[{"volume":233,"article_type":"original","date_created":"2023-04-30T22:01:05Z","author":[{"full_name":"De Simoi, Jacopo","last_name":"De Simoi","first_name":"Jacopo"},{"last_name":"Kaloshin","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","first_name":"Vadim"},{"first_name":"Martin","full_name":"Leguil, Martin","last_name":"Leguil"}],"scopus_import":"1","day":"01","title":"Marked Length Spectral determination of analytic chaotic billiards with axial symmetries","oa_version":"Preprint","publication_status":"published","publication_identifier":{"issn":["0020-9910"],"eissn":["1432-1297"]},"intvolume":"       233","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"}],"department":[{"_id":"VaKa"}],"month":"08","arxiv":1,"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.","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.","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.","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>.","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>.","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>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"language":[{"iso":"eng"}],"date_updated":"2023-10-04T11:25:37Z","_id":"12877","type":"journal_article","doi":"10.1007/s00222-023-01191-8","article_processing_charge":"No","publisher":"Springer Nature","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1905.00890","open_access":"1"}],"quality_controlled":"1","page":"829-901","year":"2023","isi":1,"external_id":{"arxiv":["1905.00890"],"isi":["000978887600001"]},"ec_funded":1,"date_published":"2023-08-01T00:00:00Z","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.","project":[{"call_identifier":"H2020","name":"Spectral rigidity and integrability for billiards and geodesic flows","grant_number":"885707","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A"}],"publication":"Inventiones Mathematicae","status":"public"},{"date_updated":"2023-08-02T14:03:20Z","_id":"10704","type":"journal_article","doi":"10.1007/s00222-021-01093-7","article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","quality_controlled":"1","page":"893-989","ddc":["510"],"year":"2022","isi":1,"external_id":{"arxiv":["2101.08583"],"isi":["000745495400001"]},"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"}]},"date_published":"2022-05-01T00:00:00Z","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).","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"publication":"Inventiones Mathematicae","status":"public","volume":228,"article_type":"original","date_created":"2022-01-30T23:01:34Z","author":[{"last_name":"Hausel","full_name":"Hausel, Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamás"},{"full_name":"Hitchin, Nigel","last_name":"Hitchin","first_name":"Nigel"}],"day":"01","scopus_import":"1","title":"Very stable Higgs bundles, equivariant multiplicity and mirror symmetry","oa_version":"Published Version","publication_status":"published","publication_identifier":{"issn":["0020-9910"],"eissn":["1432-1297"]},"file_date_updated":"2023-02-27T07:30:47Z","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"abstract":[{"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.","lang":"eng"}],"intvolume":"       228","department":[{"_id":"TaHa"}],"file":[{"file_id":"12687","date_created":"2023-02-27T07:30:47Z","file_size":1069538,"creator":"dernst","date_updated":"2023-02-27T07:30:47Z","relation":"main_file","checksum":"a382ba75acebc9adfb8fe56247cb410e","file_name":"2022_InventionesMahtematicae_Hausel.pdf","success":1,"content_type":"application/pdf","access_level":"open_access"}],"arxiv":1,"month":"05","citation":{"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>","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.","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>.","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.","short":"T. Hausel, N. Hitchin, Inventiones Mathematicae 228 (2022) 893–989.","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>"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"language":[{"iso":"eng"}]},{"quality_controlled":"1","page":"885-979","ddc":["510"],"_id":"7901","date_updated":"2023-08-21T06:30:30Z","type":"journal_article","article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00222-021-01041-5","publisher":"Springer","ec_funded":1,"date_published":"2021-05-03T00:00:00Z","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.","publication":"Inventiones Mathematicae","status":"public","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems"}],"isi":1,"year":"2021","external_id":{"isi":["000646573600001"],"arxiv":["2005.08933"]},"file_date_updated":"2022-05-16T12:23:40Z","publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]},"publication_status":"published","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","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."}],"intvolume":"       225","volume":225,"date_created":"2020-05-28T16:48:20Z","article_type":"original","day":"03","scopus_import":"1","author":[{"full_name":"Benedikter, Niels P","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","last_name":"Benedikter","orcid":"0000-0002-1071-6091","first_name":"Niels P"},{"first_name":"Phan Thành","last_name":"Nam","full_name":"Nam, Phan Thành"},{"first_name":"Marcello","full_name":"Porta, Marcello","last_name":"Porta"},{"first_name":"Benjamin","last_name":"Schlein","full_name":"Schlein, Benjamin"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert"}],"oa_version":"Published Version","title":"Correlation energy of a weakly interacting Fermi gas","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.","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.","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>.","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>.","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>"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"RoSe"}],"file":[{"file_id":"11386","date_created":"2022-05-16T12:23:40Z","file_size":1089319,"date_updated":"2022-05-16T12:23:40Z","creator":"dernst","relation":"main_file","checksum":"f38c79dfd828cdc7f49a34b37b83d376","file_name":"2021_InventMath_Benedikter.pdf","success":1,"content_type":"application/pdf","access_level":"open_access"}],"month":"05","arxiv":1}]