---
OA_place: publisher
OA_type: hybrid
_id: '20222'
abstract:
- lang: eng
  text: Let X be a smooth projective hypersurface defined over Q. We provide new bounds
    for rational points of bounded height on X. In particular, we show that if X is
    a smooth projective hypersurface in Pn with n  4 and degree d  50, then the set
    of rational points on X of height bounded by B have cardinality On,d,ε (Bn−2+ε
    ). If X is smooth and has degree d  6, we improve the dimension growth conjecture
    bound. We achieve an analogue result for affine hypersurfaces whose projective
    closure is smooth.
acknowledgement: "While working on this paper, the author was supported by the European
  Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie
  Grant Agreement No. 101034413. The author is very grateful to Tim Browning for suggesting
  the problem and for many useful discussions. We thank the anonymous referees for
  their many helpful comments, which improved the exposition of the paper. We are
  also grateful to Gal Binyamini for their interest in this work and for drawing our
  attention to the aforementioned paper [1].\r\nWe shared an early version of this
  paper with Per Salberger, who mentioned that he announced a new bound for smooth
  threefolds in P4 during a talk in 2019 (see [7] for the abstract). This result has
  not been published."
article_number: rnaf249
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Matteo
  full_name: Verzobio, Matteo
  id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
  last_name: Verzobio
  orcid: 0000-0002-0854-0306
citation:
  ama: Verzobio M. Counting rational points on smooth hypersurfaces with high degree.
    <i>International Mathematics Research Notices</i>. 2025;2025(16). doi:<a href="https://doi.org/10.1093/imrn/rnaf249">10.1093/imrn/rnaf249</a>
  apa: Verzobio, M. (2025). Counting rational points on smooth hypersurfaces with
    high degree. <i>International Mathematics Research Notices</i>. Oxford University
    Press. <a href="https://doi.org/10.1093/imrn/rnaf249">https://doi.org/10.1093/imrn/rnaf249</a>
  chicago: Verzobio, Matteo. “Counting Rational Points on Smooth Hypersurfaces with
    High Degree.” <i>International Mathematics Research Notices</i>. Oxford University
    Press, 2025. <a href="https://doi.org/10.1093/imrn/rnaf249">https://doi.org/10.1093/imrn/rnaf249</a>.
  ieee: M. Verzobio, “Counting rational points on smooth hypersurfaces with high degree,”
    <i>International Mathematics Research Notices</i>, vol. 2025, no. 16. Oxford University
    Press, 2025.
  ista: Verzobio M. 2025. Counting rational points on smooth hypersurfaces with high
    degree. International Mathematics Research Notices. 2025(16), rnaf249.
  mla: Verzobio, Matteo. “Counting Rational Points on Smooth Hypersurfaces with High
    Degree.” <i>International Mathematics Research Notices</i>, vol. 2025, no. 16,
    rnaf249, Oxford University Press, 2025, doi:<a href="https://doi.org/10.1093/imrn/rnaf249">10.1093/imrn/rnaf249</a>.
  short: M. Verzobio, International Mathematics Research Notices 2025 (2025).
corr_author: '1'
date_created: 2025-08-24T22:01:31Z
date_published: 2025-08-01T00:00:00Z
date_updated: 2025-09-30T14:26:34Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1093/imrn/rnaf249
ec_funded: 1
external_id:
  arxiv:
  - '2503.19451'
  isi:
  - '001549126000001'
file:
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issue: '16'
language:
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month: '08'
oa: 1
oa_version: Published Version
project:
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  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: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Counting rational points on smooth hypersurfaces with high degree
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---
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_id: '20504'
abstract:
- lang: eng
  text: "Let r, k,  be integers such that 0 ≤  ≤ (k/r). Given a large r-uniform hypergraph
    G, we consider the\r\nfraction of k-vertex subsets that span exactly  edges. If
    \ is 0 or (k/r), this fraction can be exactly 1 (by taking G to be empty or complete),
    but for all other values of , one might suspect that this fraction is always significantly
    smaller than 1.\r\nIn this paper we prove an essentially optimal result along
    these lines: if  is not 0 or (k/r), then this\r\nfraction is at most (1/e) + ε,
    assuming k is sufficiently large in terms of r and ε > 0, and G is sufficiently
    large in terms of k. Previously, this was only known for a very limited range
    of values of r, k,  (due to Kwan–Sudakov–Tran, Fox–Sauermann, and Martinsson–Mousset–Noever–Trujic).
    Our result answers a question of Alon–Hefetz–Krivelevich–Tyomkyn, who suggested
    this as a hypergraph generalization of their edge-statistics conjecture. We also
    prove a much stronger bound when  is far from 0 and (k/r)."
acknowledgement: "This work was supported by NSF CAREER award DMS-2237646 [to V.J.],
  ERC Starting Grant “RANDSTRUCT” [no. 101076777 to M.K.], NSF grant DMS-2153576 [to
  D.M.], and the National Key Research and Development Program of China [2023YFA101020
  to T.T.].\r\nWe would like to thank Lisa Sauermann for her helpful comments. We
  would also like to thank Alex Grebennikov for identifying an oversight in the application
  of Theorem 7.1 (in a previous version of this paper)."
article_number: rnaf273
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Vishesh
  full_name: Jain, Vishesh
  last_name: Jain
- 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: Dhruv
  full_name: Mubayi, Dhruv
  last_name: Mubayi
- first_name: Tuan
  full_name: Tran, Tuan
  last_name: Tran
citation:
  ama: Jain V, Kwan MA, Mubayi D, Tran T. The edge-statistics conjecture for hypergraphs.
    <i>International Mathematics Research Notices</i>. 2025;2025(18). doi:<a href="https://doi.org/10.1093/imrn/rnaf273">10.1093/imrn/rnaf273</a>
  apa: Jain, V., Kwan, M. A., Mubayi, D., &#38; Tran, T. (2025). The edge-statistics
    conjecture for hypergraphs. <i>International Mathematics Research Notices</i>.
    Oxford University Press. <a href="https://doi.org/10.1093/imrn/rnaf273">https://doi.org/10.1093/imrn/rnaf273</a>
  chicago: Jain, Vishesh, Matthew Alan Kwan, Dhruv Mubayi, and Tuan Tran. “The Edge-Statistics
    Conjecture for Hypergraphs.” <i>International Mathematics Research Notices</i>.
    Oxford University Press, 2025. <a href="https://doi.org/10.1093/imrn/rnaf273">https://doi.org/10.1093/imrn/rnaf273</a>.
  ieee: V. Jain, M. A. Kwan, D. Mubayi, and T. Tran, “The edge-statistics conjecture
    for hypergraphs,” <i>International Mathematics Research Notices</i>, vol. 2025,
    no. 18. Oxford University Press, 2025.
  ista: Jain V, Kwan MA, Mubayi D, Tran T. 2025. The edge-statistics conjecture for
    hypergraphs. International Mathematics Research Notices. 2025(18), rnaf273.
  mla: Jain, Vishesh, et al. “The Edge-Statistics Conjecture for Hypergraphs.” <i>International
    Mathematics Research Notices</i>, vol. 2025, no. 18, rnaf273, Oxford University
    Press, 2025, doi:<a href="https://doi.org/10.1093/imrn/rnaf273">10.1093/imrn/rnaf273</a>.
  short: V. Jain, M.A. Kwan, D. Mubayi, T. Tran, International Mathematics Research
    Notices 2025 (2025).
corr_author: '1'
date_created: 2025-10-20T11:08:57Z
date_published: 2025-09-11T00:00:00Z
date_updated: 2025-12-01T13:00:35Z
day: '11'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.1093/imrn/rnaf273
external_id:
  arxiv:
  - '2505.03954'
  isi:
  - '001575137400001'
file:
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issue: '18'
language:
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month: '09'
oa: 1
oa_version: Published Version
project:
- _id: bd95085b-d553-11ed-ba76-e55d3349be45
  grant_number: '101076777'
  name: Randomness and structure in combinatorics
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: The edge-statistics conjecture for hypergraphs
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2025
year: '2025'
...
---
OA_place: repository
OA_type: green
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abstract:
- lang: eng
  text: We explain how the (shifted) Ratios Conjecture for $L(s,\chi )$ would extend
    a randomization argument of Harper from a conductor-limited range to an unlimited
    range of “beyond square-root cancellation” for character twists of the Liouville
    function. As a corollary, the Liouville function would have nontrivial cancellation
    in arithmetic progressions of modulus just exceeding the well-known square-root
    barrier. Morally, the paper passes from random matrices to random multiplicative
    functions.
acknowledgement: The first author is supported by the European Union’s Horizon 2020
  research and innovation program under the Marie Skłodowska-Curie Grant Agreement
  No. 101034413. The second author is supported by a Simons Junior Fellowship from
  Simons Foundation. We thank Paul Bourgade and Kannan Soundararajan for discussions
  on random matrices and probability, Alexandra Florea for helpful comments on the
  Ratios Conjecture, and Joni Teräväinen for providing several references. We are
  also grateful to Alexandra Florea, Adam Harper, Joni Teräväinen, and the referee
  for helpful comments on earlier drafts.
article_number: rnaf279
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Victor
  full_name: Wang, Victor
  id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9
  last_name: Wang
  orcid: 0000-0002-0704-7026
- first_name: Max Wenqiang
  full_name: Xu, Max Wenqiang
  last_name: Xu
citation:
  ama: Wang V, Xu MW. Harper’s beyond square-root conjecture. <i>International Mathematics
    Research Notices</i>. 2025;2025(18). doi:<a href="https://doi.org/10.1093/imrn/rnaf279">10.1093/imrn/rnaf279</a>
  apa: Wang, V., &#38; Xu, M. W. (2025). Harper’s beyond square-root conjecture. <i>International
    Mathematics Research Notices</i>. Oxford University Press. <a href="https://doi.org/10.1093/imrn/rnaf279">https://doi.org/10.1093/imrn/rnaf279</a>
  chicago: Wang, Victor, and Max Wenqiang Xu. “Harper’s beyond Square-Root Conjecture.”
    <i>International Mathematics Research Notices</i>. Oxford University Press, 2025.
    <a href="https://doi.org/10.1093/imrn/rnaf279">https://doi.org/10.1093/imrn/rnaf279</a>.
  ieee: V. Wang and M. W. Xu, “Harper’s beyond square-root conjecture,” <i>International
    Mathematics Research Notices</i>, vol. 2025, no. 18. Oxford University Press,
    2025.
  ista: Wang V, Xu MW. 2025. Harper’s beyond square-root conjecture. International
    Mathematics Research Notices. 2025(18), rnaf279.
  mla: Wang, Victor, and Max Wenqiang Xu. “Harper’s beyond Square-Root Conjecture.”
    <i>International Mathematics Research Notices</i>, vol. 2025, no. 18, rnaf279,
    Oxford University Press, 2025, doi:<a href="https://doi.org/10.1093/imrn/rnaf279">10.1093/imrn/rnaf279</a>.
  short: V. Wang, M.W. Xu, International Mathematics Research Notices 2025 (2025).
date_created: 2026-02-17T07:45:45Z
date_published: 2025-09-01T00:00:00Z
date_updated: 2026-02-18T07:41:56Z
day: '01'
department:
- _id: TiBr
doi: 10.1093/imrn/rnaf279
ec_funded: 1
external_id:
  arxiv:
  - '2405.04094'
intvolume: '      2025'
issue: '18'
language:
- iso: eng
main_file_link:
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  url: https://doi.org/10.48550/arXiv.2405.04094
month: '09'
oa: 1
oa_version: Preprint
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: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Harper’s beyond square-root conjecture
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2025
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18900'
abstract:
- lang: eng
  text: We prove that certain closable derivations on the GNS Hilbert space associated
    with a non-tracial weight on a von Neumann algebra give rise to GNS-symmetric
    semigroups of contractive completely positive maps on the von Neumann algebra.
acknowledgement: 'The author was funded by the Austrian Science Fund under the Esprit
  Programme [ESP 156]. For the purpose of Open Access, the authors have applied a
  CC BY public copyright licence to any Author Accepted Manuscript version arising
  from this submission. '
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Melchior
  full_name: Wirth, Melchior
  id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
  last_name: Wirth
  orcid: 0000-0002-0519-4241
citation:
  ama: Wirth M. Modular completely Dirichlet forms as squares of derivations. <i>International
    Mathematics Research Notices</i>. 2024;2024(14):10597-10614. doi:<a href="https://doi.org/10.1093/imrn/rnae092">10.1093/imrn/rnae092</a>
  apa: Wirth, M. (2024). Modular completely Dirichlet forms as squares of derivations.
    <i>International Mathematics Research Notices</i>. Oxford University Press. <a
    href="https://doi.org/10.1093/imrn/rnae092">https://doi.org/10.1093/imrn/rnae092</a>
  chicago: Wirth, Melchior. “Modular Completely Dirichlet Forms as Squares of Derivations.”
    <i>International Mathematics Research Notices</i>. Oxford University Press, 2024.
    <a href="https://doi.org/10.1093/imrn/rnae092">https://doi.org/10.1093/imrn/rnae092</a>.
  ieee: M. Wirth, “Modular completely Dirichlet forms as squares of derivations,”
    <i>International Mathematics Research Notices</i>, vol. 2024, no. 14. Oxford University
    Press, pp. 10597–10614, 2024.
  ista: Wirth M. 2024. Modular completely Dirichlet forms as squares of derivations.
    International Mathematics Research Notices. 2024(14), 10597–10614.
  mla: Wirth, Melchior. “Modular Completely Dirichlet Forms as Squares of Derivations.”
    <i>International Mathematics Research Notices</i>, vol. 2024, no. 14, Oxford University
    Press, 2024, pp. 10597–614, doi:<a href="https://doi.org/10.1093/imrn/rnae092">10.1093/imrn/rnae092</a>.
  short: M. Wirth, International Mathematics Research Notices 2024 (2024) 10597–10614.
corr_author: '1'
date_created: 2025-01-27T12:36:10Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2025-09-09T12:02:46Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1093/imrn/rnae092
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oa: 1
oa_version: Published Version
page: 10597-10614
project:
- _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833
  grant_number: ESP156_N
  name: Gradient flow techniques for quantum Markov semigroups
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: Modular completely Dirichlet forms as squares of derivations
tmp:
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  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 2024
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19051'
abstract:
- lang: eng
  text: This paper corrects an error in an earlier work of the author.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Timothy D
  full_name: Browning, Timothy D
  id: 35827D50-F248-11E8-B48F-1D18A9856A87
  last_name: Browning
  orcid: 0000-0002-8314-0177
citation:
  ama: Browning TD. The polynomial sieve and equal sums of like polynomials. <i>International
    Mathematics Research Notices</i>. 2024;2024(13):10165-10168. doi:<a href="https://doi.org/10.1093/imrn/rnae066">10.1093/imrn/rnae066</a>
  apa: Browning, T. D. (2024). The polynomial sieve and equal sums of like polynomials.
    <i>International Mathematics Research Notices</i>. Oxford University Press. <a
    href="https://doi.org/10.1093/imrn/rnae066">https://doi.org/10.1093/imrn/rnae066</a>
  chicago: Browning, Timothy D. “The Polynomial Sieve and Equal Sums of like Polynomials.”
    <i>International Mathematics Research Notices</i>. Oxford University Press, 2024.
    <a href="https://doi.org/10.1093/imrn/rnae066">https://doi.org/10.1093/imrn/rnae066</a>.
  ieee: T. D. Browning, “The polynomial sieve and equal sums of like polynomials,”
    <i>International Mathematics Research Notices</i>, vol. 2024, no. 13. Oxford University
    Press, pp. 10165–10168, 2024.
  ista: Browning TD. 2024. The polynomial sieve and equal sums of like polynomials.
    International Mathematics Research Notices. 2024(13), 10165–10168.
  mla: Browning, Timothy D. “The Polynomial Sieve and Equal Sums of like Polynomials.”
    <i>International Mathematics Research Notices</i>, vol. 2024, no. 13, Oxford University
    Press, 2024, pp. 10165–68, doi:<a href="https://doi.org/10.1093/imrn/rnae066">10.1093/imrn/rnae066</a>.
  short: T.D. Browning, International Mathematics Research Notices 2024 (2024) 10165–10168.
corr_author: '1'
date_created: 2025-02-18T07:15:50Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2025-09-09T12:16:45Z
day: '01'
ddc:
- '510'
department:
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doi: 10.1093/imrn/rnae066
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title: The polynomial sieve and equal sums of like polynomials
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...
---
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_id: '19486'
abstract:
- lang: eng
  text: Consider the family of elliptic curves En:y2=x3+n2, where n varies over positive
    cubefree integers. There is a rational 3-isogeny ϕ from En to E^n:y2=x3−27n2 and
    a dual isogeny ϕ^:E^n→En. We show that for almost all n, the rank of Selϕ(En)
    is 0, and the rank of Selϕ^(E^n) is determined by the number of prime factors
    of n that are congruent to 2mod3 and the congruence class of nmod9.
acknowledgement: The author would like to thank Peter Koymans and Carlo Pagano for
  helpful discussions.
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. The 3-isogeny selmer groups of the elliptic curves y2=x3+n2. <i>International
    Mathematics Research Notices</i>. 2024;2024(9):7571-7593. doi:<a href="https://doi.org/10.1093/imrn/rnad266">10.1093/imrn/rnad266</a>
  apa: Chan, S. (2024). The 3-isogeny selmer groups of the elliptic curves y2=x3+n2.
    <i>International Mathematics Research Notices</i>. Oxford University Press. <a
    href="https://doi.org/10.1093/imrn/rnad266">https://doi.org/10.1093/imrn/rnad266</a>
  chicago: Chan, Stephanie. “The 3-Isogeny Selmer Groups of the Elliptic Curves Y2=x3+n2.”
    <i>International Mathematics Research Notices</i>. Oxford University Press, 2024.
    <a href="https://doi.org/10.1093/imrn/rnad266">https://doi.org/10.1093/imrn/rnad266</a>.
  ieee: S. Chan, “The 3-isogeny selmer groups of the elliptic curves y2=x3+n2,” <i>International
    Mathematics Research Notices</i>, vol. 2024, no. 9. Oxford University Press, pp.
    7571–7593, 2024.
  ista: Chan S. 2024. The 3-isogeny selmer groups of the elliptic curves y2=x3+n2.
    International Mathematics Research Notices. 2024(9), 7571–7593.
  mla: Chan, Stephanie. “The 3-Isogeny Selmer Groups of the Elliptic Curves Y2=x3+n2.”
    <i>International Mathematics Research Notices</i>, vol. 2024, no. 9, Oxford University
    Press, 2024, pp. 7571–93, doi:<a href="https://doi.org/10.1093/imrn/rnad266">10.1093/imrn/rnad266</a>.
  short: S. Chan, International Mathematics Research Notices 2024 (2024) 7571–7593.
date_created: 2025-04-05T10:50:33Z
date_published: 2024-05-01T00:00:00Z
date_updated: 2025-07-10T11:51:44Z
day: '01'
doi: 10.1093/imrn/rnad266
extern: '1'
external_id:
  arxiv:
  - '2211.06062'
intvolume: '      2024'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2211.06062
month: '05'
oa: 1
oa_version: Preprint
page: 7571-7593
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: The 3-isogeny selmer groups of the elliptic curves y2=x3+n2
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2024
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_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
  orcid: 0000-0002-4444-8718
citation:
  ama: Shen S. Tamely ramified geometric Langlands correspondence in positive characteristic.
    <i>International Mathematics Research Notices</i>. 2024;2024(7):6176-6208. 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>, vol. 2024, no. 7. Oxford University
    Press, pp. 6176–6208, 2024.
  ista: Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive
    characteristic. International Mathematics Research Notices. 2024(7), 6176–6208.
  mla: Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive
    Characteristic.” <i>International Mathematics Research Notices</i>, vol. 2024,
    no. 7, Oxford University Press, 2024, pp. 6176–208, doi:<a href="https://doi.org/10.1093/imrn/rnae005">10.1093/imrn/rnae005</a>.
  short: S. Shen, International Mathematics Research Notices 2024 (2024) 6176–6208.
corr_author: '1'
date_created: 2024-02-14T12:16:17Z
date_published: 2024-04-01T00:00:00Z
date_updated: 2025-09-09T08:30:06Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1093/imrn/rnae005
ec_funded: 1
external_id:
  arxiv:
  - '1810.12491'
  isi:
  - '001157898100001'
file:
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  file_size: 1488981
  relation: main_file
  success: 1
file_date_updated: 2024-07-22T11:41:57Z
has_accepted_license: '1'
intvolume: '      2024'
isi: 1
issue: '7'
keyword:
- General Mathematics
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 6176-6208
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: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tamely ramified geometric Langlands correspondence in positive characteristic
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: 2024
year: '2024'
...
---
_id: '17281'
abstract:
- lang: eng
  text: We extend the free convolution of Brown measures of R-diagonal elements introduced
    by Kösters and Tikhomirov [ 28] to fractional powers. We then show how this fractional
    free convolution arises naturally when studying the roots of random polynomials
    with independent coefficients under repeated differentiation. When the proportion
    of derivatives to the degree approaches one, we establish central limit theorem-type
    behavior and discuss stable distributions.
acknowledgement: This work was supported by the National Science Foundation [Grant
  No. DMS-2143142 to S.O.]; and the European Research Council [Grant No. 101020331].The
  third author acknowledges the support of the University of Colorado Boulder, where
  a portion of this work was completed. The authors thank Martin Auer, Vadim Gorin,
  Brian Hall, and Noah Williams for comments, corrections, and references. The authors
  also wish to thank the anonymous referees for useful feedback and corrections.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Andrew J
  full_name: Campbell, Andrew J
  id: 582b06a9-1f1c-11ee-b076-82ffce00dde4
  last_name: Campbell
- first_name: Sean
  full_name: O'Rourke, Sean
  last_name: O'Rourke
- first_name: David T
  full_name: Renfrew, David T
  id: 4845BF6A-F248-11E8-B48F-1D18A9856A87
  last_name: Renfrew
  orcid: 0000-0003-3493-121X
citation:
  ama: Campbell AJ, O’Rourke S, Renfrew DT. The fractional free convolution of R-diagonal
    elements and random polynomials under repeated differentiation. <i>International
    Mathematics Research Notices</i>. 2024;2024(13):10189-10218. doi:<a href="https://doi.org/10.1093/imrn/rnae062">10.1093/imrn/rnae062</a>
  apa: Campbell, A. J., O’Rourke, S., &#38; Renfrew, D. T. (2024). The fractional
    free convolution of R-diagonal elements and random polynomials under repeated
    differentiation. <i>International Mathematics Research Notices</i>. Oxford University
    Press. <a href="https://doi.org/10.1093/imrn/rnae062">https://doi.org/10.1093/imrn/rnae062</a>
  chicago: Campbell, Andrew J, Sean O’Rourke, and David T Renfrew. “The Fractional
    Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated
    Differentiation.” <i>International Mathematics Research Notices</i>. Oxford University
    Press, 2024. <a href="https://doi.org/10.1093/imrn/rnae062">https://doi.org/10.1093/imrn/rnae062</a>.
  ieee: A. J. Campbell, S. O’Rourke, and D. T. Renfrew, “The fractional free convolution
    of R-diagonal elements and random polynomials under repeated differentiation,”
    <i>International Mathematics Research Notices</i>, vol. 2024, no. 13. Oxford University
    Press, pp. 10189–10218, 2024.
  ista: Campbell AJ, O’Rourke S, Renfrew DT. 2024. The fractional free convolution
    of R-diagonal elements and random polynomials under repeated differentiation.
    International Mathematics Research Notices. 2024(13), 10189–10218.
  mla: Campbell, Andrew J., et al. “The Fractional Free Convolution of R-Diagonal
    Elements and Random Polynomials under Repeated Differentiation.” <i>International
    Mathematics Research Notices</i>, vol. 2024, no. 13, Oxford University Press,
    2024, pp. 10189–218, doi:<a href="https://doi.org/10.1093/imrn/rnae062">10.1093/imrn/rnae062</a>.
  short: A.J. Campbell, S. O’Rourke, D.T. Renfrew, International Mathematics Research
    Notices 2024 (2024) 10189–10218.
corr_author: '1'
date_created: 2024-07-21T22:01:01Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2025-09-08T08:16:32Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1093/imrn/rnae062
external_id:
  isi:
  - '001198019500001'
file:
- access_level: open_access
  checksum: f36a7dbf53f23d5833db711052e69b49
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  creator: dernst
  date_created: 2024-07-22T06:40:19Z
  date_updated: 2024-07-22T06:40:19Z
  file_id: '17288'
  file_name: 2024_IMRN_Campbell.pdf
  file_size: 1233508
  relation: main_file
  success: 1
file_date_updated: 2024-07-22T06:40:19Z
has_accepted_license: '1'
intvolume: '      2024'
isi: 1
issue: '13'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 10189-10218
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: The fractional free convolution of R-diagonal elements and random polynomials
  under repeated differentiation
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: 2024
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.
corr_author: '1'
date_created: 2024-01-08T09:48:56Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2025-09-09T14:08:25Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1093/imrn/rnad210
external_id:
  arxiv:
  - '2212.11781'
  isi:
  - '001184146800001'
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'
isi: 1
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'
scopus_import: '1'
status: public
title: Functional John and Löwner conditions for pairs of log-concave functions
tmp:
  image: /images/cc_by_nc_nd.png
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  short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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 University Press. <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 University
    Press, 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 University
    Press, 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 University Press, 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.
corr_author: '1'
date_created: 2021-01-22T09:31:09Z
date_published: 2023-04-01T00:00:00Z
date_updated: 2025-05-14T11:07:41Z
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 University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Integral points of bounded height on a log Fano threefold
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2023
year: '2023'
...
---
OA_place: repository
OA_type: green
_id: '20617'
abstract:
- lang: eng
  text: Our previous paper describes a geometric translation of the construction of
    open Gromov–Witten invariants by Solomon and Tukachinsky from a perspective of
    $A_{\infty }$-algebras of differential forms. We now use this geometric perspective
    to show that these invariants reduce to Welschinger’s open Gromov–Witten invariants
    in dimension 6, inline with their and Tian’s expectations. As an immediate corollary,
    we obtain a translation of Solomon–Tukachinsky’s open WDVV equations into relations
    for Welschinger’s invariants.
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. Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants
    of symplectic six-folds. <i>International Mathematics Research Notices</i>. 2022;2022(9):7021-7055.
    doi:<a href="https://doi.org/10.1093/imrn/rnaa318">10.1093/imrn/rnaa318</a>
  apa: Chen, X. (2022). Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten
    invariants of symplectic six-folds. <i>International Mathematics Research Notices</i>.
    Oxford University Press. <a href="https://doi.org/10.1093/imrn/rnaa318">https://doi.org/10.1093/imrn/rnaa318</a>
  chicago: Chen, Xujia. “Solomon-Tukachinsky’s versus Welschinger’s Open Gromov-Witten
    Invariants of Symplectic Six-Folds.” <i>International Mathematics Research Notices</i>.
    Oxford University Press, 2022. <a href="https://doi.org/10.1093/imrn/rnaa318">https://doi.org/10.1093/imrn/rnaa318</a>.
  ieee: X. Chen, “Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants
    of symplectic six-folds,” <i>International Mathematics Research Notices</i>, vol.
    2022, no. 9. Oxford University Press, pp. 7021–7055, 2022.
  ista: Chen X. 2022. Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten
    invariants of symplectic six-folds. International Mathematics Research Notices.
    2022(9), 7021–7055.
  mla: Chen, Xujia. “Solomon-Tukachinsky’s versus Welschinger’s Open Gromov-Witten
    Invariants of Symplectic Six-Folds.” <i>International Mathematics Research Notices</i>,
    vol. 2022, no. 9, Oxford University Press, 2022, pp. 7021–55, doi:<a href="https://doi.org/10.1093/imrn/rnaa318">10.1093/imrn/rnaa318</a>.
  short: X. Chen, International Mathematics Research Notices 2022 (2022) 7021–7055.
date_created: 2025-11-10T08:40:57Z
date_published: 2022-05-01T00:00:00Z
date_updated: 2025-11-10T14:57:33Z
day: '01'
doi: 10.1093/imrn/rnaa318
extern: '1'
external_id:
  arxiv:
  - '1912.05437'
intvolume: '      2022'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1912.05437
month: '05'
oa: 1
oa_version: Preprint
page: 7021-7055
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: Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants of
  symplectic six-folds
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_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'
...
---
OA_place: publisher
OA_type: hybrid
_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: 2024-10-16T12:20:07Z
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: 0043cee0-e5fc-11ee-9736-f83bc23afbf0
volume: 2020
year: '2020'
...
---
_id: '1012'
abstract:
- lang: eng
  text: We prove a new central limit theorem (CLT) for the difference of linear eigenvalue
    statistics of a Wigner random matrix H and its minor H and find that the fluctuation
    is much smaller than the fluctuations of the individual linear statistics, as
    a consequence of the strong correlation between the eigenvalues of H and H. In
    particular, our theorem identifies the fluctuation of Kerov's rectangular Young
    diagrams, defined by the interlacing eigenvalues ofH and H, around their asymptotic
    shape, the Vershik'Kerov'Logan'Shepp curve. Young diagrams equipped with the Plancherel
    measure follow the same limiting shape. For this, algebraically motivated, ensemble
    a CLT has been obtained in Ivanov and Olshanski [20] which is structurally similar
    to our result but the variance is different, indicating that the analogy between
    the two models has its limitations. Moreover, our theorem shows that Borodin's
    result [7] on the convergence of the spectral distribution of Wigner matrices
    to a Gaussian free field also holds in derivative sense.
article_processing_charge: No
arxiv: 1
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Dominik J
  full_name: Schröder, Dominik J
  id: 408ED176-F248-11E8-B48F-1D18A9856A87
  last_name: Schröder
  orcid: 0000-0002-2904-1856
citation:
  ama: Erdös L, Schröder DJ. Fluctuations of rectangular young diagrams of interlacing
    wigner eigenvalues. <i>International Mathematics Research Notices</i>. 2018;2018(10):3255-3298.
    doi:<a href="https://doi.org/10.1093/imrn/rnw330">10.1093/imrn/rnw330</a>
  apa: Erdös, L., &#38; Schröder, D. J. (2018). Fluctuations of rectangular young
    diagrams of interlacing wigner eigenvalues. <i>International Mathematics Research
    Notices</i>. Oxford University Press. <a href="https://doi.org/10.1093/imrn/rnw330">https://doi.org/10.1093/imrn/rnw330</a>
  chicago: Erdös, László, and Dominik J Schröder. “Fluctuations of Rectangular Young
    Diagrams of Interlacing Wigner Eigenvalues.” <i>International Mathematics Research
    Notices</i>. Oxford University Press, 2018. <a href="https://doi.org/10.1093/imrn/rnw330">https://doi.org/10.1093/imrn/rnw330</a>.
  ieee: L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of
    interlacing wigner eigenvalues,” <i>International Mathematics Research Notices</i>,
    vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018.
  ista: Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of
    interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10),
    3255–3298.
  mla: Erdös, László, and Dominik J. Schröder. “Fluctuations of Rectangular Young
    Diagrams of Interlacing Wigner Eigenvalues.” <i>International Mathematics Research
    Notices</i>, vol. 2018, no. 10, Oxford University Press, 2018, pp. 3255–98, doi:<a
    href="https://doi.org/10.1093/imrn/rnw330">10.1093/imrn/rnw330</a>.
  short: L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018
    (2018) 3255–3298.
date_created: 2018-12-11T11:49:41Z
date_published: 2018-05-18T00:00:00Z
date_updated: 2026-04-08T13:55:03Z
day: '18'
department:
- _id: LaEr
doi: 10.1093/imrn/rnw330
ec_funded: 1
external_id:
  arxiv:
  - '1608.05163'
  isi:
  - '000441668300009'
intvolume: '      2018'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1608.05163
month: '05'
oa: 1
oa_version: Preprint
page: 3255-3298
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
publication_status: published
publisher: Oxford University Press
publist_id: '6383'
quality_controlled: '1'
related_material:
  record:
  - id: '6179'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2018
year: '2018'
...
---
_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'
...