[{"year":"2021","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.","_id":"9037","date_updated":"2023-08-07T13:35:20Z","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  𝜀 ‐net theorem in Banach spaces of type  𝑝>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."}],"month":"04","oa_version":"Published Version","type":"journal_article","page":"631-641","file_date_updated":"2021-08-06T09:59:45Z","date_created":"2021-01-24T23:01:08Z","volume":53,"status":"public","external_id":{"arxiv":["1912.08561"],"isi":["000607265100001"]},"citation":{"short":"G. Ivanov, Bulletin of the London Mathematical Society 53 (2021) 631–641.","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.","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>.","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>.","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>","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>"},"intvolume":"        53","has_accepted_license":"1","oa":1,"publication_status":"published","date_published":"2021-04-01T00:00:00Z","ddc":["510"],"department":[{"_id":"UlWa"}],"publisher":"London Mathematical Society","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"article_type":"original","publication":"Bulletin of the London Mathematical Society","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","day":"01","file":[{"creator":"kschuh","relation":"main_file","content_type":"application/pdf","file_size":194550,"success":1,"file_name":"2021_BLMS_Ivanov.pdf","access_level":"open_access","date_created":"2021-08-06T09:59:45Z","checksum":"e6ceaa6470d835eb4c211cbdd38fdfd1","date_updated":"2021-08-06T09:59:45Z","file_id":"9796"}],"author":[{"first_name":"Grigory","last_name":"Ivanov","full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E"}],"title":"No-dimension Tverberg's theorem and its corollaries in Banach spaces of type p","arxiv":1,"language":[{"iso":"eng"}],"issue":"2","isi":1,"publication_identifier":{"eissn":["14692120"],"issn":["00246093"]},"quality_controlled":"1","doi":"10.1112/blms.12449"},{"volume":51,"date_created":"2019-08-11T21:59:23Z","page":"765-775","oa_version":"Preprint","month":"10","type":"journal_article","date_updated":"2023-08-29T07:08:34Z","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."}],"_id":"6793","year":"2019","date_published":"2019-10-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.04929"}],"publication_status":"published","oa":1,"intvolume":"        51","citation":{"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>","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>.","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>","short":"A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 765–775.","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."},"external_id":{"arxiv":["1903.04929"],"isi":["000478560200001"]},"status":"public","title":"The Regge symmetry, confocal conics, and the Schläfli formula","arxiv":1,"author":[{"first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Izmestiev, Ivan","first_name":"Ivan","last_name":"Izmestiev"}],"day":"01","publication":"Bulletin of the London Mathematical Society","article_type":"original","article_processing_charge":"No","scopus_import":"1","ec_funded":1,"publisher":"London Mathematical Society","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"doi":"10.1112/blms.12276","quality_controlled":"1","publication_identifier":{"eissn":["14692120"],"issn":["00246093"]},"isi":1,"issue":"5","language":[{"iso":"eng"}],"project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}]},{"publication_identifier":{"issn":["00246093"]},"doi":"10.1112/blms.12062","quality_controlled":"1","project":[{"grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"language":[{"iso":"eng"}],"issue":"4","author":[{"last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"day":"01","title":"A tight estimate for the waist of the ball ","publist_id":"6982","publisher":"Wiley-Blackwell","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"publication":"Bulletin of the London Mathematical Society","ec_funded":1,"scopus_import":1,"oa":1,"publication_status":"published","date_published":"2017-08-01T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1608.06279","open_access":"1"}],"status":"public","intvolume":"        49","citation":{"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>.","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>","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>","short":"A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017) 690–693.","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.","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>."},"page":"690 - 693","abstract":[{"lang":"eng","text":"We answer a question of M. Gromov on the waist of the unit ball."}],"date_updated":"2021-01-12T08:11:41Z","oa_version":"Preprint","month":"08","type":"journal_article","volume":49,"date_created":"2018-12-11T11:48:02Z","year":"2017","_id":"707"}]