[{"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).","_id":"14278","scopus_import":"1","OA_type":"hybrid","page":"221-298","year":"2026","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"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."}],"day":"01","article_processing_charge":"Yes (via OA deal)","oa":1,"status":"public","file":[{"file_size":2256345,"file_name":"2026_InventionesMath_Koval.pdf","file_id":"22394","date_updated":"2026-07-23T10:55:24Z","checksum":"487fa9113e1bbf32a6c70e6d1e8f63bc","relation":"main_file","access_level":"open_access","content_type":"application/pdf","creator":"dernst","success":1,"date_created":"2026-07-23T10:55:24Z"}],"publication_status":"published","citation":{"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>","short":"I. Koval, Inventiones Mathematicae 244 (2026) 221–298.","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>","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>.","ista":"Koval I. 2026. Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse. Inventiones Mathematicae. 244, 221–298.","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>.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","date_published":"2026-04-01T00:00:00Z","supplementarymaterial":"yes","OA_place":"publisher","date_created":"2023-09-06T08:35:43Z","doi":"10.1007/s00222-025-01397-y","publisher":"Springer Nature","das_tickbox":"0","author":[{"id":"2eed1f3b-896a-11ed-bdf8-93c7c4bf159e","first_name":"Illya","last_name":"Koval","full_name":"Koval, Illya"}],"mathsc":["37C83","35J05","37J70","74J25"],"intvolume":"       244","department":[{"_id":"GradSch"},{"_id":"VaKa"}],"quality_controlled":"1","article_type":"original","project":[{"_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","name":"Spectral rigidity and integrability for billiards and geodesic flows","call_identifier":"H2020","grant_number":"885707"}],"date_updated":"2026-07-23T10:58:59Z","ec_funded":1,"title":"Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse","researchdata_availability":"no","external_id":{"arxiv":["2111.12171"]},"ddc":["510"],"arxiv":1,"type":"journal_article","publication":"Inventiones Mathematicae","month":"04","volume":244,"has_accepted_license":"1","language":[{"iso":"eng"}],"file_date_updated":"2026-07-23T10:55:24Z","PlanS_conform":"1","oa_version":"Published Version","publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]}},{"arxiv":1,"external_id":{"arxiv":["2210.09064"]},"title":"Every diffeomorphism is a total renormalization of a close to identity map","type":"journal_article","issue":"2","quality_controlled":"1","article_type":"original","date_updated":"2025-12-29T12:03:10Z","oa_version":"Preprint","publication_identifier":{"issn":["0020-9910"],"eissn":["1432-1297"]},"volume":239,"month":"12","publication":"Inventiones mathematicae","language":[{"iso":"eng"}],"day":"19","article_processing_charge":"No","_id":"20838","scopus_import":"1","OA_type":"green","year":"2024","abstract":[{"lang":"eng","text":"For any 1 ≤ r ≤ ∞, we show that every diffeomorphism of a manifold of the form\r\nR/Z × M is a total renormalization of a Cr-close to identity map. In other words, for\r\nevery diffeomorphism f of R/Z×M, there exists a map g arbitrarily close to identity\r\nsuch that the first return map of g to a domain is conjugate to f and moreover the\r\norbit of this domain is equal to R/Z×M. This enables us to localize near the identity\r\nthe existence of many properties in dynamical systems, such as being Bernoulli for a\r\nsmooth volume form."}],"extern":"1","page":"431-468","OA_place":"repository","author":[{"last_name":"Berger","full_name":"Berger, Pierre","first_name":"Pierre"},{"last_name":"Gourmelon","full_name":"Gourmelon, Nicolaz","first_name":"Nicolaz"},{"first_name":"Mathieu","id":"7d296fbe-e2c6-11ee-84d3-d5c2945f9a57","last_name":"Helfter","full_name":"Helfter, Mathieu"}],"intvolume":"       239","doi":"10.1007/s00222-024-01305-w","date_created":"2025-12-19T10:15:13Z","publisher":"Springer Nature","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2210.09064","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","oa":1,"publication_status":"published","citation":{"ieee":"P. Berger, N. Gourmelon, and M. Helfter, “Every diffeomorphism is a total renormalization of a close to identity map,” <i>Inventiones mathematicae</i>, vol. 239, no. 2. Springer Nature, pp. 431–468, 2024.","chicago":"Berger, Pierre, Nicolaz Gourmelon, and Mathieu Helfter. “Every Diffeomorphism Is a Total Renormalization of a Close to Identity Map.” <i>Inventiones Mathematicae</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00222-024-01305-w\">https://doi.org/10.1007/s00222-024-01305-w</a>.","ista":"Berger P, Gourmelon N, Helfter M. 2024. Every diffeomorphism is a total renormalization of a close to identity map. Inventiones mathematicae. 239(2), 431–468.","mla":"Berger, Pierre, et al. “Every Diffeomorphism Is a Total Renormalization of a Close to Identity Map.” <i>Inventiones Mathematicae</i>, vol. 239, no. 2, Springer Nature, 2024, pp. 431–68, doi:<a href=\"https://doi.org/10.1007/s00222-024-01305-w\">10.1007/s00222-024-01305-w</a>.","short":"P. Berger, N. Gourmelon, M. Helfter, Inventiones Mathematicae 239 (2024) 431–468.","ama":"Berger P, Gourmelon N, Helfter M. Every diffeomorphism is a total renormalization of a close to identity map. <i>Inventiones mathematicae</i>. 2024;239(2):431-468. doi:<a href=\"https://doi.org/10.1007/s00222-024-01305-w\">10.1007/s00222-024-01305-w</a>","apa":"Berger, P., Gourmelon, N., &#38; Helfter, M. (2024). Every diffeomorphism is a total renormalization of a close to identity map. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-024-01305-w\">https://doi.org/10.1007/s00222-024-01305-w</a>"},"date_published":"2024-12-19T00:00:00Z"},{"date_published":"2024-06-01T00:00:00Z","publication_status":"published","citation":{"mla":"Killip, Rowan, et al. “Sharp Well-Posedness for the Benjamin–Ono Equation.” <i>Inventiones Mathematicae</i>, vol. 236, no. 3, Springer Nature, 2024, pp. 999–1054, doi:<a href=\"https://doi.org/10.1007/s00222-024-01250-8\">10.1007/s00222-024-01250-8</a>.","ista":"Killip R, Laurens T, Vişan M. 2024. Sharp well-posedness for the Benjamin–Ono equation. Inventiones mathematicae. 236(3), 999–1054.","chicago":"Killip, Rowan, Thierry Laurens, and Monica Vişan. “Sharp Well-Posedness for the Benjamin–Ono Equation.” <i>Inventiones Mathematicae</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00222-024-01250-8\">https://doi.org/10.1007/s00222-024-01250-8</a>.","ieee":"R. Killip, T. Laurens, and M. Vişan, “Sharp well-posedness for the Benjamin–Ono equation,” <i>Inventiones mathematicae</i>, vol. 236, no. 3. Springer Nature, pp. 999–1054, 2024.","short":"R. Killip, T. Laurens, M. Vişan, Inventiones Mathematicae 236 (2024) 999–1054.","apa":"Killip, R., Laurens, T., &#38; Vişan, M. (2024). Sharp well-posedness for the Benjamin–Ono equation. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-024-01250-8\">https://doi.org/10.1007/s00222-024-01250-8</a>","ama":"Killip R, Laurens T, Vişan M. Sharp well-posedness for the Benjamin–Ono equation. <i>Inventiones mathematicae</i>. 2024;236(3):999-1054. doi:<a href=\"https://doi.org/10.1007/s00222-024-01250-8\">10.1007/s00222-024-01250-8</a>"},"status":"public","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2304.00124"}],"publisher":"Springer Nature","date_created":"2026-06-19T08:13:06Z","doi":"10.1007/s00222-024-01250-8","intvolume":"       236","das_tickbox":"1","author":[{"last_name":"Killip","full_name":"Killip, Rowan","first_name":"Rowan"},{"first_name":"Thierry","full_name":"Laurens, Thierry","last_name":"Laurens"},{"full_name":"Visan, Monica","last_name":"Visan","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","first_name":"Monica"}],"OA_place":"repository","extern":"1","page":"999-1054","abstract":[{"lang":"eng","text":"The Benjamin–Ono equation is shown to be well-posed, both on the line and on the circle, in the Sobolev spaces H^s for s > -1/2. The proof rests on a new gauge transformation and benefits from our introduction of a modified Lax pair representation of the full hierarchy. As we will show, these developments yield important additional dividends beyond well-posedness, including (i) the unification of the diverse approaches to polynomial conservation laws; (ii) a generalization of Gérard’s explicit formula to the full hierarchy; and (iii) new virial-type identities covering all equations in the hierarchy."}],"year":"2024","scopus_import":"1","OA_type":"green","_id":"22065","article_processing_charge":"No","day":"01","language":[{"iso":"eng"}],"month":"06","publication":"Inventiones mathematicae","volume":236,"publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]},"oa_version":"Preprint","date_updated":"2026-06-30T07:11:40Z","article_type":"original","quality_controlled":"1","issue":"3","type":"journal_article","arxiv":1,"title":"Sharp well-posedness for the Benjamin–Ono equation","external_id":{"arxiv":["2304.00124"]}},{"date_updated":"2025-04-14T07:53:46Z","project":[{"call_identifier":"H2020","grant_number":"885707","name":"Spectral rigidity and integrability for billiards and geodesic flows","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A"}],"article_type":"original","department":[{"_id":"VaKa"}],"quality_controlled":"1","type":"journal_article","title":"Marked Length Spectral determination of analytic chaotic billiards with axial symmetries","external_id":{"isi":["000978887600001"],"arxiv":["1905.00890"]},"arxiv":1,"ec_funded":1,"language":[{"iso":"eng"}],"volume":233,"isi":1,"publication":"Inventiones Mathematicae","month":"08","oa_version":"Preprint","publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]},"abstract":[{"text":"We consider billiards obtained by removing from the plane finitely many strictly convex analytic obstacles satisfying the non-eclipse condition. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift, which provides a natural labeling of periodic orbits. We show that under suitable symmetry and genericity assumptions, the Marked Length Spectrum determines the geometry of the billiard table.","lang":"eng"}],"year":"2023","page":"829-901","scopus_import":"1","_id":"12877","acknowledgement":"J.D.S. and M.L. have been partially supported by the NSERC Discovery grant, reference number 502617-2017. M.L. was also supported by the ERC project 692925 NUHGD of Sylvain Crovisier, by the ANR AAPG 2021 PRC CoSyDy: Conformally symplectic dynamics, beyond symplectic dynamics (ANR-CE40-0014), and by the ANR JCJC PADAWAN: Parabolic dynamics, bifurcations and wandering domains (ANR-21-CE40-0012). V.K. acknowledges partial support of the NSF grant DMS-1402164 and ERC Grant # 885707.","day":"01","article_processing_charge":"No","date_published":"2023-08-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1905.00890"}],"publication_status":"published","citation":{"ama":"De Simoi J, Kaloshin V, Leguil M. Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. <i>Inventiones Mathematicae</i>. 2023;233:829-901. doi:<a href=\"https://doi.org/10.1007/s00222-023-01191-8\">10.1007/s00222-023-01191-8</a>","short":"J. De Simoi, V. Kaloshin, M. Leguil, Inventiones Mathematicae 233 (2023) 829–901.","apa":"De Simoi, J., Kaloshin, V., &#38; Leguil, M. (2023). Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-023-01191-8\">https://doi.org/10.1007/s00222-023-01191-8</a>","ieee":"J. De Simoi, V. Kaloshin, and M. Leguil, “Marked Length Spectral determination of analytic chaotic billiards with axial symmetries,” <i>Inventiones Mathematicae</i>, vol. 233. Springer Nature, pp. 829–901, 2023.","chicago":"De Simoi, Jacopo, Vadim Kaloshin, and Martin Leguil. “Marked Length Spectral Determination of Analytic Chaotic Billiards with Axial Symmetries.” <i>Inventiones Mathematicae</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00222-023-01191-8\">https://doi.org/10.1007/s00222-023-01191-8</a>.","ista":"De Simoi J, Kaloshin V, Leguil M. 2023. Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. Inventiones Mathematicae. 233, 829–901.","mla":"De Simoi, Jacopo, et al. “Marked Length Spectral Determination of Analytic Chaotic Billiards with Axial Symmetries.” <i>Inventiones Mathematicae</i>, vol. 233, Springer Nature, 2023, pp. 829–901, doi:<a href=\"https://doi.org/10.1007/s00222-023-01191-8\">10.1007/s00222-023-01191-8</a>."},"status":"public","oa":1,"intvolume":"       233","author":[{"full_name":"De Simoi, Jacopo","last_name":"De Simoi","first_name":"Jacopo"},{"last_name":"Kaloshin","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim"},{"full_name":"Leguil, Martin","last_name":"Leguil","first_name":"Martin"}],"publisher":"Springer Nature","doi":"10.1007/s00222-023-01191-8","date_created":"2023-04-30T22:01:05Z"},{"_id":"10704","scopus_import":"1","acknowledgement":"We would like to thank Brian Collier, Davide Gaiotto, Peter Gothen, Jochen Heinloth, Daniel Huybrechts, Quoc Ho, Joel Kamnitzer, Gérard Laumon, Luca Migliorini, Alexander Minets, Brent Pym, Peng Shan, Carlos Simpson, András Szenes, Fernando R. Villegas, Richard Wentworth, Edward Witten and Kōta Yoshioka for interesting comments and discussions. Most of all we are grateful for a long list of very helpful comments by the referee. We would also like to thank the organizers of the Summer School on Higgs bundles in Hamburg in September 2018, where the authors and Richard Wentworth were giving lectures and where the work in this paper started by considering the mirror of the Lagrangian upward flows W+E investigated in [17]. The second author wishes to thank EPSRC and ICMAT for support. Open access funding provided by Institute of Science and Technology (IST Austria).","year":"2022","abstract":[{"lang":"eng","text":"We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it implies a precise formula for the multiplicity of the very stable components of the global nilpotent cone and its relationship to mirror symmetry. The main ingredients are the Bialynicki-Birula theory of C∗-actions on semiprojective varieties, C∗ characters of indices of C∗-equivariant coherent sheaves, Hecke transformation for Higgs bundles, relative Fourier–Mukai transform along the Hitchin fibration, hyperholomorphic structures on universal bundles and cominuscule Higgs bundles."}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"page":"893-989","day":"01","article_processing_charge":"Yes (via OA deal)","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","oa":1,"file":[{"date_updated":"2023-02-27T07:30:47Z","file_id":"12687","file_size":1069538,"file_name":"2022_InventionesMahtematicae_Hausel.pdf","content_type":"application/pdf","relation":"main_file","checksum":"a382ba75acebc9adfb8fe56247cb410e","access_level":"open_access","date_created":"2023-02-27T07:30:47Z","success":1,"creator":"dernst"}],"publication_status":"published","citation":{"ama":"Hausel T, Hitchin N. Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. <i>Inventiones Mathematicae</i>. 2022;228:893-989. doi:<a href=\"https://doi.org/10.1007/s00222-021-01093-7\">10.1007/s00222-021-01093-7</a>","short":"T. Hausel, N. Hitchin, Inventiones Mathematicae 228 (2022) 893–989.","apa":"Hausel, T., &#38; Hitchin, N. (2022). Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-021-01093-7\">https://doi.org/10.1007/s00222-021-01093-7</a>","ieee":"T. Hausel and N. Hitchin, “Very stable Higgs bundles, equivariant multiplicity and mirror symmetry,” <i>Inventiones Mathematicae</i>, vol. 228. Springer Nature, pp. 893–989, 2022.","chicago":"Hausel, Tamás, and Nigel Hitchin. “Very Stable Higgs Bundles, Equivariant Multiplicity and Mirror Symmetry.” <i>Inventiones Mathematicae</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00222-021-01093-7\">https://doi.org/10.1007/s00222-021-01093-7</a>.","mla":"Hausel, Tamás, and Nigel Hitchin. “Very Stable Higgs Bundles, Equivariant Multiplicity and Mirror Symmetry.” <i>Inventiones Mathematicae</i>, vol. 228, Springer Nature, 2022, pp. 893–989, doi:<a href=\"https://doi.org/10.1007/s00222-021-01093-7\">10.1007/s00222-021-01093-7</a>.","ista":"Hausel T, Hitchin N. 2022. Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. Inventiones Mathematicae. 228, 893–989."},"corr_author":"1","date_published":"2022-05-01T00:00:00Z","author":[{"first_name":"Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Hausel, Tamás","orcid":"0000-0002-9582-2634","last_name":"Hausel"},{"full_name":"Hitchin, Nigel","last_name":"Hitchin","first_name":"Nigel"}],"intvolume":"       228","date_created":"2022-01-30T23:01:34Z","doi":"10.1007/s00222-021-01093-7","publisher":"Springer Nature","quality_controlled":"1","department":[{"_id":"TaHa"}],"article_type":"original","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"date_updated":"2025-04-15T06:53:08Z","arxiv":1,"ddc":["510"],"title":"Very stable Higgs bundles, equivariant multiplicity and mirror symmetry","external_id":{"isi":["000745495400001"],"arxiv":["2101.08583"]},"type":"journal_article","volume":228,"has_accepted_license":"1","publication":"Inventiones Mathematicae","isi":1,"month":"05","related_material":{"link":[{"description":"News on the ISTA Website","url":"https://ista.ac.at/en/news/the-tip-of-the-mathematical-iceberg/","relation":"press_release"}]},"file_date_updated":"2023-02-27T07:30:47Z","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]},"oa_version":"Published Version"},{"type":"journal_article","ec_funded":1,"external_id":{"isi":["000646573600001"],"arxiv":["2005.08933"]},"arxiv":1,"ddc":["510"],"title":"Correlation energy of a weakly interacting Fermi gas","date_updated":"2025-04-14T07:27:00Z","article_type":"original","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","department":[{"_id":"RoSe"}],"publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]},"oa_version":"Published Version","language":[{"iso":"eng"}],"file_date_updated":"2022-05-16T12:23:40Z","publication":"Inventiones Mathematicae","isi":1,"month":"05","has_accepted_license":"1","volume":225,"article_processing_charge":"Yes (via OA deal)","day":"03","page":"885-979","abstract":[{"text":"We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree–Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy.","lang":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"year":"2021","acknowledgement":"We thank Christian Hainzl for helpful discussions and a referee for very careful reading of the paper and many helpful suggestions. NB and RS were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 694227). Part of the research of NB was conducted on the RZD18 Nice–Milan–Vienna–Moscow. NB thanks Elliott H. Lieb and Peter Otte for explanations about the Luttinger model. PTN has received funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy (EXC-2111-390814868). MP acknowledges financial support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (ERC StG MaMBoQ, grant agreement No. 802901). BS gratefully acknowledges financial support from the NCCR SwissMAP, from the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose-Einstein condensates” and from the European Research Council through the ERC-AdG CLaQS (grant agreement No. 834782). All authors acknowledge support for workshop participation from Mathematisches Forschungsinstitut Oberwolfach (Leibniz Association). NB, PTN, BS, and RS acknowledge support for workshop participation from Fondation des Treilles.","scopus_import":"1","_id":"7901","publisher":"Springer","doi":"10.1007/s00222-021-01041-5","date_created":"2020-05-28T16:48:20Z","intvolume":"       225","author":[{"first_name":"Niels P","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","last_name":"Benedikter","orcid":"0000-0002-1071-6091","full_name":"Benedikter, Niels P"},{"first_name":"Phan Thành","full_name":"Nam, Phan Thành","last_name":"Nam"},{"last_name":"Porta","full_name":"Porta, Marcello","first_name":"Marcello"},{"first_name":"Benjamin","last_name":"Schlein","full_name":"Schlein, Benjamin"},{"full_name":"Seiringer, Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"date_published":"2021-05-03T00:00:00Z","publication_status":"published","file":[{"creator":"dernst","success":1,"date_created":"2022-05-16T12:23:40Z","checksum":"f38c79dfd828cdc7f49a34b37b83d376","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"11386","date_updated":"2022-05-16T12:23:40Z","file_name":"2021_InventMath_Benedikter.pdf","file_size":1089319}],"citation":{"ama":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Correlation energy of a weakly interacting Fermi gas. <i>Inventiones Mathematicae</i>. 2021;225:885-979. doi:<a href=\"https://doi.org/10.1007/s00222-021-01041-5\">10.1007/s00222-021-01041-5</a>","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Inventiones Mathematicae 225 (2021) 885–979.","apa":"Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R. (2021). Correlation energy of a weakly interacting Fermi gas. <i>Inventiones Mathematicae</i>. Springer. <a href=\"https://doi.org/10.1007/s00222-021-01041-5\">https://doi.org/10.1007/s00222-021-01041-5</a>","ista":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Correlation energy of a weakly interacting Fermi gas. Inventiones Mathematicae. 225, 885–979.","mla":"Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi Gas.” <i>Inventiones Mathematicae</i>, vol. 225, Springer, 2021, pp. 885–979, doi:<a href=\"https://doi.org/10.1007/s00222-021-01041-5\">10.1007/s00222-021-01041-5</a>.","chicago":"Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas.” <i>Inventiones Mathematicae</i>. Springer, 2021. <a href=\"https://doi.org/10.1007/s00222-021-01041-5\">https://doi.org/10.1007/s00222-021-01041-5</a>.","ieee":"N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Correlation energy of a weakly interacting Fermi gas,” <i>Inventiones Mathematicae</i>, vol. 225. Springer, pp. 885–979, 2021."},"oa":1,"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"article_type":"original","date_updated":"2026-06-25T08:39:30Z","quality_controlled":"1","issue":"1","type":"journal_article","external_id":{"arxiv":["1904.11910"]},"title":"Invariance of white noise for KdV on the line","arxiv":1,"language":[{"iso":"eng"}],"publication":"Inventiones mathematicae","month":"10","volume":222,"publication_identifier":{"issn":["0020-9910"],"eissn":["1432-1297"]},"oa_version":"Preprint","page":"203-282","extern":"1","year":"2020","abstract":[{"text":"We consider the Korteweg–de Vries equation with white noise initial data, posed on the whole real line, and prove the almost sure existence of solutions. Moreover, we show that the solutions obey the group property and follow a white noise law at all times, past or future. As an offshoot of our methods, we also obtain a new proof of the existence of solutions and the invariance of white noise measure in the torus setting.","lang":"eng"}],"_id":"22054","scopus_import":"1","OA_type":"green","day":"01","article_processing_charge":"No","date_published":"2020-10-01T00:00:00Z","oa":1,"status":"public","publication_status":"published","citation":{"short":"R. Killip, J. Murphy, M. Vişan, Inventiones Mathematicae 222 (2020) 203–282.","ama":"Killip R, Murphy J, Vişan M. Invariance of white noise for KdV on the line. <i>Inventiones mathematicae</i>. 2020;222(1):203-282. doi:<a href=\"https://doi.org/10.1007/s00222-020-00964-9\">10.1007/s00222-020-00964-9</a>","apa":"Killip, R., Murphy, J., &#38; Vişan, M. (2020). Invariance of white noise for KdV on the line. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-020-00964-9\">https://doi.org/10.1007/s00222-020-00964-9</a>","ieee":"R. Killip, J. Murphy, and M. Vişan, “Invariance of white noise for KdV on the line,” <i>Inventiones mathematicae</i>, vol. 222, no. 1. Springer Nature, pp. 203–282, 2020.","chicago":"Killip, Rowan, Jason Murphy, and Monica Vişan. “Invariance of White Noise for KdV on the Line.” <i>Inventiones Mathematicae</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00222-020-00964-9\">https://doi.org/10.1007/s00222-020-00964-9</a>.","ista":"Killip R, Murphy J, Vişan M. 2020. Invariance of white noise for KdV on the line. Inventiones mathematicae. 222(1), 203–282.","mla":"Killip, Rowan, et al. “Invariance of White Noise for KdV on the Line.” <i>Inventiones Mathematicae</i>, vol. 222, no. 1, Springer Nature, 2020, pp. 203–82, doi:<a href=\"https://doi.org/10.1007/s00222-020-00964-9\">10.1007/s00222-020-00964-9</a>."},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1904.11910","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1007/s00222-020-00964-9","date_created":"2026-06-19T07:56:16Z","publisher":"Springer Nature","das_tickbox":"1","author":[{"first_name":"Rowan","full_name":"Killip, Rowan","last_name":"Killip"},{"first_name":"Jason","last_name":"Murphy","full_name":"Murphy, Jason"},{"id":"056daca0-b8d1-11f0-964f-f91054abf8ca","first_name":"Monica","last_name":"Visan","full_name":"Visan, Monica"}],"intvolume":"       222","OA_place":"repository"},{"publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]},"oa_version":"Preprint","volume":153,"month":"07","publication":"Inventiones Mathematicae","language":[{"iso":"eng"}],"external_id":{"arxiv":["0205236"]},"title":"Mirror symmetry, langlands duality, and the Hitchin system","arxiv":1,"type":"journal_article","quality_controlled":"1","article_type":"original","date_updated":"2026-05-28T11:54:13Z","OA_place":"repository","author":[{"first_name":"Tamas","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9582-2634","last_name":"Hausel","full_name":"Hausel, Tamas"},{"last_name":"Thaddeus","full_name":"Thaddeus, Michael","first_name":"Michael"}],"intvolume":"       153","date_created":"2018-12-11T11:52:08Z","doi":"10.1007/s00222-003-0286-7","publisher":"Springer Nature","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.math/0205236","open_access":"1"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","status":"public","oa":1,"publication_status":"published","citation":{"ista":"Hausel T, Thaddeus M. 2003. Mirror symmetry, langlands duality, and the Hitchin system. Inventiones Mathematicae. 153, 197–229.","mla":"Hausel, Tamás, and Michael Thaddeus. “Mirror Symmetry, Langlands Duality, and the Hitchin System.” <i>Inventiones Mathematicae</i>, vol. 153, Springer Nature, 2003, pp. 197–229, doi:<a href=\"https://doi.org/10.1007/s00222-003-0286-7\">10.1007/s00222-003-0286-7</a>.","chicago":"Hausel, Tamás, and Michael Thaddeus. “Mirror Symmetry, Langlands Duality, and the Hitchin System.” <i>Inventiones Mathematicae</i>. Springer Nature, 2003. <a href=\"https://doi.org/10.1007/s00222-003-0286-7\">https://doi.org/10.1007/s00222-003-0286-7</a>.","ieee":"T. Hausel and M. Thaddeus, “Mirror symmetry, langlands duality, and the Hitchin system,” <i>Inventiones Mathematicae</i>, vol. 153. Springer Nature, pp. 197–229, 2003.","short":"T. Hausel, M. Thaddeus, Inventiones Mathematicae 153 (2003) 197–229.","ama":"Hausel T, Thaddeus M. Mirror symmetry, langlands duality, and the Hitchin system. <i>Inventiones Mathematicae</i>. 2003;153:197-229. doi:<a href=\"https://doi.org/10.1007/s00222-003-0286-7\">10.1007/s00222-003-0286-7</a>","apa":"Hausel, T., &#38; Thaddeus, M. (2003). Mirror symmetry, langlands duality, and the Hitchin system. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-003-0286-7\">https://doi.org/10.1007/s00222-003-0286-7</a>"},"date_published":"2003-07-01T00:00:00Z","publist_id":"5738","article_processing_charge":"No","day":"01","_id":"1457","scopus_import":"1","OA_type":"green","year":"2003","abstract":[{"text":"Among the major mathematical approaches to mirror symmetry are those of Batyrev-Borisov and Stromdnger-Yau-Zaslow (SYZ). The first is explicit and amenable to computation but is not clearly related to the physical motivation; the second is the opposite. Furthermore, it is far from obvious that mirror partners in one sense will also be mirror partners in the other. This paper concerns a class of examples that can be shown to satisfy the requirements of SYZ, but whose Hodge numbers are also equal. This provides significant evidence in support of SYZ. Moreover, the examples are of great interest in their own right: they are spaces of flat SLr-connections on a smooth curve. The mirror is the corresponding space for the Langlands dual group PGLr. These examples therefore throw a bridge from mirror symmetry to the duality theory of Lie groups and, more broadly, to the geometric Langlands program.","lang":"eng"}],"page":"197 - 229","extern":"1"}]