---
OA_place: repository
OA_type: green
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abstract:
- lang: eng
  text: "The local angle property of the (order-1) Delaunay triangulations of a generic
    set in R2\r\n asserts that the sum of two angles opposite a common edge is less
    than π. This paper extends this property to higher order and uses it to generalize
    two classic properties from order-1 to order-2: (1) among the complete level-2
    hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation
    lexicographically maximizes the sorted angle vector; (2) among the maximal level-2
    hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation
    is the only one that has the local angle property. We also use our method of establishing
    (2) to give a new short proof of the angle vector optimality for the (order-1)
    Delaunay triangulation. For order-1, both properties have been instrumental in
    numerous applications of Delaunay triangulations, and we expect that their generalization
    will make order-2 Delaunay triangulations more attractive to applications as well."
acknowledgement: Work by the first and third authors is partially supported by the
  European Research Council (ERC), grant no. 788183, by the Wittgenstein Prize, Austrian
  Science Fund (FWF), grant no. Z 342-N31, and by the DFG Collaborative Research Center
  TRR 109, Austrian Science Fund (FWF), grant no. I 02979-N35. Work by the second
  author is partially supported by the Alexander von Humboldt Foundation.
article_number: '110055'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Alexey
  full_name: Garber, Alexey
  last_name: Garber
- first_name: Morteza
  full_name: Saghafian, Morteza
  id: f86f7148-b140-11ec-9577-95435b8df824
  last_name: Saghafian
citation:
  ama: Edelsbrunner H, Garber A, Saghafian M. Order-2 Delaunay triangulations optimize
    angles. <i>Advances in Mathematics</i>. 2025;461. doi:<a href="https://doi.org/10.1016/j.aim.2024.110055">10.1016/j.aim.2024.110055</a>
  apa: Edelsbrunner, H., Garber, A., &#38; Saghafian, M. (2025). Order-2 Delaunay
    triangulations optimize angles. <i>Advances in Mathematics</i>. Elsevier. <a href="https://doi.org/10.1016/j.aim.2024.110055">https://doi.org/10.1016/j.aim.2024.110055</a>
  chicago: Edelsbrunner, Herbert, Alexey Garber, and Morteza Saghafian. “Order-2 Delaunay
    Triangulations Optimize Angles.” <i>Advances in Mathematics</i>. Elsevier, 2025.
    <a href="https://doi.org/10.1016/j.aim.2024.110055">https://doi.org/10.1016/j.aim.2024.110055</a>.
  ieee: H. Edelsbrunner, A. Garber, and M. Saghafian, “Order-2 Delaunay triangulations
    optimize angles,” <i>Advances in Mathematics</i>, vol. 461. Elsevier, 2025.
  ista: Edelsbrunner H, Garber A, Saghafian M. 2025. Order-2 Delaunay triangulations
    optimize angles. Advances in Mathematics. 461, 110055.
  mla: Edelsbrunner, Herbert, et al. “Order-2 Delaunay Triangulations Optimize Angles.”
    <i>Advances in Mathematics</i>, vol. 461, 110055, Elsevier, 2025, doi:<a href="https://doi.org/10.1016/j.aim.2024.110055">10.1016/j.aim.2024.110055</a>.
  short: H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).
corr_author: '1'
date_created: 2024-12-08T23:01:54Z
date_published: 2025-02-01T00:00:00Z
date_updated: 2025-04-15T07:16:53Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.aim.2024.110055
ec_funded: 1
external_id:
  arxiv:
  - '2310.18238'
  isi:
  - '001370682500001'
intvolume: '       461'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2310.18238
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '788183'
  name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: Z00342
  name: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I02979-N35
  name: Persistence and stability of geometric complexes
publication: Advances in Mathematics
publication_identifier:
  eissn:
  - 1090-2082
  issn:
  - 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Order-2 Delaunay triangulations optimize angles
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 461
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
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_id: '19727'
abstract:
- lang: eng
  text: By studying some Clausen-like multiple Dirichlet series, we complete the proof
    of Manin's conjecture for sufficiently split smooth equivariant compactifications
    of the translation-dilation group over the rationals. Secondary terms remain elusive
    in general.
acknowledgement: I thank Yuri Tschinkel for introducing me to the beautiful paper
  [53] and associated open questions, and thank him as well as Ramin Takloo-Bighash
  and Sho Tanimoto for their encouragement and comments. Also, I thank Tim Browning
  and Dan Loughran for comments and suggestions concerning Manin–Peyre, homogeneous
  spaces, and splitness. Thanks also to Anshul Adve, Peter Sarnak, Philip Tosteson,
  Katy Woo, and Nina Zubrilina for some interesting discussions. I thank the Browning
  Group and Andy O'Desky for many conversations. This project has received funding
  from the European Union's Horizon 2020 research and innovation program under the
  Marie Skłodowska-Curie Grant Agreement No. 101034413. Finally, I thank the editors
  and referees for their detailed input, which substantially improved the paper.
article_number: '110341'
article_processing_charge: Yes (via OA deal)
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
citation:
  ama: Wang V. Asymptotic growth of translation-dilation orbits. <i>Advances in Mathematics</i>.
    2025;475. doi:<a href="https://doi.org/10.1016/j.aim.2025.110341">10.1016/j.aim.2025.110341</a>
  apa: Wang, V. (2025). Asymptotic growth of translation-dilation orbits. <i>Advances
    in Mathematics</i>. Elsevier. <a href="https://doi.org/10.1016/j.aim.2025.110341">https://doi.org/10.1016/j.aim.2025.110341</a>
  chicago: Wang, Victor. “Asymptotic Growth of Translation-Dilation Orbits.” <i>Advances
    in Mathematics</i>. Elsevier, 2025. <a href="https://doi.org/10.1016/j.aim.2025.110341">https://doi.org/10.1016/j.aim.2025.110341</a>.
  ieee: V. Wang, “Asymptotic growth of translation-dilation orbits,” <i>Advances in
    Mathematics</i>, vol. 475. Elsevier, 2025.
  ista: Wang V. 2025. Asymptotic growth of translation-dilation orbits. Advances in
    Mathematics. 475, 110341.
  mla: Wang, Victor. “Asymptotic Growth of Translation-Dilation Orbits.” <i>Advances
    in Mathematics</i>, vol. 475, 110341, Elsevier, 2025, doi:<a href="https://doi.org/10.1016/j.aim.2025.110341">10.1016/j.aim.2025.110341</a>.
  short: V. Wang, Advances in Mathematics 475 (2025).
corr_author: '1'
das_tickbox: '0'
date_created: 2025-05-25T22:16:41Z
date_published: 2025-07-01T00:00:00Z
date_updated: 2026-07-16T10:45:31Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1016/j.aim.2025.110341
ec_funded: 1
external_id:
  arxiv:
  - '2309.07626'
  isi:
  - '001495142300002'
file:
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  checksum: 01f2589b678ba840d6a4066c1d8d7642
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  creator: dernst
  date_created: 2025-12-30T08:30:17Z
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has_accepted_license: '1'
intvolume: '       475'
isi: 1
language:
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month: '07'
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: Advances in Mathematics
publication_identifier:
  eissn:
  - 1090-2082
  issn:
  - 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Asymptotic growth of translation-dilation orbits
tmp:
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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: 475
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15248'
abstract:
- lang: eng
  text: Applying the technique of p-adic integration, we prove the topological mirror
    symmetry conjecture of Hausel-Thaddeus for the moduli spaces of (strongly) parabolic
    Higgs bundles for the structure groups SLn and PGLn, building on previous work
    of Groechenig-Wyss-Ziegler on the non-parabolic case. We also prove the E-polynomial
    of the smooth moduli space of parabolic GLn-Higgs bundles is independent of the
    degree of the underlying vector bundles.
acknowledgement: Shiyu Shen has received funding from the European Union's Horizon
  2020 research and innovation program under the Marie Skłodowska-Curie grant agreement
  No. 101034413.
article_number: '109616'
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. Mirror symmetry for parabolic Higgs bundles via p-adic integration.
    <i>Advances in Mathematics</i>. 2024;443(5). doi:<a href="https://doi.org/10.1016/j.aim.2024.109616">10.1016/j.aim.2024.109616</a>
  apa: Shen, S. (2024). Mirror symmetry for parabolic Higgs bundles via p-adic integration.
    <i>Advances in Mathematics</i>. Elsevier. <a href="https://doi.org/10.1016/j.aim.2024.109616">https://doi.org/10.1016/j.aim.2024.109616</a>
  chicago: Shen, Shiyu. “Mirror Symmetry for Parabolic Higgs Bundles via P-Adic Integration.”
    <i>Advances in Mathematics</i>. Elsevier, 2024. <a href="https://doi.org/10.1016/j.aim.2024.109616">https://doi.org/10.1016/j.aim.2024.109616</a>.
  ieee: S. Shen, “Mirror symmetry for parabolic Higgs bundles via p-adic integration,”
    <i>Advances in Mathematics</i>, vol. 443, no. 5. Elsevier, 2024.
  ista: Shen S. 2024. Mirror symmetry for parabolic Higgs bundles via p-adic integration.
    Advances in Mathematics. 443(5), 109616.
  mla: Shen, Shiyu. “Mirror Symmetry for Parabolic Higgs Bundles via P-Adic Integration.”
    <i>Advances in Mathematics</i>, vol. 443, no. 5, 109616, Elsevier, 2024, doi:<a
    href="https://doi.org/10.1016/j.aim.2024.109616">10.1016/j.aim.2024.109616</a>.
  short: S. Shen, Advances in Mathematics 443 (2024).
corr_author: '1'
date_created: 2024-03-31T22:01:11Z
date_published: 2024-05-01T00:00:00Z
date_updated: 2025-09-04T13:21:18Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1016/j.aim.2024.109616
ec_funded: 1
external_id:
  arxiv:
  - '2302.02817'
  isi:
  - '001216128200001'
file:
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  checksum: 68f2f08136ccf547891a16a2c0621e97
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  creator: dernst
  date_created: 2024-07-22T12:10:03Z
  date_updated: 2024-07-22T12:10:03Z
  file_id: '17315'
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intvolume: '       443'
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issue: '5'
language:
- iso: eng
month: '05'
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: Advances in Mathematics
publication_identifier:
  eissn:
  - 1090-2082
  issn:
  - 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Mirror symmetry for parabolic Higgs bundles via p-adic integration
tmp:
  image: /images/cc_by.png
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  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 443
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18065'
abstract:
- lang: eng
  text: We establish a close connection between acceleration and dynamical degree
    for one-frequency quasi-periodic compact cocycles, by showing that two vectors
    derived separately from each coincide. Based on this, we provide a dynamical classification
    of one-frequency quasi-periodic  SO(3, R)-cocycles.
acknowledgement: "X. Hou is partially supported by National Natural Science Foundation
  of China (Grant \r\n12071083) and Funds for Distinguished Youths of Hubei Province
  of China (\r\n2019CFA680). Y. Pan is supported by ERC Advanced Grant (#885707).
  Q. Zhou is partially supported by National Key R&D Program of China (2020YFA0713300),
  NSFC grant (\r\n12071232) and Nankai Zhide Foundation."
article_number: '109943'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Xuanji
  full_name: Hou, Xuanji
  last_name: Hou
- first_name: Yi
  full_name: Pan, Yi
  id: 1e21c7f7-9070-11eb-847d-8b04c7169523
  last_name: Pan
- first_name: Qi
  full_name: Zhou, Qi
  last_name: Zhou
citation:
  ama: Hou X, Pan Y, Zhou Q. Dynamical classification of analytic one-frequency quasi-periodic
    SO(3,R)-cocycles. <i>Advances in Mathematics</i>. 2024;457. doi:<a href="https://doi.org/10.1016/j.aim.2024.109943">10.1016/j.aim.2024.109943</a>
  apa: Hou, X., Pan, Y., &#38; Zhou, Q. (2024). Dynamical classification of analytic
    one-frequency quasi-periodic SO(3,R)-cocycles. <i>Advances in Mathematics</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.aim.2024.109943">https://doi.org/10.1016/j.aim.2024.109943</a>
  chicago: Hou, Xuanji, Yi Pan, and Qi Zhou. “Dynamical Classification of Analytic
    One-Frequency Quasi-Periodic SO(3,R)-Cocycles.” <i>Advances in Mathematics</i>.
    Elsevier, 2024. <a href="https://doi.org/10.1016/j.aim.2024.109943">https://doi.org/10.1016/j.aim.2024.109943</a>.
  ieee: X. Hou, Y. Pan, and Q. Zhou, “Dynamical classification of analytic one-frequency
    quasi-periodic SO(3,R)-cocycles,” <i>Advances in Mathematics</i>, vol. 457. Elsevier,
    2024.
  ista: Hou X, Pan Y, Zhou Q. 2024. Dynamical classification of analytic one-frequency
    quasi-periodic SO(3,R)-cocycles. Advances in Mathematics. 457, 109943.
  mla: Hou, Xuanji, et al. “Dynamical Classification of Analytic One-Frequency Quasi-Periodic
    SO(3,R)-Cocycles.” <i>Advances in Mathematics</i>, vol. 457, 109943, Elsevier,
    2024, doi:<a href="https://doi.org/10.1016/j.aim.2024.109943">10.1016/j.aim.2024.109943</a>.
  short: X. Hou, Y. Pan, Q. Zhou, Advances in Mathematics 457 (2024).
corr_author: '1'
date_created: 2024-09-15T22:01:39Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2025-09-08T09:44:19Z
day: '01'
ddc:
- '510'
department:
- _id: VaKa
doi: 10.1016/j.aim.2024.109943
ec_funded: 1
external_id:
  arxiv:
  - '2311.17537'
  isi:
  - '001315306500001'
file:
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- iso: eng
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
  call_identifier: H2020
  grant_number: '885707'
  name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Advances in Mathematics
publication_identifier:
  eissn:
  - 1090-2082
  issn:
  - 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles
tmp:
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  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 457
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18064'
abstract:
- lang: eng
  text: " We show that the total number of non-torsion integral points on the elliptic
    curves ED : y\r\n2 = x3 − D2x, where D ranges over positive squarefree integers
    less than N, is O(N(log N)\r\n−1/4+ǫ). The proof involves a discriminant-lowering
    procedure on integral binary quartic forms and an application of Heath-Brown’s
    method on estimating the average size of the 2-Selmer group of the curves in this
    family."
article_number: '109946'
article_processing_charge: Yes (via OA deal)
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 average number of integral points on the congruent number curves.
    <i>Advances in Mathematics</i>. 2024;457(11). doi:<a href="https://doi.org/10.1016/j.aim.2024.109946">10.1016/j.aim.2024.109946</a>
  apa: Chan, S. (2024). The average number of integral points on the congruent number
    curves. <i>Advances in Mathematics</i>. Elsevier. <a href="https://doi.org/10.1016/j.aim.2024.109946">https://doi.org/10.1016/j.aim.2024.109946</a>
  chicago: Chan, Stephanie. “The Average Number of Integral Points on the Congruent
    Number Curves.” <i>Advances in Mathematics</i>. Elsevier, 2024. <a href="https://doi.org/10.1016/j.aim.2024.109946">https://doi.org/10.1016/j.aim.2024.109946</a>.
  ieee: S. Chan, “The average number of integral points on the congruent number curves,”
    <i>Advances in Mathematics</i>, vol. 457, no. 11. Elsevier, 2024.
  ista: Chan S. 2024. The average number of integral points on the congruent number
    curves. Advances in Mathematics. 457(11), 109946.
  mla: Chan, Stephanie. “The Average Number of Integral Points on the Congruent Number
    Curves.” <i>Advances in Mathematics</i>, vol. 457, no. 11, 109946, Elsevier, 2024,
    doi:<a href="https://doi.org/10.1016/j.aim.2024.109946">10.1016/j.aim.2024.109946</a>.
  short: S. Chan, Advances in Mathematics 457 (2024).
corr_author: '1'
das_tickbox: '0'
date_created: 2024-09-15T22:01:39Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2026-07-29T10:03:09Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1016/j.aim.2024.109946
external_id:
  arxiv:
  - '2112.01615'
file:
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month: '11'
oa: 1
oa_version: Published Version
publication: Advances in Mathematics
publication_identifier:
  eissn:
  - 1090-2082
  issn:
  - 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: The average number of integral points on the congruent number curves
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  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 457
year: '2024'
...
---
_id: '10765'
abstract:
- lang: eng
  text: We establish the Hardy-Littlewood property (à la Borovoi-Rudnick) for Zariski
    open subsets in affine quadrics of the form q(x1,...,xn)=m, where q is a non-degenerate
    integral quadratic form in  n>3 variables and m is a non-zero integer. This gives
    asymptotic formulas for the density of integral points taking coprime polynomial
    values, which is a quantitative version of the arithmetic purity of strong approximation
    property off infinity for affine quadrics.
acknowledgement: "We are grateful to Mikhail Borovoi, Zeev Rudnick and Olivier Wienberg
  for their interest in our\r\nwork. We would like to address our gratitude to Ulrich
  Derenthal for his generous support at Leibniz Universitat Hannover. We are in debt
  to Tim Browning for an enlightening discussion and to the anonymous referees for
  critical comments, which lead to overall improvements of various preliminary versions
  of this paper. Part of this work was carried out and reported during a visit to
  the University of Science and Technology of China. We thank Yongqi Liang for offering
  warm hospitality. The first author was supported by a Humboldt-Forschungsstipendium.
  The second author was supported by grant DE 1646/4-2 of the Deutsche Forschungsgemeinschaft."
article_number: '108236'
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author:
- first_name: Yang
  full_name: Cao, Yang
  last_name: Cao
- first_name: Zhizhong
  full_name: Huang, Zhizhong
  id: 21f1b52f-2fd1-11eb-a347-a4cdb9b18a51
  last_name: Huang
citation:
  ama: Cao Y, Huang Z. Arithmetic purity of the Hardy-Littlewood property and geometric
    sieve for affine quadrics. <i>Advances in Mathematics</i>. 2022;398(3). doi:<a
    href="https://doi.org/10.1016/j.aim.2022.108236">10.1016/j.aim.2022.108236</a>
  apa: Cao, Y., &#38; Huang, Z. (2022). Arithmetic purity of the Hardy-Littlewood
    property and geometric sieve for affine quadrics. <i>Advances in Mathematics</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.aim.2022.108236">https://doi.org/10.1016/j.aim.2022.108236</a>
  chicago: Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood
    Property and Geometric Sieve for Affine Quadrics.” <i>Advances in Mathematics</i>.
    Elsevier, 2022. <a href="https://doi.org/10.1016/j.aim.2022.108236">https://doi.org/10.1016/j.aim.2022.108236</a>.
  ieee: Y. Cao and Z. Huang, “Arithmetic purity of the Hardy-Littlewood property and
    geometric sieve for affine quadrics,” <i>Advances in Mathematics</i>, vol. 398,
    no. 3. Elsevier, 2022.
  ista: Cao Y, Huang Z. 2022. Arithmetic purity of the Hardy-Littlewood property and
    geometric sieve for affine quadrics. Advances in Mathematics. 398(3), 108236.
  mla: Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood Property
    and Geometric Sieve for Affine Quadrics.” <i>Advances in Mathematics</i>, vol.
    398, no. 3, 108236, Elsevier, 2022, doi:<a href="https://doi.org/10.1016/j.aim.2022.108236">10.1016/j.aim.2022.108236</a>.
  short: Y. Cao, Z. Huang, Advances in Mathematics 398 (2022).
corr_author: '1'
das_tickbox: '0'
date_created: 2022-02-20T23:01:30Z
date_published: 2022-03-26T00:00:00Z
date_updated: 2026-08-19T13:00:41Z
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department:
- _id: TiBr
doi: 10.1016/j.aim.2022.108236
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publication_identifier:
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  issn:
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publication_status: published
publisher: Elsevier
quality_controlled: '1'
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title: Arithmetic purity of the Hardy-Littlewood property and geometric sieve for
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...
---
_id: '10033'
abstract:
- lang: eng
  text: The ⊗*-monoidal structure on the category of sheaves on the Ran space is not
    pro-nilpotent in the sense of [3]. However, under some connectivity assumptions,
    we prove that Koszul duality induces an equivalence of categories and that this
    equivalence behaves nicely with respect to Verdier duality on the Ran space and
    integrating along the Ran space, i.e. taking factorization homology. Based on
    ideas sketched in [4], we show that these results also offer a simpler alternative
    to one of the two main steps in the proof of the Atiyah-Bott formula given in
    [7] and [5].
acknowledgement: 'The author would like to express his gratitude to D. Gaitsgory,
  without whose tireless guidance and encouragement in pursuing this problem, this
  work would not have been possible. The author is grateful to his advisor B.C. Ngô
  for many years of patient guidance and support. This paper is revised while the
  author is a postdoc in Hausel group at IST Austria. We thank him and the group for
  providing a wonderful research environment. The author also gratefully acknowledges
  the support of the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization
  Homology,” Austrian Science Fund (FWF): M 2751.'
article_number: '107992'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Quoc P
  full_name: Ho, Quoc P
  id: 3DD82E3C-F248-11E8-B48F-1D18A9856A87
  last_name: Ho
  orcid: 0000-0001-6889-1418
citation:
  ama: Ho QP. The Atiyah-Bott formula and connectivity in chiral Koszul duality. <i>Advances
    in Mathematics</i>. 2021;392. doi:<a href="https://doi.org/10.1016/j.aim.2021.107992">10.1016/j.aim.2021.107992</a>
  apa: Ho, Q. P. (2021). The Atiyah-Bott formula and connectivity in chiral Koszul
    duality. <i>Advances in Mathematics</i>. Elsevier. <a href="https://doi.org/10.1016/j.aim.2021.107992">https://doi.org/10.1016/j.aim.2021.107992</a>
  chicago: Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul
    Duality.” <i>Advances in Mathematics</i>. Elsevier, 2021. <a href="https://doi.org/10.1016/j.aim.2021.107992">https://doi.org/10.1016/j.aim.2021.107992</a>.
  ieee: Q. P. Ho, “The Atiyah-Bott formula and connectivity in chiral Koszul duality,”
    <i>Advances in Mathematics</i>, vol. 392. Elsevier, 2021.
  ista: Ho QP. 2021. The Atiyah-Bott formula and connectivity in chiral Koszul duality.
    Advances in Mathematics. 392, 107992.
  mla: Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.”
    <i>Advances in Mathematics</i>, vol. 392, 107992, Elsevier, 2021, doi:<a href="https://doi.org/10.1016/j.aim.2021.107992">10.1016/j.aim.2021.107992</a>.
  short: Q.P. Ho, Advances in Mathematics 392 (2021).
corr_author: '1'
date_created: 2021-09-21T15:58:59Z
date_published: 2021-09-21T00:00:00Z
date_updated: 2025-04-14T09:09:35Z
day: '21'
ddc:
- '514'
department:
- _id: TaHa
doi: 10.1016/j.aim.2021.107992
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  - '1610.00212'
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intvolume: '       392'
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keyword:
- Chiral algebras
- Chiral homology
- Factorization algebras
- Koszul duality
- Ran space
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 26B96266-B435-11E9-9278-68D0E5697425
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  grant_number: M02751
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publication: Advances in Mathematics
publication_identifier:
  eissn:
  - 1090-2082
  issn:
  - 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
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title: The Atiyah-Bott formula and connectivity in chiral Koszul duality
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...
---
_id: '6310'
abstract:
- lang: eng
  text: An asymptotic formula is established for the number of rational points of
    bounded anticanonical height which lie on a certain Zariskiopen subset of an arbitrary
    smooth biquadratic hypersurface in sufficiently many variables. The proof uses
    the Hardy–Littlewood circle method.
article_processing_charge: No
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: L.Q.
  full_name: Hu, L.Q.
  last_name: Hu
citation:
  ama: Browning TD, Hu LQ. Counting rational points on biquadratic hypersurfaces.
    <i>Advances in Mathematics</i>. 2019;349:920-940. doi:<a href="https://doi.org/10.1016/j.aim.2019.04.031">10.1016/j.aim.2019.04.031</a>
  apa: Browning, T. D., &#38; Hu, L. Q. (2019). Counting rational points on biquadratic
    hypersurfaces. <i>Advances in Mathematics</i>. Elsevier. <a href="https://doi.org/10.1016/j.aim.2019.04.031">https://doi.org/10.1016/j.aim.2019.04.031</a>
  chicago: Browning, Timothy D, and L.Q. Hu. “Counting Rational Points on Biquadratic
    Hypersurfaces.” <i>Advances in Mathematics</i>. Elsevier, 2019. <a href="https://doi.org/10.1016/j.aim.2019.04.031">https://doi.org/10.1016/j.aim.2019.04.031</a>.
  ieee: T. D. Browning and L. Q. Hu, “Counting rational points on biquadratic hypersurfaces,”
    <i>Advances in Mathematics</i>, vol. 349. Elsevier, pp. 920–940, 2019.
  ista: Browning TD, Hu LQ. 2019. Counting rational points on biquadratic hypersurfaces.
    Advances in Mathematics. 349, 920–940.
  mla: Browning, Timothy D., and L. Q. Hu. “Counting Rational Points on Biquadratic
    Hypersurfaces.” <i>Advances in Mathematics</i>, vol. 349, Elsevier, 2019, pp.
    920–40, doi:<a href="https://doi.org/10.1016/j.aim.2019.04.031">10.1016/j.aim.2019.04.031</a>.
  short: T.D. Browning, L.Q. Hu, Advances in Mathematics 349 (2019) 920–940.
das_tickbox: '0'
date_created: 2019-04-16T09:13:25Z
date_published: 2019-06-20T00:00:00Z
date_updated: 2026-08-06T12:11:51Z
day: '20'
ddc:
- '512'
department:
- _id: TiBr
doi: 10.1016/j.aim.2019.04.031
external_id:
  arxiv:
  - '1810.08426'
  isi:
  - '000468857300025'
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  date_created: 2019-04-16T09:12:20Z
  date_updated: 2020-07-14T12:47:27Z
  file_id: '6311'
  file_name: wliqun.pdf
  file_size: 379158
  relation: main_file
file_date_updated: 2020-07-14T12:47:27Z
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intvolume: '       349'
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language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 920-940
publication: Advances in Mathematics
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  eissn:
  - 1090-2082
  issn:
  - 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Counting rational points on biquadratic hypersurfaces
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 349
year: '2019'
...