[{"OA_type":"hybrid","OA_place":"publisher","language":[{"iso":"eng"}],"scopus_import":"1","publication":"Inventiones Mathematicae","ec_funded":1,"publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]},"acknowledgement":"The author acknowledges the partial support of the European Research Council Grant #885707. He also thanks Vadim Kaloshin for proposing the idea of the project and greatly aiding the implementation. The author is also grateful to Hamid Hezari, Amir Vig, Steve Zelditch, Comlan E. Koudjinan, Corentin Fierobe, Ngo Nhok Tkhai Shon and Roman Sarapin for useful discussions. The author also acknowledges partial support of ISTern summer program. The project started in the summer of 2021, when the author was an intern at ISTA. Open access funding provided by Institute of Science and Technology (IST Austria).","project":[{"grant_number":"885707","name":"Spectral rigidity and integrability for billiards and geodesic flows","call_identifier":"H2020","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A"}],"citation":{"ieee":"I. Koval, “Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse,” <i>Inventiones Mathematicae</i>, vol. 244. Springer Nature, pp. 221–298, 2026.","short":"I. Koval, Inventiones Mathematicae 244 (2026) 221–298.","ista":"Koval I. 2026. Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse. Inventiones Mathematicae. 244, 221–298.","mla":"Koval, Illya. “Local Strong Birkhoff Conjecture and Local Spectral Rigidity of Almost Every Ellipse.” <i>Inventiones Mathematicae</i>, vol. 244, Springer Nature, 2026, pp. 221–98, doi:<a href=\"https://doi.org/10.1007/s00222-025-01397-y\">10.1007/s00222-025-01397-y</a>.","ama":"Koval I. Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse. <i>Inventiones Mathematicae</i>. 2026;244:221-298. doi:<a href=\"https://doi.org/10.1007/s00222-025-01397-y\">10.1007/s00222-025-01397-y</a>","apa":"Koval, I. (2026). Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-025-01397-y\">https://doi.org/10.1007/s00222-025-01397-y</a>","chicago":"Koval, Illya. “Local Strong Birkhoff Conjecture and Local Spectral Rigidity of Almost Every Ellipse.” <i>Inventiones Mathematicae</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00222-025-01397-y\">https://doi.org/10.1007/s00222-025-01397-y</a>."},"page":"221-298","license":"https://creativecommons.org/licenses/by/4.0/","PlanS_conform":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","supplementarymaterial":"yes","date_updated":"2026-07-23T10:58:59Z","author":[{"id":"2eed1f3b-896a-11ed-bdf8-93c7c4bf159e","last_name":"Koval","first_name":"Illya","full_name":"Koval, Illya"}],"date_created":"2023-09-06T08:35:43Z","status":"public","_id":"14278","title":"Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse","abstract":[{"lang":"eng","text":"The Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrability, namely, integrability close to the boundary, and prove a local version of this conjecture: a small perturbation of almost every ellipse that preserves integrability near the boundary, is itself an ellipse. We apply this result to study local spectral uniqueness of ellipses using the connection between the wave trace of the Laplacian and the dynamics near the boundary and establish local uniqueness for almost all of them."}],"article_type":"original","oa_version":"Published Version","type":"journal_article","file":[{"creator":"dernst","relation":"main_file","access_level":"open_access","checksum":"487fa9113e1bbf32a6c70e6d1e8f63bc","date_created":"2026-07-23T10:55:24Z","success":1,"file_size":2256345,"date_updated":"2026-07-23T10:55:24Z","content_type":"application/pdf","file_name":"2026_InventionesMath_Koval.pdf","file_id":"22394"}],"researchdata_availability":"no","doi":"10.1007/s00222-025-01397-y","volume":244,"corr_author":"1","oa":1,"day":"01","mathsc":["37C83","35J05","37J70","74J25"],"department":[{"_id":"GradSch"},{"_id":"VaKa"}],"month":"04","publisher":"Springer Nature","external_id":{"arxiv":["2111.12171"]},"article_processing_charge":"Yes (via OA deal)","file_date_updated":"2026-07-23T10:55:24Z","date_published":"2026-04-01T00:00:00Z","has_accepted_license":"1","arxiv":1,"fulldoi":"https://doi.org/10.1007/s00222-025-01397-y","das_tickbox":"0","tmp":{"image":"/images/cc_by.png","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)"},"ddc":["510"],"intvolume":"       244","year":"2026","quality_controlled":"1","publication_status":"published"}]