10-01T00:00:00Z
date_updated: 2026-01-05T13:15:53Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1007/s00208-025-03285-5
ec_funded: 1
external_id:
  arxiv:
  - '2409.01920'
  isi:
  - '001567740200001'
file:
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  checksum: 1e94da1a67306e03c8e0086518faf4bc
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  date_created: 2026-01-05T13:15:44Z
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  file_id: '20950'
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intvolume: '       393'
isi: 1
language:
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month: '10'
oa: 1
oa_version: Published Version
page: 1863–1880
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
  grant_number: P36278
  name: Rational curves via function field analytic number theory
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Mathematische Annalen
publication_identifier:
  eissn:
  - 1432-1807
  issn:
  - 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Pairs of commuting integer matrices
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 393
year: '2025'
...
---
_id: '13318'
abstract:
- lang: eng
  text: Bohnenblust–Hille inequalities for Boolean cubes have been proven with dimension-free
    constants that grow subexponentially in the degree (Defant et al. in Math Ann
    374(1):653–680, 2019). Such inequalities have found great applications in learning
    low-degree Boolean functions (Eskenazis and Ivanisvili in Proceedings of the 54th
    annual ACM SIGACT symposium on theory of computing, pp 203–207, 2022). Motivated
    by learning quantum observables, a qubit analogue of Bohnenblust–Hille inequality
    for Boolean cubes was recently conjectured in Rouzé et al. (Quantum Talagrand,
    KKL and Friedgut’s theorems and the learnability of quantum Boolean functions,
    2022. arXiv preprint arXiv:2209.07279). The conjecture was resolved in Huang et
    al. (Learning to predict arbitrary quantum processes, 2022. arXiv preprint arXiv:2210.14894).
    In this paper, we give a new proof of these Bohnenblust–Hille inequalities for
    qubit system with constants that are dimension-free and of exponential growth
    in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials.
    Using similar ideas, we also study learning problems of low degree quantum observables
    and Bohr’s radius phenomenon on quantum Boolean cubes.
acknowledgement: The research of A.V. is supported by NSF DMS-1900286, DMS-2154402
  and by Hausdorff Center for Mathematics. H.Z. is supported by the Lise Meitner fellowship,
  Austrian Science Fund (FWF) M3337. This work is partially supported by NSF DMS-1929284
  while both authors were in residence at the Institute for Computational and Experimental
  Research in Mathematics in Providence, RI, during the Harmonic Analysis and Convexity
  program.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Alexander
  full_name: Volberg, Alexander
  last_name: Volberg
- first_name: Haonan
  full_name: Zhang, Haonan
  id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
  last_name: Zhang
citation:
  ama: Volberg A, Zhang H. Noncommutative Bohnenblust–Hille inequalities. <i>Mathematische
    Annalen</i>. 2024;389:1657-1676. doi:<a href="https://doi.org/10.1007/s00208-023-02680-0">10.1007/s00208-023-02680-0</a>
  apa: Volberg, A., &#38; Zhang, H. (2024). Noncommutative Bohnenblust–Hille inequalities.
    <i>Mathematische Annalen</i>. Springer Nature. <a href="https://doi.org/10.1007/s00208-023-02680-0">https://doi.org/10.1007/s00208-023-02680-0</a>
  chicago: Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille
    Inequalities.” <i>Mathematische Annalen</i>. Springer Nature, 2024. <a href="https://doi.org/10.1007/s00208-023-02680-0">https://doi.org/10.1007/s00208-023-02680-0</a>.
  ieee: A. Volberg and H. Zhang, “Noncommutative Bohnenblust–Hille inequalities,”
    <i>Mathematische Annalen</i>, vol. 389. Springer Nature, pp. 1657–1676, 2024.
  ista: Volberg A, Zhang H. 2024. Noncommutative Bohnenblust–Hille inequalities. Mathematische
    Annalen. 389, 1657–1676.
  mla: Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.”
    <i>Mathematische Annalen</i>, vol. 389, Springer Nature, 2024, pp. 1657–76, doi:<a
    href="https://doi.org/10.1007/s00208-023-02680-0">10.1007/s00208-023-02680-0</a>.
  short: A. Volberg, H. Zhang, Mathematische Annalen 389 (2024) 1657–1676.
corr_author: '1'
date_created: 2023-07-30T22:01:03Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2025-04-23T07:50:55Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00208-023-02680-0
external_id:
  arxiv:
  - '2210.14468'
  isi:
  - '001035665500001'
  pmid:
  - '38751410'
file:
- access_level: open_access
  checksum: 56e67756e4c6c97589a8385e15ea2d2a
  content_type: application/pdf
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  date_created: 2024-07-22T09:38:15Z
  date_updated: 2024-07-22T09:38:15Z
  file_id: '17299'
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intvolume: '       389'
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language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 1657-1676
pmid: 1
project:
- _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6
  grant_number: M03337
  name: Curvature-dimension in noncommutative analysis
publication: Mathematische Annalen
publication_identifier:
  eissn:
  - 1432-1807
  issn:
  - 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Noncommutative Bohnenblust–Hille inequalities
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 389
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15098'
abstract:
- lang: eng
  text: The paper is devoted to the analysis of the global well-posedness and the
    interior regularity of the 2D Navier–Stokes equations with inhomogeneous stochastic
    boundary conditions. The noise, white in time and coloured in space, can be interpreted
    as the physical law describing the driving mechanism on the atmosphere–ocean interface,
    i.e. as a balance of the shear stress of the ocean and the horizontal wind force.
acknowledgement: The authors thank Professor Franco Flandoli for useful discussions
  and valuable insight into the subject. In particular, A.A. would like to thank professor
  Franco Flandoli for hosting and financially contributing to his research visit at
  Scuola Normale di Pisa in January 2023, where this work started. E.L. would like
  to express sincere gratitude to Professor Marco Fuhrman for igniting his interest
  in this particular field of research. E.L. want to thank Professor Matthias Hieber
  and Dr. Martin Saal for useful discussions. Finally, the authors thank the anonymous
  referee for helpful comments which improved the paper from its initial version.Open
  access funding provided by Scuola Normale Superiore within the CRUI-CARE Agreement.
  A. Agresti has received funding from the European Research Council (ERC) under the
  European Union’s Horizon 2020 research and innovation programme (Grant Agreement
  No. 948819).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Antonio
  full_name: Agresti, Antonio
  id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
  last_name: Agresti
  orcid: 0000-0002-9573-2962
- first_name: Eliseo
  full_name: Luongo, Eliseo
  last_name: Luongo
citation:
  ama: Agresti A, Luongo E. Global well-posedness and interior regularity of 2D Navier-Stokes
    equations with stochastic boundary conditions. <i>Mathematische Annalen</i>. 2024;390:2727-2766.
    doi:<a href="https://doi.org/10.1007/s00208-024-02812-0">10.1007/s00208-024-02812-0</a>
  apa: Agresti, A., &#38; Luongo, E. (2024). Global well-posedness and interior regularity
    of 2D Navier-Stokes equations with stochastic boundary conditions. <i>Mathematische
    Annalen</i>. Springer Nature. <a href="https://doi.org/10.1007/s00208-024-02812-0">https://doi.org/10.1007/s00208-024-02812-0</a>
  chicago: Agresti, Antonio, and Eliseo Luongo. “Global Well-Posedness and Interior
    Regularity of 2D Navier-Stokes Equations with Stochastic Boundary Conditions.”
    <i>Mathematische Annalen</i>. Springer Nature, 2024. <a href="https://doi.org/10.1007/s00208-024-02812-0">https://doi.org/10.1007/s00208-024-02812-0</a>.
  ieee: A. Agresti and E. Luongo, “Global well-posedness and interior regularity of
    2D Navier-Stokes equations with stochastic boundary conditions,” <i>Mathematische
    Annalen</i>, vol. 390. Springer Nature, pp. 2727–2766, 2024.
  ista: Agresti A, Luongo E. 2024. Global well-posedness and interior regularity of
    2D Navier-Stokes equations with stochastic boundary conditions. Mathematische
    Annalen. 390, 2727–2766.
  mla: Agresti, Antonio, and Eliseo Luongo. “Global Well-Posedness and Interior Regularity
    of 2D Navier-Stokes Equations with Stochastic Boundary Conditions.” <i>Mathematische
    Annalen</i>, vol. 390, Springer Nature, 2024, pp. 2727–66, doi:<a href="https://doi.org/10.1007/s00208-024-02812-0">10.1007/s00208-024-02812-0</a>.
  short: A. Agresti, E. Luongo, Mathematische Annalen 390 (2024) 2727–2766.
date_created: 2024-03-10T23:00:54Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2025-09-04T12:19:59Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00208-024-02812-0
ec_funded: 1
external_id:
  arxiv:
  - '2306.11081'
  isi:
  - '001172711400002'
  pmid:
  - '39351582'
file:
- access_level: open_access
  checksum: d55cac8bddea09a97f06612825c4f229
  content_type: application/pdf
  creator: dernst
  date_created: 2025-01-09T08:23:36Z
  date_updated: 2025-01-09T08:23:36Z
  file_id: '18790'
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  file_size: 661557
  relation: main_file
  success: 1
file_date_updated: 2025-01-09T08:23:36Z
has_accepted_license: '1'
intvolume: '       390'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 2727-2766
pmid: 1
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
  call_identifier: H2020
  grant_number: '948819'
  name: Bridging Scales in Random Materials
publication: Mathematische Annalen
publication_identifier:
  eissn:
  - 1432-1807
  issn:
  - 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Global well-posedness and interior regularity of 2D Navier-Stokes equations
  with stochastic boundary conditions
tmp:
  image: /images/cc_by.png
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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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 390
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15337'
abstract:
- lang: eng
  text: We prove the Manin–Peyre conjecture for the number of rational points of bounded
    height outside of a thin subset on a family of Fano threefolds of bidegree (1,
    2).
acknowledgement: Open access funding provided by Institute of Science and Technology
  (IST Austria).The authors are grateful to Florian Wilsch for useful comments. While
  working on this paper the authors were supported by FWF grant P 32428.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Dante
  full_name: Bonolis, Dante
  id: 6A459894-5FDD-11E9-AF35-BB24E6697425
  last_name: Bonolis
- 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: Zhizhong
  full_name: Huang, Zhizhong
  id: 21f1b52f-2fd1-11eb-a347-a4cdb9b18a51
  last_name: Huang
citation:
  ama: Bonolis D, Browning TD, Huang Z. Density of rational points on some quadric
    bundle threefolds. <i>Mathematische Annalen</i>. 2024;390:4123-4207. doi:<a href="https://doi.org/10.1007/s00208-024-02854-4">10.1007/s00208-024-02854-4</a>
  apa: Bonolis, D., Browning, T. D., &#38; Huang, Z. (2024). Density of rational points
    on some quadric bundle threefolds. <i>Mathematische Annalen</i>. Springer Nature.
    <a href="https://doi.org/10.1007/s00208-024-02854-4">https://doi.org/10.1007/s00208-024-02854-4</a>
  chicago: Bonolis, Dante, Timothy D Browning, and Zhizhong Huang. “Density of Rational
    Points on Some Quadric Bundle Threefolds.” <i>Mathematische Annalen</i>. Springer
    Nature, 2024. <a href="https://doi.org/10.1007/s00208-024-02854-4">https://doi.org/10.1007/s00208-024-02854-4</a>.
  ieee: D. Bonolis, T. D. Browning, and Z. Huang, “Density of rational points on some
    quadric bundle threefolds,” <i>Mathematische Annalen</i>, vol. 390. Springer Nature,
    pp. 4123–4207, 2024.
  ista: Bonolis D, Browning TD, Huang Z. 2024. Density of rational points on some
    quadric bundle threefolds. Mathematische Annalen. 390, 4123–4207.
  mla: Bonolis, Dante, et al. “Density of Rational Points on Some Quadric Bundle Threefolds.”
    <i>Mathematische Annalen</i>, vol. 390, Springer Nature, 2024, pp. 4123–207, doi:<a
    href="https://doi.org/10.1007/s00208-024-02854-4">10.1007/s00208-024-02854-4</a>.
  short: D. Bonolis, T.D. Browning, Z. Huang, Mathematische Annalen 390 (2024) 4123–4207.
corr_author: '1'
date_created: 2024-04-21T22:00:53Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2025-09-04T13:41:19Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1007/s00208-024-02854-4
external_id:
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  - '2204.09322'
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  - '001204670500001'
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  grant_number: P32428
  name: New frontiers of the Manin conjecture
publication: Mathematische Annalen
publication_identifier:
  eissn:
  - 1432-1807
  issn:
  - 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Density of rational points on some quadric bundle threefolds
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
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...
---
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OA_type: green
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abstract:
- lang: eng
  text: "Fix a non-square integer \U0001D458≠0. We show that the number of curves
    \U0001D438\U0001D435:\U0001D466^2=\U0001D465^3+\U0001D458\U0001D435^2 containing
    an integral point, where B ranges over positive integers less than N, is bounded
    by ≪\U0001D458\U0001D441(log\U0001D441)−1/2+\U0001D716. In particular, this implies
    that the number of positive integers \U0001D435≤\U0001D441 such that −3\U0001D458\U0001D435^2
    is the discriminant of an elliptic curve over \U0001D444 is o(N). The proof involves
    a discriminant-lowering procedure on integral binary cubic forms."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- 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: Chan S. Integral points on cubic twists of Mordell curves. <i>Mathematische
    Annalen</i>. 2023;388(3):2275-2288. doi:<a href="https://doi.org/10.1007/s00208-023-02578-x">10.1007/s00208-023-02578-x</a>
  apa: Chan, S. (2023). Integral points on cubic twists of Mordell curves. <i>Mathematische
    Annalen</i>. Springer Nature. <a href="https://doi.org/10.1007/s00208-023-02578-x">https://doi.org/10.1007/s00208-023-02578-x</a>
  chicago: Chan, Stephanie. “Integral Points on Cubic Twists of Mordell Curves.” <i>Mathematische
    Annalen</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s00208-023-02578-x">https://doi.org/10.1007/s00208-023-02578-x</a>.
  ieee: S. Chan, “Integral points on cubic twists of Mordell curves,” <i>Mathematische
    Annalen</i>, vol. 388, no. 3. Springer Nature, pp. 2275–2288, 2023.
  ista: Chan S. 2023. Integral points on cubic twists of Mordell curves. Mathematische
    Annalen. 388(3), 2275–2288.
  mla: Chan, Stephanie. “Integral Points on Cubic Twists of Mordell Curves.” <i>Mathematische
    Annalen</i>, vol. 388, no. 3, Springer Nature, 2023, pp. 2275–88, doi:<a href="https://doi.org/10.1007/s00208-023-02578-x">10.1007/s00208-023-02578-x</a>.
  short: S. Chan, Mathematische Annalen 388 (2023) 2275–2288.
date_created: 2025-04-05T10:50:37Z
date_published: 2023-02-07T00:00:00Z
date_updated: 2025-07-10T11:51:45Z
day: '07'
doi: 10.1007/s00208-023-02578-x
extern: '1'
external_id:
  arxiv:
  - '2203.11366'
intvolume: '       388'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2203.11366
month: '02'
oa: 1
oa_version: Preprint
page: 2275-2288
publication: Mathematische Annalen
publication_identifier:
  eissn:
  - 1432-1807
  issn:
  - 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Integral points on cubic twists of Mordell curves
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 388
year: '2023'
...
---
_id: '10588'
abstract:
- lang: eng
  text: We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying
    the quasi curvature-dimension condition recently introduced in Milman (Commun
    Pure Appl Math, to appear). We provide several applications to properties of the
    corresponding heat semigroup. In particular, under the additional assumption of
    infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the
    heat semigroup with respect to the distance, and prove the irreducibility of the
    heat semigroup. These results apply in particular to large classes of (ideal)
    sub-Riemannian manifolds.
acknowledgement: "The authors are grateful to Dr. Bang-Xian Han for helpful discussions
  on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor
  Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino
  Antonelli for reading a preliminary version of this work and for their valuable
  comments and suggestions. Finally, they wish to express their gratitude to two anonymous
  Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S.
  gratefully acknowledges funding of his position by the Austrian Science Fund (FWF)
  grant F65, and by the European Research Council (ERC, grant No. 716117, awarded
  to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS
  Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research
  Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research
  on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number
  17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium."
article_processing_charge: Yes (via OA deal)
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: Kohei
  full_name: Suzuki, Kohei
  last_name: Suzuki
citation:
  ama: Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and
    applications. <i>Mathematische Annalen</i>. 2022;384:1815-1832. doi:<a href="https://doi.org/10.1007/s00208-021-02331-2">10.1007/s00208-021-02331-2</a>
  apa: Dello Schiavo, L., &#38; Suzuki, K. (2022). Sobolev-to-Lipschitz property on
    QCD- spaces and applications. <i>Mathematische Annalen</i>. Springer Nature. <a
    href="https://doi.org/10.1007/s00208-021-02331-2">https://doi.org/10.1007/s00208-021-02331-2</a>
  chicago: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property
    on QCD- Spaces and Applications.” <i>Mathematische Annalen</i>. Springer Nature,
    2022. <a href="https://doi.org/10.1007/s00208-021-02331-2">https://doi.org/10.1007/s00208-021-02331-2</a>.
  ieee: L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces
    and applications,” <i>Mathematische Annalen</i>, vol. 384. Springer Nature, pp.
    1815–1832, 2022.
  ista: Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces
    and applications. Mathematische Annalen. 384, 1815–1832.
  mla: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on
    QCD- Spaces and Applications.” <i>Mathematische Annalen</i>, vol. 384, Springer
    Nature, 2022, pp. 1815–32, doi:<a href="https://doi.org/10.1007/s00208-021-02331-2">10.1007/s00208-021-02331-2</a>.
  short: L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832.
corr_author: '1'
date_created: 2022-01-02T23:01:35Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2025-04-14T07:27:46Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00208-021-02331-2
ec_funded: 1
external_id:
  arxiv:
  - '2110.05137'
  isi:
  - '000734150200001'
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  success: 1
file_date_updated: 2022-01-03T11:08:31Z
has_accepted_license: '1'
intvolume: '       384'
isi: 1
keyword:
- quasi curvature-dimension condition
- sub-riemannian geometry
- Sobolev-to-Lipschitz property
- Varadhan short-time asymptotics
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 1815-1832
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
  grant_number: F6504
  name: Taming Complexity in Partial Differential Systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Mathematische Annalen
publication_identifier:
  eissn:
  - 1432-1807
  issn:
  - 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sobolev-to-Lipschitz property on QCD- spaces and applications
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 384
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...
---
OA_place: repository
OA_type: green
_id: '20619'
abstract:
- lang: eng
  text: The first author’s previous work established Solomon’s WDVV-type relations
    for Welschinger’s invariant curve counts in real symplectic fourfolds by lifting
    geometric relations over possibly unorientable morphisms. We apply her framework
    to obtain WDVV-style relations for the disk invariants of real symplectic sixfolds
    with some symmetry, in particular confirming Alcolado’s prediction for P^3 and
    extending it to other spaces. These relations reduce the computation of Welschinger’s
    invariants of many real symplectic sixfolds to invariants in small degrees and
    provide lower bounds for counts of real rational curves with positive-dimensional
    insertions in some cases. In the case of P^3, our lower bounds fit perfectly with
    Kollár’s vanishing results.
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
- first_name: Aleksey
  full_name: Zinger, Aleksey
  last_name: Zinger
citation:
  ama: Chen X, Zinger A. WDVV-type relations for disk Gromov–Witten invariants in
    dimension 6. <i>Mathematische Annalen</i>. 2021;379(3-4):1231-1313. doi:<a href="https://doi.org/10.1007/s00208-020-02130-1">10.1007/s00208-020-02130-1</a>
  apa: Chen, X., &#38; Zinger, A. (2021). WDVV-type relations for disk Gromov–Witten
    invariants in dimension 6. <i>Mathematische Annalen</i>. Springer Nature. <a href="https://doi.org/10.1007/s00208-020-02130-1">https://doi.org/10.1007/s00208-020-02130-1</a>
  chicago: Chen, Xujia, and Aleksey Zinger. “WDVV-Type Relations for Disk Gromov–Witten
    Invariants in Dimension 6.” <i>Mathematische Annalen</i>. Springer Nature, 2021.
    <a href="https://doi.org/10.1007/s00208-020-02130-1">https://doi.org/10.1007/s00208-020-02130-1</a>.
  ieee: X. Chen and A. Zinger, “WDVV-type relations for disk Gromov–Witten invariants
    in dimension 6,” <i>Mathematische Annalen</i>, vol. 379, no. 3–4. Springer Nature,
    pp. 1231–1313, 2021.
  ista: Chen X, Zinger A. 2021. WDVV-type relations for disk Gromov–Witten invariants
    in dimension 6. Mathematische Annalen. 379(3–4), 1231–1313.
  mla: Chen, Xujia, and Aleksey Zinger. “WDVV-Type Relations for Disk Gromov–Witten
    Invariants in Dimension 6.” <i>Mathematische Annalen</i>, vol. 379, no. 3–4, Springer
    Nature, 2021, pp. 1231–313, doi:<a href="https://doi.org/10.1007/s00208-020-02130-1">10.1007/s00208-020-02130-1</a>.
  short: X. Chen, A. Zinger, Mathematische Annalen 379 (2021) 1231–1313.
date_created: 2025-11-10T08:41:40Z
date_published: 2021-01-25T00:00:00Z
date_updated: 2025-11-10T15:11:29Z
day: '25'
doi: 10.1007/s00208-020-02130-1
extern: '1'
external_id:
  arxiv:
  - '1904.04254'
intvolume: '       379'
issue: 3-4
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1904.04254
month: '01'
oa: 1
oa_version: Preprint
page: 1231-1313
publication: Mathematische Annalen
publication_identifier:
  eissn:
  - 1432-1807
  issn:
  - 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: WDVV-type relations for disk Gromov–Witten invariants in dimension 6
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 379
year: '2021'
...