---
_id: '9037'
abstract:
- lang: eng
  text: "We continue our study of ‘no‐dimension’ analogues of basic theorems in combinatorial
    and convex geometry in Banach spaces. We generalize some results of the paper
    (Adiprasito, Bárány and Mustafa, ‘Theorems of Carathéodory, Helly, and Tverberg
    without dimension’, Proceedings of the Thirtieth Annual ACM‐SIAM Symposium on
    Discrete Algorithms (Society for Industrial and Applied Mathematics, San Diego,
    California, 2019) 2350–2360) and prove no‐dimension versions of the colored Tverberg
    theorem, the selection lemma and the weak  \U0001D700 ‐net theorem in Banach spaces
    of type  \U0001D45D>1 . To prove these results, we use the original ideas of Adiprasito,
    Bárány and Mustafa for the Euclidean case, our no‐dimension version of the Radon
    theorem and slightly modified version of the celebrated Maurey lemma."
acknowledgement: "I wish to thank Imre Bárány for bringing the problem to my attention.
  I am grateful to Marton Naszódi and Igor Tsiutsiurupa for useful remarks and help
  with the text.\r\nThe author acknowledges the financial support from the Ministry
  of Educational and Science of the Russian Federation in the framework of MegaGrant
  no 075‐15‐2019‐1926."
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
citation:
  ama: Ivanov G. No-dimension Tverberg’s theorem and its corollaries in Banach spaces
    of type p. <i>Bulletin of the London Mathematical Society</i>. 2021;53(2):631-641.
    doi:<a href="https://doi.org/10.1112/blms.12449">10.1112/blms.12449</a>
  apa: Ivanov, G. (2021). No-dimension Tverberg’s theorem and its corollaries in Banach
    spaces of type p. <i>Bulletin of the London Mathematical Society</i>. London Mathematical
    Society. <a href="https://doi.org/10.1112/blms.12449">https://doi.org/10.1112/blms.12449</a>
  chicago: Ivanov, Grigory. “No-Dimension Tverberg’s Theorem and Its Corollaries in
    Banach Spaces of Type P.” <i>Bulletin of the London Mathematical Society</i>.
    London Mathematical Society, 2021. <a href="https://doi.org/10.1112/blms.12449">https://doi.org/10.1112/blms.12449</a>.
  ieee: G. Ivanov, “No-dimension Tverberg’s theorem and its corollaries in Banach
    spaces of type p,” <i>Bulletin of the London Mathematical Society</i>, vol. 53,
    no. 2. London Mathematical Society, pp. 631–641, 2021.
  ista: Ivanov G. 2021. No-dimension Tverberg’s theorem and its corollaries in Banach
    spaces of type p. Bulletin of the London Mathematical Society. 53(2), 631–641.
  mla: Ivanov, Grigory. “No-Dimension Tverberg’s Theorem and Its Corollaries in Banach
    Spaces of Type P.” <i>Bulletin of the London Mathematical Society</i>, vol. 53,
    no. 2, London Mathematical Society, 2021, pp. 631–41, doi:<a href="https://doi.org/10.1112/blms.12449">10.1112/blms.12449</a>.
  short: G. Ivanov, Bulletin of the London Mathematical Society 53 (2021) 631–641.
date_created: 2021-01-24T23:01:08Z
date_published: 2021-04-01T00:00:00Z
date_updated: 2023-08-07T13:35:20Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1112/blms.12449
external_id:
  arxiv:
  - '1912.08561'
  isi:
  - '000607265100001'
file:
- access_level: open_access
  checksum: e6ceaa6470d835eb4c211cbdd38fdfd1
  content_type: application/pdf
  creator: kschuh
  date_created: 2021-08-06T09:59:45Z
  date_updated: 2021-08-06T09:59:45Z
  file_id: '9796'
  file_name: 2021_BLMS_Ivanov.pdf
  file_size: 194550
  relation: main_file
  success: 1
file_date_updated: 2021-08-06T09:59:45Z
has_accepted_license: '1'
intvolume: '        53'
isi: 1
issue: '2'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 631-641
publication: Bulletin of the London Mathematical Society
publication_identifier:
  eissn:
  - '14692120'
  issn:
  - '00246093'
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: No-dimension Tverberg's theorem and its corollaries in Banach spaces of type
  p
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 53
year: '2021'
...
---
_id: '6793'
abstract:
- lang: eng
  text: The Regge symmetry is a set of remarkable relations between two tetrahedra
    whose edge lengths are related in a simple fashion. It was first discovered as
    a consequence of an asymptotic formula in mathematical physics. Here, we give
    a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic
    geometry.
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: Ivan
  full_name: Izmestiev, Ivan
  last_name: Izmestiev
citation:
  ama: Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli
    formula. <i>Bulletin of the London Mathematical Society</i>. 2019;51(5):765-775.
    doi:<a href="https://doi.org/10.1112/blms.12276">10.1112/blms.12276</a>
  apa: Akopyan, A., &#38; Izmestiev, I. (2019). The Regge symmetry, confocal conics,
    and the Schläfli formula. <i>Bulletin of the London Mathematical Society</i>.
    London Mathematical Society. <a href="https://doi.org/10.1112/blms.12276">https://doi.org/10.1112/blms.12276</a>
  chicago: Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics,
    and the Schläfli Formula.” <i>Bulletin of the London Mathematical Society</i>.
    London Mathematical Society, 2019. <a href="https://doi.org/10.1112/blms.12276">https://doi.org/10.1112/blms.12276</a>.
  ieee: A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the
    Schläfli formula,” <i>Bulletin of the London Mathematical Society</i>, vol. 51,
    no. 5. London Mathematical Society, pp. 765–775, 2019.
  ista: Akopyan A, Izmestiev I. 2019. The Regge symmetry, confocal conics, and the
    Schläfli formula. Bulletin of the London Mathematical Society. 51(5), 765–775.
  mla: Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics,
    and the Schläfli Formula.” <i>Bulletin of the London Mathematical Society</i>,
    vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:<a href="https://doi.org/10.1112/blms.12276">10.1112/blms.12276</a>.
  short: A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51
    (2019) 765–775.
date_created: 2019-08-11T21:59:23Z
date_published: 2019-10-01T00:00:00Z
date_updated: 2023-08-29T07:08:34Z
day: '01'
department:
- _id: HeEd
doi: 10.1112/blms.12276
ec_funded: 1
external_id:
  arxiv:
  - '1903.04929'
  isi:
  - '000478560200001'
intvolume: '        51'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1903.04929
month: '10'
oa: 1
oa_version: Preprint
page: 765-775
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '788183'
  name: Alpha Shape Theory Extended
publication: Bulletin of the London Mathematical Society
publication_identifier:
  eissn:
  - '14692120'
  issn:
  - '00246093'
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Regge symmetry, confocal conics, and the Schläfli formula
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 51
year: '2019'
...
---
_id: '707'
abstract:
- lang: eng
  text: We answer a question of M. Gromov on the waist of the unit ball.
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. A tight estimate for the waist of the ball . <i>Bulletin
    of the London Mathematical Society</i>. 2017;49(4):690-693. doi:<a href="https://doi.org/10.1112/blms.12062">10.1112/blms.12062</a>
  apa: Akopyan, A., &#38; Karasev, R. (2017). A tight estimate for the waist of the
    ball . <i>Bulletin of the London Mathematical Society</i>. Wiley-Blackwell. <a
    href="https://doi.org/10.1112/blms.12062">https://doi.org/10.1112/blms.12062</a>
  chicago: Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of
    the Ball .” <i>Bulletin of the London Mathematical Society</i>. Wiley-Blackwell,
    2017. <a href="https://doi.org/10.1112/blms.12062">https://doi.org/10.1112/blms.12062</a>.
  ieee: A. Akopyan and R. Karasev, “A tight estimate for the waist of the ball ,”
    <i>Bulletin of the London Mathematical Society</i>, vol. 49, no. 4. Wiley-Blackwell,
    pp. 690–693, 2017.
  ista: Akopyan A, Karasev R. 2017. A tight estimate for the waist of the ball . Bulletin
    of the London Mathematical Society. 49(4), 690–693.
  mla: Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the
    Ball .” <i>Bulletin of the London Mathematical Society</i>, vol. 49, no. 4, Wiley-Blackwell,
    2017, pp. 690–93, doi:<a href="https://doi.org/10.1112/blms.12062">10.1112/blms.12062</a>.
  short: A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017)
    690–693.
date_created: 2018-12-11T11:48:02Z
date_published: 2017-08-01T00:00:00Z
date_updated: 2021-01-12T08:11:41Z
day: '01'
department:
- _id: HeEd
doi: 10.1112/blms.12062
ec_funded: 1
intvolume: '        49'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1608.06279
month: '08'
oa: 1
oa_version: Preprint
page: 690 - 693
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
publication: Bulletin of the London Mathematical Society
publication_identifier:
  issn:
  - '00246093'
publication_status: published
publisher: Wiley-Blackwell
publist_id: '6982'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'A tight estimate for the waist of the ball '
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 49
year: '2017'
...