[{"file":[{"file_id":"18833","date_created":"2025-01-13T09:14:24Z","file_name":"2024_GeometricFunctionalAnalysis_Kaloshin.pdf","relation":"main_file","date_updated":"2025-01-13T09:14:24Z","content_type":"application/pdf","access_level":"open_access","checksum":"e7fcd9f78beb40408c7d858ac0625e27","file_size":2260980,"creator":"dernst","success":1}],"oa_version":"Published Version","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"OA_type":"hybrid","OA_place":"publisher","publication_identifier":{"eissn":["1420-8970"],"issn":["1016-443X"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","has_accepted_license":"1","corr_author":"1","year":"2024","status":"public","publisher":"Springer Nature","ec_funded":1,"article_type":"original","date_published":"2024-12-01T00:00:00Z","month":"12","publication_status":"published","date_updated":"2025-09-08T14:27:45Z","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"VaKa"}],"oa":1,"citation":{"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>","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>","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.","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."},"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).","external_id":{"isi":["001329804200001"],"arxiv":["2306.12301"]},"ddc":["510"],"arxiv":1,"intvolume":"        34","type":"journal_article","publication":"Geometric and Functional Analysis","doi":"10.1007/s00039-024-00695-6","_id":"18483","project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","grant_number":"885707","call_identifier":"H2020","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A"}],"quality_controlled":"1","author":[{"full_name":"Kaloshin, Vadim","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","last_name":"Kaloshin"},{"last_name":"Koudjinan","orcid":"0000-0003-2640-4049","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","first_name":"Edmond","full_name":"Koudjinan, Edmond"},{"first_name":"Ke","full_name":"Zhang, Ke","last_name":"Zhang"}],"page":"1973-2007","scopus_import":"1","isi":1,"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."}],"day":"01","date_created":"2024-10-27T23:01:45Z","title":"Birkhoff conjecture for nearly centrally symmetric domains","language":[{"iso":"eng"}],"file_date_updated":"2025-01-13T09:14:24Z","volume":34},{"article_processing_charge":"No","oa":1,"publisher":"Springer Nature","article_type":"original","date_published":"2022-04-15T00:00:00Z","month":"04","date_updated":"2025-11-10T15:18:07Z","publication_status":"published","issue":"3","year":"2022","status":"public","OA_type":"green","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_place":"repository","publication_identifier":{"eissn":["1420-8970"],"issn":["1016-443X"]},"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."}],"day":"15","date_created":"2025-11-10T08:40:40Z","volume":32,"title":"Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1809.08919","open_access":"1"}],"language":[{"iso":"eng"}],"extern":"1","doi":"10.1007/s00039-022-00596-6","_id":"20616","author":[{"first_name":"Xujia","full_name":"Chen, Xujia","id":"968ad14a-fd86-11ee-a420-ea29715511a3","last_name":"Chen"}],"page":"490-567","quality_controlled":"1","arxiv":1,"intvolume":"        32","citation":{"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>","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>","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>.","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.","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>.","short":"X. Chen, Geometric and Functional Analysis 32 (2022) 490–567.","ista":"Chen X. 2022. Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants. Geometric and Functional Analysis. 32(3), 490–567."},"external_id":{"arxiv":["1809.08919"]},"publication":"Geometric and Functional Analysis","type":"journal_article"},{"title":"Low regularity conservation laws for integrable PDE","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1708.05362","open_access":"1"}],"language":[{"iso":"eng"}],"volume":28,"day":"01","abstract":[{"lang":"eng","text":"We present a general method for obtaining conservation laws for integrable PDE at negative regularity and exhibit its application to KdV, NLS, and mKdV. Our method works uniformly for these problems posed both on the line and on the circle."}],"date_created":"2026-06-19T07:56:48Z","extern":"1","scopus_import":"1","quality_controlled":"1","author":[{"full_name":"Killip, Rowan","first_name":"Rowan","last_name":"Killip"},{"last_name":"Visan","full_name":"Visan, Monica","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"},{"last_name":"Zhang","full_name":"Zhang, Xiaoyi","first_name":"Xiaoyi"}],"page":"1062-1090","doi":"10.1007/s00039-018-0444-0","_id":"22055","publication":"Geometric and Functional Analysis","type":"journal_article","citation":{"mla":"Killip, Rowan, et al. “Low Regularity Conservation Laws for Integrable PDE.” <i>Geometric and Functional Analysis</i>, vol. 28, no. 4, Springer Nature, 2018, pp. 1062–90, doi:<a href=\"https://doi.org/10.1007/s00039-018-0444-0\">10.1007/s00039-018-0444-0</a>.","ieee":"R. Killip, M. Vişan, and X. Zhang, “Low regularity conservation laws for integrable PDE,” <i>Geometric and Functional Analysis</i>, vol. 28, no. 4. Springer Nature, pp. 1062–1090, 2018.","ama":"Killip R, Vişan M, Zhang X. Low regularity conservation laws for integrable PDE. <i>Geometric and Functional Analysis</i>. 2018;28(4):1062-1090. doi:<a href=\"https://doi.org/10.1007/s00039-018-0444-0\">10.1007/s00039-018-0444-0</a>","apa":"Killip, R., Vişan, M., &#38; Zhang, X. (2018). Low regularity conservation laws for integrable PDE. <i>Geometric and Functional Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00039-018-0444-0\">https://doi.org/10.1007/s00039-018-0444-0</a>","ista":"Killip R, Vişan M, Zhang X. 2018. Low regularity conservation laws for integrable PDE. Geometric and Functional Analysis. 28(4), 1062–1090.","short":"R. Killip, M. Vişan, X. Zhang, Geometric and Functional Analysis 28 (2018) 1062–1090.","chicago":"Killip, Rowan, Monica Vişan, and Xiaoyi Zhang. “Low Regularity Conservation Laws for Integrable PDE.” <i>Geometric and Functional Analysis</i>. Springer Nature, 2018. <a href=\"https://doi.org/10.1007/s00039-018-0444-0\">https://doi.org/10.1007/s00039-018-0444-0</a>."},"external_id":{"arxiv":["1708.05362"]},"arxiv":1,"intvolume":"        28","oa":1,"article_processing_charge":"No","date_published":"2018-07-01T00:00:00Z","month":"07","article_type":"original","date_updated":"2026-06-29T09:55:53Z","publication_status":"published","publisher":"Springer Nature","das_tickbox":"1","year":"2018","issue":"4","status":"public","OA_place":"repository","publication_identifier":{"issn":["1016-443X"],"eissn":["1420-8970"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","OA_type":"green"},{"date_published":"2015-06-11T00:00:00Z","month":"06","article_type":"original","publication_status":"published","date_updated":"2026-05-19T09:46:04Z","publisher":"Springer Nature","oa":1,"article_processing_charge":"No","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","OA_place":"repository","publication_identifier":{"eissn":["1420-8970"],"issn":["1016-443X"]},"OA_type":"green","oa_version":"Preprint","year":"2015","status":"public","issue":"3","scopus_import":"1","extern":"1","volume":25,"title":"Rational points on cubic hypersurfaces over F_q(t) ","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.1502.00772","open_access":"1"}],"language":[{"iso":"eng"}],"abstract":[{"text":"The Hasse principle and weak approximation is established for\r\nnon-singular cubic hypersurfaces X over the function field Fq(t), provided that\r\nchar(Fq) > 3 and X has dimension at least 6.","lang":"eng"}],"day":"11","date_created":"2018-12-11T11:45:29Z","publication":"Geometric and Functional Analysis","type":"journal_article","publist_id":"7643","arxiv":1,"intvolume":"        25","citation":{"chicago":"Browning, Timothy D, and Pankaj Vishe. “Rational Points on Cubic Hypersurfaces over F_q(T) .” <i>Geometric and Functional Analysis</i>. Springer Nature, 2015. <a href=\"https://doi.org/10.1007/s00039-015-0328-5\">https://doi.org/10.1007/s00039-015-0328-5</a>.","short":"T.D. Browning, P. Vishe, Geometric and Functional Analysis 25 (2015) 671–732.","ista":"Browning TD, Vishe P. 2015. Rational points on cubic hypersurfaces over F_q(t) . Geometric and Functional Analysis. 25(3), 671–732.","apa":"Browning, T. D., &#38; Vishe, P. (2015). Rational points on cubic hypersurfaces over F_q(t) . <i>Geometric and Functional Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00039-015-0328-5\">https://doi.org/10.1007/s00039-015-0328-5</a>","ama":"Browning TD, Vishe P. Rational points on cubic hypersurfaces over F_q(t) . <i>Geometric and Functional Analysis</i>. 2015;25(3):671-732. doi:<a href=\"https://doi.org/10.1007/s00039-015-0328-5\">10.1007/s00039-015-0328-5</a>","ieee":"T. D. Browning and P. Vishe, “Rational points on cubic hypersurfaces over F_q(t) ,” <i>Geometric and Functional Analysis</i>, vol. 25, no. 3. Springer Nature, pp. 671–732, 2015.","mla":"Browning, Timothy D., and Pankaj Vishe. “Rational Points on Cubic Hypersurfaces over F_q(T) .” <i>Geometric and Functional Analysis</i>, vol. 25, no. 3, Springer Nature, 2015, pp. 671–732, doi:<a href=\"https://doi.org/10.1007/s00039-015-0328-5\">10.1007/s00039-015-0328-5</a>."},"acknowledgement":"EP/J018260/1\tEngineering and Physical Sciences Research Council EPSRC","external_id":{"arxiv":["1502.00772"]},"page":"671 - 732","author":[{"first_name":"Timothy D","full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","last_name":"Browning"},{"last_name":"Vishe","first_name":"Pankaj","full_name":"Vishe, Pankaj"}],"quality_controlled":"1","doi":"10.1007/s00039-015-0328-5","_id":"259"}]