---
_id: '14986'
abstract:
- lang: eng
  text: We prove a version of the tamely ramified geometric Langlands correspondence
    in positive characteristic for GLn(k). Let k be an algebraically closed field
    of characteristic p>n. Let X be a smooth projective curve over k with marked points,
    and fix a parabolic subgroup of GLn(k) at each marked point. We denote by Bunn,P
    the moduli stack of (quasi-)parabolic vector bundles on X, and by Locn,P the moduli
    stack of parabolic flat connections such that the residue is nilpotent with respect
    to the parabolic reduction at each marked point. We construct an equivalence between
    the bounded derived category Db(Qcoh(Loc0n,P)) of quasi-coherent sheaves on an
    open substack Loc0n,P⊂Locn,P, and the bounded derived category Db(D0Bunn,P-mod)
    of D0Bunn,P-modules, where D0Bunn,P is a localization of DBunn,P the sheaf of
    crystalline differential operators on Bunn,P. Thus we extend the work of Bezrukavnikov-Braverman
    to the tamely ramified case. We also prove a correspondence between flat connections
    on X with regular singularities and meromorphic Higgs bundles on the Frobenius
    twist X(1) of X with first order poles .
acknowledgement: "This work was supported by the NSF [DMS-1502125to S.S.]; and the
  European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie
  grant agreement [101034413 to S.S.].\r\nI would like to thank my advisor Tom Nevins
  for many helpful discussions on this subject and for his comments on this paper.
  I would like to thank Christopher Dodd, Michael Groechenig, and Tamas Hausel for
  helpful conversations. I would like to thank Tsao-Hsien Chen for useful comments
  on an earlier version of this paper."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Shiyu
  full_name: Shen, Shiyu
  id: 544cccd3-9005-11ec-87bc-94aef1c5b814
  last_name: Shen
citation:
  ama: Shen S. Tamely ramified geometric Langlands correspondence in positive characteristic.
    <i>International Mathematics Research Notices</i>. 2024. doi:<a href="https://doi.org/10.1093/imrn/rnae005">10.1093/imrn/rnae005</a>
  apa: Shen, S. (2024). Tamely ramified geometric Langlands correspondence in positive
    characteristic. <i>International Mathematics Research Notices</i>. Oxford University
    Press. <a href="https://doi.org/10.1093/imrn/rnae005">https://doi.org/10.1093/imrn/rnae005</a>
  chicago: Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive
    Characteristic.” <i>International Mathematics Research Notices</i>. Oxford University
    Press, 2024. <a href="https://doi.org/10.1093/imrn/rnae005">https://doi.org/10.1093/imrn/rnae005</a>.
  ieee: S. Shen, “Tamely ramified geometric Langlands correspondence in positive characteristic,”
    <i>International Mathematics Research Notices</i>. Oxford University Press, 2024.
  ista: Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive
    characteristic. International Mathematics Research Notices.
  mla: Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive
    Characteristic.” <i>International Mathematics Research Notices</i>, Oxford University
    Press, 2024, doi:<a href="https://doi.org/10.1093/imrn/rnae005">10.1093/imrn/rnae005</a>.
  short: S. Shen, International Mathematics Research Notices (2024).
date_created: 2024-02-14T12:16:17Z
date_published: 2024-02-05T00:00:00Z
date_updated: 2024-02-19T10:22:44Z
day: '05'
department:
- _id: TaHa
doi: 10.1093/imrn/rnae005
ec_funded: 1
external_id:
  arxiv:
  - '1810.12491'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1093/imrn/rnae005
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: International Mathematics Research Notices
publication_identifier:
  eissn:
  - 1687-0247
  issn:
  - 1073-7928
publication_status: epub_ahead
publisher: Oxford University Press
quality_controlled: '1'
status: public
title: Tamely ramified geometric Langlands correspondence in positive characteristic
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '14737'
abstract:
- lang: eng
  text: 'John’s fundamental theorem characterizing the largest volume ellipsoid contained
    in a convex body $K$ in $\mathbb{R}^{d}$ has seen several generalizations and
    extensions. One direction, initiated by V. Milman is to replace ellipsoids by
    positions (affine images) of another body $L$. Another, more recent direction
    is to consider logarithmically concave functions on $\mathbb{R}^{d}$ instead of
    convex bodies: we designate some special, radially symmetric log-concave function
    $g$ as the analogue of the Euclidean ball, and want to find its largest integral
    position under the constraint that it is pointwise below some given log-concave
    function $f$. We follow both directions simultaneously: we consider the functional
    question, and allow essentially any meaningful function to play the role of $g$
    above. Our general theorems jointly extend known results in both directions. The
    dual problem in the setting of convex bodies asks for the smallest volume ellipsoid,
    called Löwner’s ellipsoid, containing $K$. We consider the analogous problem for
    functions: we characterize the solutions of the optimization problem of finding
    a smallest integral position of some log-concave function $g$ under the constraint
    that it is pointwise above $f$. It turns out that in the functional setting, the
    relationship between the John and the Löwner problems is more intricate than it
    is in the setting of convex bodies.'
acknowledgement: "We thank Alexander Litvak for the many discussions on Theorem 1.1.
  Igor Tsiutsiurupa participated in the early stage of this project. To our deep regret,
  Igor chose another road for his life and stopped working with us.\r\nThis work was
  supported by the János Bolyai Scholarship of the Hungarian Academy of Sciences [to
  M.N.]; the National Research, Development, and Innovation Fund (NRDI) [K119670 and
  K131529 to M.N.]; and the ÚNKP-22-5 New National Excellence Program of the Ministry
  for Innovation and Technology from the source of the NRDI [to M.N.]."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Grigory
  full_name: Ivanov, Grigory
  id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
  last_name: Ivanov
- first_name: Márton
  full_name: Naszódi, Márton
  last_name: Naszódi
citation:
  ama: Ivanov G, Naszódi M. Functional John and Löwner conditions for pairs of log-concave
    functions. <i>International Mathematics Research Notices</i>. 2023;2023(23):20613-20669.
    doi:<a href="https://doi.org/10.1093/imrn/rnad210">10.1093/imrn/rnad210</a>
  apa: Ivanov, G., &#38; Naszódi, M. (2023). Functional John and Löwner conditions
    for pairs of log-concave functions. <i>International Mathematics Research Notices</i>.
    Oxford University Press. <a href="https://doi.org/10.1093/imrn/rnad210">https://doi.org/10.1093/imrn/rnad210</a>
  chicago: Ivanov, Grigory, and Márton Naszódi. “Functional John and Löwner Conditions
    for Pairs of Log-Concave Functions.” <i>International Mathematics Research Notices</i>.
    Oxford University Press, 2023. <a href="https://doi.org/10.1093/imrn/rnad210">https://doi.org/10.1093/imrn/rnad210</a>.
  ieee: G. Ivanov and M. Naszódi, “Functional John and Löwner conditions for pairs
    of log-concave functions,” <i>International Mathematics Research Notices</i>,
    vol. 2023, no. 23. Oxford University Press, pp. 20613–20669, 2023.
  ista: Ivanov G, Naszódi M. 2023. Functional John and Löwner conditions for pairs
    of log-concave functions. International Mathematics Research Notices. 2023(23),
    20613–20669.
  mla: Ivanov, Grigory, and Márton Naszódi. “Functional John and Löwner Conditions
    for Pairs of Log-Concave Functions.” <i>International Mathematics Research Notices</i>,
    vol. 2023, no. 23, Oxford University Press, 2023, pp. 20613–69, doi:<a href="https://doi.org/10.1093/imrn/rnad210">10.1093/imrn/rnad210</a>.
  short: G. Ivanov, M. Naszódi, International Mathematics Research Notices 2023 (2023)
    20613–20669.
date_created: 2024-01-08T09:48:56Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-01-08T09:57:25Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1093/imrn/rnad210
external_id:
  arxiv:
  - '2212.11781'
file:
- access_level: open_access
  checksum: 353666cea80633beb0f1ffd342dff6d4
  content_type: application/pdf
  creator: dernst
  date_created: 2024-01-08T09:53:09Z
  date_updated: 2024-01-08T09:53:09Z
  file_id: '14738'
  file_name: 2023_IMRN_Ivanov.pdf
  file_size: 815777
  relation: main_file
  success: 1
file_date_updated: 2024-01-08T09:53:09Z
has_accepted_license: '1'
intvolume: '      2023'
issue: '23'
keyword:
- General Mathematics
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 20613-20669
publication: International Mathematics Research Notices
publication_identifier:
  eissn:
  - 1687-0247
  issn:
  - 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
status: public
title: Functional John and Löwner conditions for pairs of log-concave functions
tmp:
  image: /images/cc_by_nc_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
  name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
    (CC BY-NC-ND 4.0)
  short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2023
year: '2023'
...
---
_id: '9034'
abstract:
- lang: eng
  text: We determine an asymptotic formula for the number of integral points of bounded
    height on a blow-up of P3 outside certain planes using universal torsors.
acknowledgement: This work was supported by the German Academic Exchange Service.
  Parts of this article were prepared at the Institut de Mathémathiques de Jussieu—Paris
  Rive Gauche. I wish to thank Antoine Chambert-Loir for his remarks and the institute
  for its hospitality, as well as the anonymous referee for several useful remarks
  and suggestions for improvements.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Florian Alexander
  full_name: Wilsch, Florian Alexander
  id: 560601DA-8D36-11E9-A136-7AC1E5697425
  last_name: Wilsch
  orcid: 0000-0001-7302-8256
citation:
  ama: Wilsch FA. Integral points of bounded height on a log Fano threefold. <i>International
    Mathematics Research Notices</i>. 2023;2023(8):6780-6808. doi:<a href="https://doi.org/10.1093/imrn/rnac048">10.1093/imrn/rnac048</a>
  apa: Wilsch, F. A. (2023). Integral points of bounded height on a log Fano threefold.
    <i>International Mathematics Research Notices</i>. Oxford Academic. <a href="https://doi.org/10.1093/imrn/rnac048">https://doi.org/10.1093/imrn/rnac048</a>
  chicago: Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Log
    Fano Threefold.” <i>International Mathematics Research Notices</i>. Oxford Academic,
    2023. <a href="https://doi.org/10.1093/imrn/rnac048">https://doi.org/10.1093/imrn/rnac048</a>.
  ieee: F. A. Wilsch, “Integral points of bounded height on a log Fano threefold,”
    <i>International Mathematics Research Notices</i>, vol. 2023, no. 8. Oxford Academic,
    pp. 6780–6808, 2023.
  ista: Wilsch FA. 2023. Integral points of bounded height on a log Fano threefold.
    International Mathematics Research Notices. 2023(8), 6780–6808.
  mla: Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Log Fano
    Threefold.” <i>International Mathematics Research Notices</i>, vol. 2023, no.
    8, Oxford Academic, 2023, pp. 6780–808, doi:<a href="https://doi.org/10.1093/imrn/rnac048">10.1093/imrn/rnac048</a>.
  short: F.A. Wilsch, International Mathematics Research Notices 2023 (2023) 6780–6808.
date_created: 2021-01-22T09:31:09Z
date_published: 2023-04-01T00:00:00Z
date_updated: 2023-08-01T12:23:55Z
day: '01'
department:
- _id: TiBr
doi: 10.1093/imrn/rnac048
external_id:
  arxiv:
  - '1901.08503'
  isi:
  - '000773116000001'
intvolume: '      2023'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1901.08503
month: '04'
oa: 1
oa_version: Preprint
page: 6780-6808
publication: International Mathematics Research Notices
publication_identifier:
  eissn:
  - 1687-0247
  issn:
  - 1073-7928
publication_status: published
publisher: Oxford Academic
quality_controlled: '1'
status: public
title: Integral points of bounded height on a log Fano threefold
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2023
year: '2023'
...
---
_id: '10867'
abstract:
- lang: eng
  text: In this paper we find a tight estimate for Gromov’s waist of the balls in
    spaces of constant curvature, deduce the estimates for the balls in Riemannian
    manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar
    result for normed spaces.
acknowledgement: ' Supported by the Russian Foundation for Basic Research grant 18-01-00036.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Arseniy
  full_name: Akopyan, Arseniy
  id: 430D2C90-F248-11E8-B48F-1D18A9856A87
  last_name: Akopyan
  orcid: 0000-0002-2548-617X
- first_name: Roman
  full_name: Karasev, Roman
  last_name: Karasev
citation:
  ama: Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. <i>International
    Mathematics Research Notices</i>. 2020;2020(3):669-697. doi:<a href="https://doi.org/10.1093/imrn/rny037">10.1093/imrn/rny037</a>
  apa: Akopyan, A., &#38; Karasev, R. (2020). Waist of balls in hyperbolic and spherical
    spaces. <i>International Mathematics Research Notices</i>. Oxford University Press.
    <a href="https://doi.org/10.1093/imrn/rny037">https://doi.org/10.1093/imrn/rny037</a>
  chicago: Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and
    Spherical Spaces.” <i>International Mathematics Research Notices</i>. Oxford University
    Press, 2020. <a href="https://doi.org/10.1093/imrn/rny037">https://doi.org/10.1093/imrn/rny037</a>.
  ieee: A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,”
    <i>International Mathematics Research Notices</i>, vol. 2020, no. 3. Oxford University
    Press, pp. 669–697, 2020.
  ista: Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces.
    International Mathematics Research Notices. 2020(3), 669–697.
  mla: Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical
    Spaces.” <i>International Mathematics Research Notices</i>, vol. 2020, no. 3,
    Oxford University Press, 2020, pp. 669–97, doi:<a href="https://doi.org/10.1093/imrn/rny037">10.1093/imrn/rny037</a>.
  short: A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020)
    669–697.
date_created: 2022-03-18T11:39:30Z
date_published: 2020-02-01T00:00:00Z
date_updated: 2023-08-24T14:19:55Z
day: '01'
department:
- _id: HeEd
doi: 10.1093/imrn/rny037
external_id:
  arxiv:
  - '1702.07513'
  isi:
  - '000522852700002'
intvolume: '      2020'
isi: 1
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1702.07513
month: '02'
oa: 1
oa_version: Preprint
page: 669-697
publication: International Mathematics Research Notices
publication_identifier:
  eissn:
  - 1687-0247
  issn:
  - 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Waist of balls in hyperbolic and spherical spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2020
year: '2020'
...
---
_id: '9576'
abstract:
- lang: eng
  text: In 1989, Rota made the following conjecture. Given n bases B1,…,Bn in an n-dimensional
    vector space V⁠, one can always find n disjoint bases of V⁠, each containing exactly
    one element from each Bi (we call such bases transversal bases). Rota’s basis
    conjecture remains wide open despite its apparent simplicity and the efforts of
    many researchers (e.g., the conjecture was recently the subject of the collaborative
    “Polymath” project). In this paper we prove that one can always find (1/2−o(1))n
    disjoint transversal bases, improving on the previous best bound of Ω(n/logn)⁠.
    Our results also apply to the more general setting of matroids.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Matija
  full_name: Bucić, Matija
  last_name: Bucić
- first_name: Matthew Alan
  full_name: Kwan, Matthew Alan
  id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
  last_name: Kwan
  orcid: 0000-0002-4003-7567
- first_name: Alexey
  full_name: Pokrovskiy, Alexey
  last_name: Pokrovskiy
- first_name: Benny
  full_name: Sudakov, Benny
  last_name: Sudakov
citation:
  ama: Bucić M, Kwan MA, Pokrovskiy A, Sudakov B. Halfway to Rota’s basis conjecture.
    <i>International Mathematics Research Notices</i>. 2020;2020(21):8007-8026. doi:<a
    href="https://doi.org/10.1093/imrn/rnaa004">10.1093/imrn/rnaa004</a>
  apa: Bucić, M., Kwan, M. A., Pokrovskiy, A., &#38; Sudakov, B. (2020). Halfway to
    Rota’s basis conjecture. <i>International Mathematics Research Notices</i>. Oxford
    University Press. <a href="https://doi.org/10.1093/imrn/rnaa004">https://doi.org/10.1093/imrn/rnaa004</a>
  chicago: Bucić, Matija, Matthew Alan Kwan, Alexey Pokrovskiy, and Benny Sudakov.
    “Halfway to Rota’s Basis Conjecture.” <i>International Mathematics Research Notices</i>.
    Oxford University Press, 2020. <a href="https://doi.org/10.1093/imrn/rnaa004">https://doi.org/10.1093/imrn/rnaa004</a>.
  ieee: M. Bucić, M. A. Kwan, A. Pokrovskiy, and B. Sudakov, “Halfway to Rota’s basis
    conjecture,” <i>International Mathematics Research Notices</i>, vol. 2020, no.
    21. Oxford University Press, pp. 8007–8026, 2020.
  ista: Bucić M, Kwan MA, Pokrovskiy A, Sudakov B. 2020. Halfway to Rota’s basis conjecture.
    International Mathematics Research Notices. 2020(21), 8007–8026.
  mla: Bucić, Matija, et al. “Halfway to Rota’s Basis Conjecture.” <i>International
    Mathematics Research Notices</i>, vol. 2020, no. 21, Oxford University Press,
    2020, pp. 8007–26, doi:<a href="https://doi.org/10.1093/imrn/rnaa004">10.1093/imrn/rnaa004</a>.
  short: M. Bucić, M.A. Kwan, A. Pokrovskiy, B. Sudakov, International Mathematics
    Research Notices 2020 (2020) 8007–8026.
date_created: 2021-06-21T08:12:30Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2023-02-23T14:01:30Z
day: '01'
doi: 10.1093/imrn/rnaa004
extern: '1'
external_id:
  arxiv:
  - '1810.07462'
intvolume: '      2020'
issue: '21'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv-export-lb.library.cornell.edu/abs/1810.07462
month: '11'
oa: 1
oa_version: Preprint
page: 8007-8026
publication: International Mathematics Research Notices
publication_identifier:
  eissn:
  - 1687-0247
  issn:
  - 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Halfway to Rota’s basis conjecture
type: journal_article
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 2020
year: '2020'
...
---
_id: '9577'
abstract:
- lang: eng
  text: An n-vertex graph is called C-Ramsey if it has no clique or independent set
    of size Clogn⁠. All known constructions of Ramsey graphs involve randomness in
    an essential way, and there is an ongoing line of research towards showing that
    in fact all Ramsey graphs must obey certain “richness” properties characteristic
    of random graphs. Motivated by an old problem of Erd̋s and McKay, recently Narayanan,
    Sahasrabudhe, and Tomon conjectured that for any fixed C, every n-vertex C-Ramsey
    graph induces subgraphs of Θ(n2) different sizes. In this paper we prove this
    conjecture.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Matthew Alan
  full_name: Kwan, Matthew Alan
  id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
  last_name: Kwan
  orcid: 0000-0002-4003-7567
- first_name: Benny
  full_name: Sudakov, Benny
  last_name: Sudakov
citation:
  ama: Kwan MA, Sudakov B. Ramsey graphs induce subgraphs of quadratically many sizes.
    <i>International Mathematics Research Notices</i>. 2020;2020(6):1621–1638. doi:<a
    href="https://doi.org/10.1093/imrn/rny064">10.1093/imrn/rny064</a>
  apa: Kwan, M. A., &#38; Sudakov, B. (2020). Ramsey graphs induce subgraphs of quadratically
    many sizes. <i>International Mathematics Research Notices</i>. Oxford University
    Press. <a href="https://doi.org/10.1093/imrn/rny064">https://doi.org/10.1093/imrn/rny064</a>
  chicago: Kwan, Matthew Alan, and Benny Sudakov. “Ramsey Graphs Induce Subgraphs
    of Quadratically Many Sizes.” <i>International Mathematics Research Notices</i>.
    Oxford University Press, 2020. <a href="https://doi.org/10.1093/imrn/rny064">https://doi.org/10.1093/imrn/rny064</a>.
  ieee: M. A. Kwan and B. Sudakov, “Ramsey graphs induce subgraphs of quadratically
    many sizes,” <i>International Mathematics Research Notices</i>, vol. 2020, no.
    6. Oxford University Press, pp. 1621–1638, 2020.
  ista: Kwan MA, Sudakov B. 2020. Ramsey graphs induce subgraphs of quadratically
    many sizes. International Mathematics Research Notices. 2020(6), 1621–1638.
  mla: Kwan, Matthew Alan, and Benny Sudakov. “Ramsey Graphs Induce Subgraphs of Quadratically
    Many Sizes.” <i>International Mathematics Research Notices</i>, vol. 2020, no.
    6, Oxford University Press, 2020, pp. 1621–1638, doi:<a href="https://doi.org/10.1093/imrn/rny064">10.1093/imrn/rny064</a>.
  short: M.A. Kwan, B. Sudakov, International Mathematics Research Notices 2020 (2020)
    1621–1638.
date_created: 2021-06-21T08:30:12Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2023-02-23T14:01:33Z
day: '01'
doi: 10.1093/imrn/rny064
extern: '1'
external_id:
  arxiv:
  - '1711.02937'
intvolume: '      2020'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1093/imrn/rny064
month: '03'
oa: 1
oa_version: Published Version
page: 1621–1638
publication: International Mathematics Research Notices
publication_identifier:
  eissn:
  - 1687-0247
  issn:
  - 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Ramsey graphs induce subgraphs of quadratically many sizes
type: journal_article
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 2020
year: '2020'
...
---
_id: '268'
abstract:
- lang: eng
  text: We show that any subset of the squares of positive relative upper density
    contains nontrivial solutions to a translation-invariant linear equation in five
    or more variables, with explicit quantitative bounds. As a consequence, we establish
    the partition regularity of any diagonal quadric in five or more variables whose
    coefficients sum to zero. Unlike previous approaches, which are limited to equations
    in seven or more variables, we employ transference technology of Green to import
    bounds from the linear setting.
acknowledgement: Whilst working on this paper the authors were supported by ERC grant
  306457.
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: Sean
  full_name: Prendiville, Sean
  last_name: Prendiville
citation:
  ama: Browning TD, Prendiville S. A transference approach to a Roth-type theorem
    in the squares. <i>International Mathematics Research Notices</i>. 2017;2017(7):2219-2248.
    doi:<a href="https://doi.org/10.1093/imrn/rnw096">10.1093/imrn/rnw096</a>
  apa: Browning, T. D., &#38; Prendiville, S. (2017). A transference approach to a
    Roth-type theorem in the squares. <i>International Mathematics Research Notices</i>.
    Oxford University Press. <a href="https://doi.org/10.1093/imrn/rnw096">https://doi.org/10.1093/imrn/rnw096</a>
  chicago: Browning, Timothy D, and Sean Prendiville. “A Transference Approach to
    a Roth-Type Theorem in the Squares.” <i>International Mathematics Research Notices</i>.
    Oxford University Press, 2017. <a href="https://doi.org/10.1093/imrn/rnw096">https://doi.org/10.1093/imrn/rnw096</a>.
  ieee: T. D. Browning and S. Prendiville, “A transference approach to a Roth-type
    theorem in the squares,” <i>International Mathematics Research Notices</i>, vol.
    2017, no. 7. Oxford University Press, pp. 2219–2248, 2017.
  ista: Browning TD, Prendiville S. 2017. A transference approach to a Roth-type theorem
    in the squares. International Mathematics Research Notices. 2017(7), 2219–2248.
  mla: Browning, Timothy D., and Sean Prendiville. “A Transference Approach to a Roth-Type
    Theorem in the Squares.” <i>International Mathematics Research Notices</i>, vol.
    2017, no. 7, Oxford University Press, 2017, pp. 2219–48, doi:<a href="https://doi.org/10.1093/imrn/rnw096">10.1093/imrn/rnw096</a>.
  short: T.D. Browning, S. Prendiville, International Mathematics Research Notices
    2017 (2017) 2219–2248.
date_created: 2018-12-11T11:45:31Z
date_published: 2017-04-01T00:00:00Z
date_updated: 2024-03-05T11:52:36Z
day: '01'
doi: 10.1093/imrn/rnw096
extern: '1'
external_id:
  arxiv:
  - '1510.00136'
intvolume: '      2017'
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1510.00136
month: '04'
oa: 1
oa_version: Preprint
page: 2219 - 2248
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
publication_status: published
publisher: Oxford University Press
publist_id: '7634'
quality_controlled: '1'
status: public
title: A transference approach to a Roth-type theorem in the squares
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2017
year: '2017'
...