[{"_id":"18483","isi":1,"date_published":"2024-12-01T00:00:00Z","language":[{"iso":"eng"}],"publication_status":"published","intvolume":"        34","department":[{"_id":"VaKa"}],"article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00039-024-00695-6","oa_version":"Published Version","date_created":"2024-10-27T23:01:45Z","title":"Birkhoff conjecture for nearly centrally symmetric domains","project":[{"_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707","name":"Spectral rigidity and integrability for billiards and geodesic flows","call_identifier":"H2020"}],"external_id":{"isi":["001329804200001"],"arxiv":["2306.12301"]},"abstract":[{"lang":"eng","text":"In this paper we prove a perturbative version of a remarkable Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) result. They prove non perturbative Birkhoff conjecture for centrally-symmetric convex domains, namely, a centrally-symmetric convex domain with integrable billiard is ellipse. We combine techniques from Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) with a local result by Kaloshin–Sorrentino (Ann. Math. 188(1):315–380, 2018) and show that a domain close enough to a centrally symmetric one with integrable billiard is ellipse. To combine these results we derive a slight extension of Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) by proving that a notion of rational integrability is equivalent to the C0-integrability condition used in their paper."}],"type":"journal_article","file_date_updated":"2025-01-13T09:14:24Z","arxiv":1,"month":"12","corr_author":"1","acknowledgement":"We are grateful to the anonymous referee for their careful reading and valuable remarks and comments which helped to improve significantly the paper. Open access funding provided by Institute of Science and Technology (IST Austria). V.K. and C.E.K. gratefully acknowledge support from the European Research Council (ERC) through the Advanced Grant “SPERIG” (#885 707).","publication_identifier":{"eissn":["1420-8970"],"issn":["1016-443X"]},"year":"2024","author":[{"first_name":"Vadim","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"orcid":"0000-0003-2640-4049","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","full_name":"Koudjinan, Edmond","last_name":"Koudjinan","first_name":"Edmond"},{"full_name":"Zhang, Ke","first_name":"Ke","last_name":"Zhang"}],"date_updated":"2025-09-08T14:27:45Z","ec_funded":1,"scopus_import":"1","has_accepted_license":"1","publisher":"Springer Nature","file":[{"date_updated":"2025-01-13T09:14:24Z","access_level":"open_access","success":1,"date_created":"2025-01-13T09:14:24Z","checksum":"e7fcd9f78beb40408c7d858ac0625e27","content_type":"application/pdf","file_size":2260980,"file_name":"2024_GeometricFunctionalAnalysis_Kaloshin.pdf","creator":"dernst","file_id":"18833","relation":"main_file"}],"page":"1973-2007","ddc":["510"],"OA_type":"hybrid","citation":{"chicago":"Kaloshin, Vadim, Edmond Koudjinan, and Ke Zhang. “Birkhoff Conjecture for Nearly Centrally Symmetric Domains.” <i>Geometric and Functional Analysis</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00039-024-00695-6\">https://doi.org/10.1007/s00039-024-00695-6</a>.","short":"V. Kaloshin, E. Koudjinan, K. Zhang, Geometric and Functional Analysis 34 (2024) 1973–2007.","ista":"Kaloshin V, Koudjinan E, Zhang K. 2024. Birkhoff conjecture for nearly centrally symmetric domains. Geometric and Functional Analysis. 34, 1973–2007.","ama":"Kaloshin V, Koudjinan E, Zhang K. Birkhoff conjecture for nearly centrally symmetric domains. <i>Geometric and Functional Analysis</i>. 2024;34:1973-2007. doi:<a href=\"https://doi.org/10.1007/s00039-024-00695-6\">10.1007/s00039-024-00695-6</a>","apa":"Kaloshin, V., Koudjinan, E., &#38; Zhang, K. (2024). Birkhoff conjecture for nearly centrally symmetric domains. <i>Geometric and Functional Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00039-024-00695-6\">https://doi.org/10.1007/s00039-024-00695-6</a>","mla":"Kaloshin, Vadim, et al. “Birkhoff Conjecture for Nearly Centrally Symmetric Domains.” <i>Geometric and Functional Analysis</i>, vol. 34, Springer Nature, 2024, pp. 1973–2007, doi:<a href=\"https://doi.org/10.1007/s00039-024-00695-6\">10.1007/s00039-024-00695-6</a>.","ieee":"V. Kaloshin, E. Koudjinan, and K. Zhang, “Birkhoff conjecture for nearly centrally symmetric domains,” <i>Geometric and Functional Analysis</i>, vol. 34. Springer Nature, pp. 1973–2007, 2024."},"status":"public","publication":"Geometric and Functional Analysis","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","OA_place":"publisher","day":"01","volume":34,"oa":1,"quality_controlled":"1","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"}},{"external_id":{"arxiv":["1809.08919"]},"type":"journal_article","arxiv":1,"month":"04","abstract":[{"lang":"eng","text":"We establish two WDVV-style relations for the disk invariants of real symplectic fourfolds by implementing Georgieva’s suggestion to lift homology relations from the Deligne–Mumford moduli spaces of stable real curves. This is accomplished by lifting judiciously chosen cobordisms realizing these relations. The resulting lifted relations lead to the recursions for Welschinger invariants announced by Solomon in 2007 and have the same structure as his WDVV-style relations, but differ by signs from the latter. Our topological approach provides a general framework for lifting relations via morphisms between not necessarily orientable spaces."}],"publication_identifier":{"issn":["1016-443X"],"eissn":["1420-8970"]},"date_created":"2025-11-10T08:40:40Z","oa_version":"Preprint","doi":"10.1007/s00039-022-00596-6","article_processing_charge":"No","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1809.08919","open_access":"1"}],"title":"Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants","language":[{"iso":"eng"}],"intvolume":"        32","publication_status":"published","_id":"20616","date_published":"2022-04-15T00:00:00Z","oa":1,"article_type":"original","quality_controlled":"1","OA_place":"repository","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"15","issue":"3","volume":32,"publisher":"Springer Nature","page":"490-567","OA_type":"green","citation":{"mla":"Chen, Xujia. “Steenrod Pseudocycles, Lifted Cobordisms, and Solomon’s Relations for Welschinger Invariants.” <i>Geometric and Functional Analysis</i>, vol. 32, no. 3, Springer Nature, 2022, pp. 490–567, doi:<a href=\"https://doi.org/10.1007/s00039-022-00596-6\">10.1007/s00039-022-00596-6</a>.","ama":"Chen X. Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants. <i>Geometric and Functional Analysis</i>. 2022;32(3):490-567. doi:<a href=\"https://doi.org/10.1007/s00039-022-00596-6\">10.1007/s00039-022-00596-6</a>","ieee":"X. Chen, “Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants,” <i>Geometric and Functional Analysis</i>, vol. 32, no. 3. Springer Nature, pp. 490–567, 2022.","apa":"Chen, X. (2022). Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants. <i>Geometric and Functional Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00039-022-00596-6\">https://doi.org/10.1007/s00039-022-00596-6</a>","ista":"Chen X. 2022. Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants. Geometric and Functional Analysis. 32(3), 490–567.","short":"X. Chen, Geometric and Functional Analysis 32 (2022) 490–567.","chicago":"Chen, Xujia. “Steenrod Pseudocycles, Lifted Cobordisms, and Solomon’s Relations for Welschinger Invariants.” <i>Geometric and Functional Analysis</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00039-022-00596-6\">https://doi.org/10.1007/s00039-022-00596-6</a>."},"publication":"Geometric and Functional Analysis","status":"public","author":[{"last_name":"Chen","first_name":"Xujia","full_name":"Chen, Xujia","id":"968ad14a-fd86-11ee-a420-ea29715511a3"}],"year":"2022","extern":"1","date_updated":"2025-11-10T15:18:07Z"}]