[{"oa":1,"das_tickbox":"1","citation":{"chicago":"Glasgow, Margalit, Matthew Alan Kwan, Ashwin Sah, and Mehtaab Sawhney. “The Exact Rank of Sparse Random Graphs.” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/jems/1692\">https://doi.org/10.4171/jems/1692</a>.","short":"M. Glasgow, M.A. Kwan, A. Sah, M. Sawhney, Journal of the European Mathematical Society (2025).","ieee":"M. Glasgow, M. A. Kwan, A. Sah, and M. Sawhney, “The exact rank of sparse random graphs,” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025.","ista":"Glasgow M, Kwan MA, Sah A, Sawhney M. 2025. The exact rank of sparse random graphs. Journal of the European Mathematical Society.","ama":"Glasgow M, Kwan MA, Sah A, Sawhney M. The exact rank of sparse random graphs. <i>Journal of the European Mathematical Society</i>. 2025. doi:<a href=\"https://doi.org/10.4171/jems/1692\">10.4171/jems/1692</a>","apa":"Glasgow, M., Kwan, M. A., Sah, A., &#38; Sawhney, M. (2025). The exact rank of sparse random graphs. <i>Journal of the European Mathematical Society</i>. EMS Press. <a href=\"https://doi.org/10.4171/jems/1692\">https://doi.org/10.4171/jems/1692</a>","mla":"Glasgow, Margalit, et al. “The Exact Rank of Sparse Random Graphs.” <i>Journal of the European Mathematical Society</i>, EMS Press, 2025, doi:<a href=\"https://doi.org/10.4171/jems/1692\">10.4171/jems/1692</a>."},"article_type":"original","date_created":"2026-02-17T07:41:59Z","DOAJ_listed":"1","publisher":"EMS Press","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"fulldoi":"https://doi.org/10.4171/jems/1692","acknowledgement":"We would like to thank Noga Alon for suggesting that our main result gives\r\na linear-time algorithm for computing the rank. We also thank the referees for a number of thoughtful comments and suggestions. Glasgow was supported by NSF graduate research fellowship program award DGE1656518. Kwan was supported by ERC Starting Grant “RANDSTRUCT” No. 101076777. Sah and Sawhney were supported by NSF Graduate Research Fellowship Program DGE-1745302.\r\n","PlanS_conform":"1","article_processing_charge":"No","day":"02","publication_status":"epub_ahead","arxiv":1,"date_updated":"2026-07-06T11:51:31Z","title":"The exact rank of sparse random graphs","author":[{"first_name":"Margalit","last_name":"Glasgow","full_name":"Glasgow, Margalit"},{"orcid":"0000-0002-4003-7567","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan","last_name":"Kwan","full_name":"Kwan, Matthew Alan"},{"full_name":"Sah, Ashwin","last_name":"Sah","first_name":"Ashwin"},{"first_name":"Mehtaab","full_name":"Sawhney, Mehtaab","last_name":"Sawhney"}],"publication":"Journal of the European Mathematical Society","abstract":[{"text":"Two landmark results in combinatorial random matrix theory, due to Komlós and Costello–Tao–Vu, show that discrete random matrices and symmetric discrete random matrices are typically nonsingular. In particular, in the language of graph theory, when p is a fixed constant, the biadjacency matrix of a random Erdős–Rényi bipartite graph G(n,n,p) and the adjacency matrix of an Erdős–Rényi random graph G(n,p) are both nonsingular with high probability. However, very sparse random graphs (i.e., where p is allowed to decay rapidly with n) are typically singular, due to the presence of “local” dependencies such as isolated vertices and pairs of degree-1 vertices with the same neighbour. In this paper, we give a combinatorial description of the rank of a sparse random graph G(n,n,c/n) or G(n,c/n) in terms of such local dependencies, for all constants c=e (and we present some evidence that the situation is very different for c=e). This gives an essentially complete answer to a question raised by Vu (2014). As applications of our main theorem and its proof, we also determine the asymptotic singularity probability of the 2-core of a sparse random graph, we show that the rank of a sparse random graph is extremely well approximated by its matching number, and we deduce a central limit theorem for the rank of G(n,c/n).","lang":"eng"}],"year":"2025","_id":"21263","publication_identifier":{"issn":["1435-9855"],"eissn":["1435-9863"]},"type":"journal_article","date_published":"2025-09-02T00:00:00Z","oa_version":"Published Version","language":[{"iso":"eng"}],"external_id":{"arxiv":["2303.05435"]},"month":"09","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.4171/JEMS/1692","open_access":"1"}],"ddc":["510"],"OA_type":"diamond","doi":"10.4171/jems/1692","department":[{"_id":"MaKw"}],"OA_place":"publisher","project":[{"grant_number":"101076777","name":"Randomness and structure in combinatorics","_id":"bd95085b-d553-11ed-ba76-e55d3349be45"}],"status":"public","has_accepted_license":"1","corr_author":"1"},{"fulldoi":"https://doi.org/10.4171/jems/1697","acknowledgement":"The first author would like to thank Samir Siksek for introducing the problem\r\nto him. The material in Section 6 is a result of discussing with many people, and the second author is very grateful to Tim Browning, Stephanie Chan, Jakob Glas, Jakub Löwit, Mirko Mauri, Marta Pieropan, Mike Roth, Matteo Verzobio and Victor Wang for taking the time to answer his questions and for their valuable suggestions. We thank Tim Browning, Yijie Diao, Ana Marija Vego and the anonymous referee for their helpful comments.\r\nThe first author was supported by NSERC Discovery Grant RGPIN-2024-06810. The\r\nsecond author was supported by the NWO Veni Grant 016.Veni.192.047 during his time at\r\nUtrecht University and by a FWF grant (DOI 10.55776/P32428) at the Institute of Science and\r\nTechnology Austria while working on this paper.","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"EMS Press","date_created":"2026-02-16T16:00:02Z","article_type":"original","citation":{"ista":"Yao Xiao S, Yamagishi S. 2025. Quartic polynomials in two variables do not represent all non-negative integers. Journal of the European Mathematical Society.","mla":"Yao Xiao, Stanley, and Shuntaro Yamagishi. “Quartic Polynomials in Two Variables Do Not Represent All Non-Negative Integers.” <i>Journal of the European Mathematical Society</i>, EMS Press, 2025, doi:<a href=\"https://doi.org/10.4171/jems/1697\">10.4171/jems/1697</a>.","ama":"Yao Xiao S, Yamagishi S. Quartic polynomials in two variables do not represent all non-negative integers. <i>Journal of the European Mathematical Society</i>. 2025. doi:<a href=\"https://doi.org/10.4171/jems/1697\">10.4171/jems/1697</a>","apa":"Yao Xiao, S., &#38; Yamagishi, S. (2025). Quartic polynomials in two variables do not represent all non-negative integers. <i>Journal of the European Mathematical Society</i>. EMS Press. <a href=\"https://doi.org/10.4171/jems/1697\">https://doi.org/10.4171/jems/1697</a>","ieee":"S. Yao Xiao and S. Yamagishi, “Quartic polynomials in two variables do not represent all non-negative integers,” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025.","short":"S. Yao Xiao, S. Yamagishi, Journal of the European Mathematical Society (2025).","chicago":"Yao Xiao, Stanley, and Shuntaro Yamagishi. “Quartic Polynomials in Two Variables Do Not Represent All Non-Negative Integers.” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/jems/1697\">https://doi.org/10.4171/jems/1697</a>."},"supplementarymaterial":"no","researchdata_availability":"no","das_tickbox":"0","oa":1,"publication_identifier":{"eissn":["1435-9863"],"issn":["1435-9855"]},"year":"2025","_id":"21260","abstract":[{"lang":"eng","text":"We prove that there does not exist F∈Q[x,y] of degree 4 such that F(Z^2 )=Z ≥0. In particular, this answers a question by John S. Lew and Bjorn Poonen for quartic polynomials."}],"author":[{"first_name":"Stanley","last_name":"Yao Xiao","full_name":"Yao Xiao, Stanley"},{"id":"0c3fbc5c-f7a6-11ec-8d70-9485e75b416b","first_name":"Shuntaro","last_name":"Yamagishi","full_name":"Yamagishi, Shuntaro"}],"publication":"Journal of the European Mathematical Society","title":"Quartic polynomials in two variables do not represent all non-negative integers","arxiv":1,"date_updated":"2026-07-16T08:54:37Z","publication_status":"epub_ahead","day":"06","article_processing_charge":"No","OA_type":"diamond","ddc":["500"],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.4171/JEMS/1697"}],"month":"08","external_id":{"arxiv":["2307.05712"]},"language":[{"iso":"eng"}],"oa_version":"Published Version","date_published":"2025-08-06T00:00:00Z","type":"journal_article","corr_author":"1","status":"public","OA_place":"publisher","project":[{"call_identifier":"FWF","name":"New frontiers of the Manin conjecture","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428"}],"department":[{"_id":"TiBr"}],"doi":"10.4171/jems/1697"},{"department":[{"_id":"TiBr"}],"project":[{"name":"Rational curves via function field analytic number theory","grant_number":"P36278","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3"}],"OA_place":"publisher","status":"public","corr_author":"1","doi":"10.4171/jems/1704","month":"09","main_file_link":[{"open_access":"1","url":"https://doi.org/10.4171/JEMS/1704"}],"quality_controlled":"1","OA_type":"diamond","ddc":["510"],"date_published":"2025-09-17T00:00:00Z","type":"journal_article","oa_version":"Published Version","language":[{"iso":"eng"}],"external_id":{"arxiv":["2401.04375"]},"title":"Almost all quadratic twists of an elliptic curve have no integral points","author":[{"full_name":"Browning, Timothy D","last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177"},{"full_name":"Chan, Yik Tung","last_name":"Chan","first_name":"Yik Tung","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","orcid":"0000-0001-8467-4106"}],"publication":"Journal of the European Mathematical Society","abstract":[{"lang":"eng","text":"For a given elliptic curve E in short Weierstrass form, we show that almost all quadratic twists E \r\nD have no integral points, as D ranges over square-free integers ordered by size. Our result is conditional on a weak form of the Hall–Lang conjecture in the case that E has partial 2-torsion. The proof uses a correspondence of Mordell and the reduction theory of binary quartic forms in order to transfer the problem to counting rational points of bounded height on a certain singular cubic surface, together with extensive use of cancellation in character sum estimates, drawn from Heath-Brown’s analysis of Selmer group statistics for the congruent number curve."}],"year":"2025","_id":"21266","publication_identifier":{"eissn":["1435-9863"],"issn":["1435-9855"]},"article_processing_charge":"No","day":"17","publication_status":"epub_ahead","date_updated":"2026-07-16T09:00:02Z","arxiv":1,"date_created":"2026-02-17T07:46:26Z","DOAJ_listed":"1","publisher":"EMS Press","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","acknowledgement":"The authors are grateful to Roger Heath-Brown and to the anonymous referees for useful comments. The first author was supported by an FWF grant (DOI 10.55776/P36278).","fulldoi":"https://doi.org/10.4171/jems/1704","oa":1,"das_tickbox":"0","supplementarymaterial":"no","researchdata_availability":"no","citation":{"ieee":"T. D. Browning and S. Chan, “Almost all quadratic twists of an elliptic curve have no integral points,” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025.","ama":"Browning TD, Chan S. Almost all quadratic twists of an elliptic curve have no integral points. <i>Journal of the European Mathematical Society</i>. 2025. doi:<a href=\"https://doi.org/10.4171/jems/1704\">10.4171/jems/1704</a>","apa":"Browning, T. D., &#38; Chan, S. (2025). Almost all quadratic twists of an elliptic curve have no integral points. <i>Journal of the European Mathematical Society</i>. EMS Press. <a href=\"https://doi.org/10.4171/jems/1704\">https://doi.org/10.4171/jems/1704</a>","mla":"Browning, Timothy D., and Stephanie Chan. “Almost All Quadratic Twists of an Elliptic Curve Have No Integral Points.” <i>Journal of the European Mathematical Society</i>, EMS Press, 2025, doi:<a href=\"https://doi.org/10.4171/jems/1704\">10.4171/jems/1704</a>.","ista":"Browning TD, Chan S. 2025. Almost all quadratic twists of an elliptic curve have no integral points. Journal of the European Mathematical Society.","short":"T.D. Browning, S. Chan, Journal of the European Mathematical Society (2025).","chicago":"Browning, Timothy D, and Stephanie Chan. “Almost All Quadratic Twists of an Elliptic Curve Have No Integral Points.” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/jems/1704\">https://doi.org/10.4171/jems/1704</a>."},"article_type":"original"},{"mathsc":["14H60","19L50"],"arxiv":1,"date_updated":"2026-07-23T11:16:00Z","article_processing_charge":"Yes","day":"20","publication_status":"epub_ahead","ec_funded":1,"year":"2025","_id":"20043","publication_identifier":{"issn":["1435-9855"],"eissn":["1435-9863"]},"title":"Complex K-theory of moduli spaces of Higgs bundles","publication":"Journal of the European Mathematical Society","author":[{"full_name":"Groechenig, Michael","last_name":"Groechenig","first_name":"Michael"},{"last_name":"Shen","full_name":"Shen, Shiyu","id":"544cccd3-9005-11ec-87bc-94aef1c5b814","first_name":"Shiyu","orcid":"0000-0002-4444-8718"}],"abstract":[{"text":"We establish an isomorphism of complex K-theory of the moduli space  M  of “SL n​ ”-Higgs bundles of degree d and rank n (in the sense of Hausel–Thaddeus) and twisted complex K-theory of the orbifold  M  of PGL n​ -Higgs bundles of degree e, where (n,d)=(n,e)=1. Along the way, we prove the vanishing of torsion for H ∗ ( M ) and certain twisted complex K-theory groups of  M . We also extend Arinkin’s autoduality of compactified Jacobian to a derived equivalence between SL n​ - and PGL n​ -Hitchin systems over the elliptic locus. In the appendix, we develop a formalism of G-sheaves of spectra, generalising equivariant homotopy theory to a relative setting.","lang":"eng"}],"article_type":"original","oa":1,"das_tickbox":"1","citation":{"chicago":"Groechenig, Michael, and Shiyu Shen. “Complex K-Theory of Moduli Spaces of Higgs Bundles.” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/jems/1601\">https://doi.org/10.4171/jems/1601</a>.","short":"M. Groechenig, S. Shen, Journal of the European Mathematical Society (2025).","ieee":"M. Groechenig and S. Shen, “Complex K-theory of moduli spaces of Higgs bundles,” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025.","mla":"Groechenig, Michael, and Shiyu Shen. “Complex K-Theory of Moduli Spaces of Higgs Bundles.” <i>Journal of the European Mathematical Society</i>, EMS Press, 2025, doi:<a href=\"https://doi.org/10.4171/jems/1601\">10.4171/jems/1601</a>.","ama":"Groechenig M, Shen S. Complex K-theory of moduli spaces of Higgs bundles. <i>Journal of the European Mathematical Society</i>. 2025. doi:<a href=\"https://doi.org/10.4171/jems/1601\">10.4171/jems/1601</a>","apa":"Groechenig, M., &#38; Shen, S. (2025). Complex K-theory of moduli spaces of Higgs bundles. <i>Journal of the European Mathematical Society</i>. EMS Press. <a href=\"https://doi.org/10.4171/jems/1601\">https://doi.org/10.4171/jems/1601</a>","ista":"Groechenig M, Shen S. 2025. Complex K-theory of moduli spaces of Higgs bundles. Journal of the European Mathematical Society."},"acknowledgement":"It is a pleasure to thank Tom Baird for sharing his insights about vanishing of torsion for H.M{1\r\n2/. Furthermore, we would like to thank him for bringing [25] to our attention. We also thank Alexander Kupers for enlightening conversations about the Atiyah–Hirzebruch spectral sequence and for pointing out a reference. We are grateful to Victoria Hoskins and Simon Pepin-Lehalleur for sharing a preprint of their recent paper on a motivic version of topological mirror symmetry and for useful remarks on Section 6. Anne Larsen pointed out that our previous proof Lemma 4.5 was incomplete, we thank her for bringing this to our attention. We are grateful to the anonymous referee for many valuable comments that have improved the paper tremendously. The report we received was one of the most detailed referee report either of us has ever seen. We thank them for their hard work and the resulting contribution to this paper. Michael Groechenig was supported by an NSERC discovery grant and an Alfred P. Sloan\r\nfellowship. Shiyu Shen has received funding from the European Union’s Horizon 2020 research\r\nand innovation program under the Marie Skłodowska-Curie grant agreement No. 101034413.","fulldoi":"https://doi.org/10.4171/jems/1601","date_created":"2025-07-21T07:54:50Z","isi":1,"publisher":"EMS Press","DOAJ_listed":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.4171/jems/1601","corr_author":"1","department":[{"_id":"TaHa"}],"project":[{"name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020"}],"OA_place":"publisher","status":"public","language":[{"iso":"eng"}],"external_id":{"isi":["001608254800001"],"arxiv":["2212.10695"]},"type":"journal_article","date_published":"2025-03-20T00:00:00Z","oa_version":"Published Version","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.4171/JEMS/1601"}],"ddc":["510"],"OA_type":"gold","month":"03"},{"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2204.12548","open_access":"1"}],"quality_controlled":"1","OA_type":"green","month":"06","volume":28,"external_id":{"arxiv":["2204.12548"]},"language":[{"iso":"eng"}],"intvolume":"        28","type":"journal_article","date_published":"2024-06-26T00:00:00Z","oa_version":"Preprint","OA_place":"repository","status":"public","doi":"10.4171/jems/1490","scopus_import":"1","fulldoi":"https://doi.org/10.4171/jems/1490","publisher":"EMS Press","date_created":"2026-06-19T08:11:46Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"2","article_type":"original","oa":1,"citation":{"ieee":"B. Harrop-Griffiths, R. Killip, M. Ntekoume, and M. Vişan, “Global well-posedness for the derivative nonlinear Schrödinger equation in L^2(R),” <i>Journal of the European Mathematical Society</i>, vol. 28, no. 2. EMS Press, pp. 843–924, 2024.","ista":"Harrop-Griffiths B, Killip R, Ntekoume M, Vişan M. 2024. Global well-posedness for the derivative nonlinear Schrödinger equation in L^2(R). Journal of the European Mathematical Society. 28(2), 843–924.","apa":"Harrop-Griffiths, B., Killip, R., Ntekoume, M., &#38; Vişan, M. (2024). Global well-posedness for the derivative nonlinear Schrödinger equation in L^2(R). <i>Journal of the European Mathematical Society</i>. EMS Press. <a href=\"https://doi.org/10.4171/jems/1490\">https://doi.org/10.4171/jems/1490</a>","mla":"Harrop-Griffiths, Benjamin, et al. “Global Well-Posedness for the Derivative Nonlinear Schrödinger Equation in L^2(R).” <i>Journal of the European Mathematical Society</i>, vol. 28, no. 2, EMS Press, 2024, pp. 843–924, doi:<a href=\"https://doi.org/10.4171/jems/1490\">10.4171/jems/1490</a>.","ama":"Harrop-Griffiths B, Killip R, Ntekoume M, Vişan M. Global well-posedness for the derivative nonlinear Schrödinger equation in L^2(R). <i>Journal of the European Mathematical Society</i>. 2024;28(2):843-924. doi:<a href=\"https://doi.org/10.4171/jems/1490\">10.4171/jems/1490</a>","chicago":"Harrop-Griffiths, Benjamin, Rowan Killip, Maria Ntekoume, and Monica Vişan. “Global Well-Posedness for the Derivative Nonlinear Schrödinger Equation in L^2(R).” <i>Journal of the European Mathematical Society</i>. EMS Press, 2024. <a href=\"https://doi.org/10.4171/jems/1490\">https://doi.org/10.4171/jems/1490</a>.","short":"B. Harrop-Griffiths, R. Killip, M. Ntekoume, M. Vişan, Journal of the European Mathematical Society 28 (2024) 843–924."},"year":"2024","_id":"22062","publication_identifier":{"issn":["1435-9855"],"eissn":["1435-9863"]},"author":[{"full_name":"Harrop-Griffiths, Benjamin","last_name":"Harrop-Griffiths","first_name":"Benjamin"},{"first_name":"Rowan","last_name":"Killip","full_name":"Killip, Rowan"},{"full_name":"Ntekoume, Maria","last_name":"Ntekoume","first_name":"Maria"},{"first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","full_name":"Visan, Monica","last_name":"Visan"}],"title":"Global well-posedness for the derivative nonlinear Schrödinger equation in L^2(R)","publication":"Journal of the European Mathematical Society","abstract":[{"lang":"eng","text":"We prove that the derivative nonlinear Schrödinger equation in one space dimension is globally well-posed on the line in L^2 (R), which is the scaling-critical space for this equation."}],"page":"843-924","mathsc":["35Q55"],"arxiv":1,"date_updated":"2026-06-30T07:04:07Z","publication_status":"published","day":"26","article_processing_charge":"No","extern":"1"},{"volume":22,"external_id":{"isi":["000548174700006"],"arxiv":["1704.04819"]},"language":[{"iso":"eng"}],"oa_version":"Preprint","intvolume":"        22","type":"journal_article","date_published":"2020-07-01T00:00:00Z","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1704.04819"}],"month":"07","doi":"10.4171/JEMS/966","scopus_import":"1","status":"public","department":[{"_id":"RoSe"}],"issue":"7","article_type":"original","citation":{"chicago":"Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein. “The Excitation Spectrum of Bose Gases Interacting through Singular Potentials.” <i>Journal of the European Mathematical Society</i>. EMS Press, 2020. <a href=\"https://doi.org/10.4171/JEMS/966\">https://doi.org/10.4171/JEMS/966</a>.","short":"C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Journal of the European Mathematical Society 22 (2020) 2331–2403.","ieee":"C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “The excitation spectrum of Bose gases interacting through singular potentials,” <i>Journal of the European Mathematical Society</i>, vol. 22, no. 7. EMS Press, pp. 2331–2403, 2020.","mla":"Boccato, Chiara, et al. “The Excitation Spectrum of Bose Gases Interacting through Singular Potentials.” <i>Journal of the European Mathematical Society</i>, vol. 22, no. 7, EMS Press, 2020, pp. 2331–403, doi:<a href=\"https://doi.org/10.4171/JEMS/966\">10.4171/JEMS/966</a>.","apa":"Boccato, C., Brennecke, C., Cenatiempo, S., &#38; Schlein, B. (2020). The excitation spectrum of Bose gases interacting through singular potentials. <i>Journal of the European Mathematical Society</i>. EMS Press. <a href=\"https://doi.org/10.4171/JEMS/966\">https://doi.org/10.4171/JEMS/966</a>","ama":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. The excitation spectrum of Bose gases interacting through singular potentials. <i>Journal of the European Mathematical Society</i>. 2020;22(7):2331-2403. doi:<a href=\"https://doi.org/10.4171/JEMS/966\">10.4171/JEMS/966</a>","ista":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. The excitation spectrum of Bose gases interacting through singular potentials. Journal of the European Mathematical Society. 22(7), 2331–2403."},"das_tickbox":"1","oa":1,"fulldoi":"https://doi.org/10.4171/JEMS/966","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"EMS Press","isi":1,"date_created":"2020-06-29T07:59:35Z","arxiv":1,"date_updated":"2026-07-06T11:53:41Z","publication_status":"published","article_processing_charge":"No","day":"01","publication_identifier":{"issn":["1435-9855"]},"year":"2020","_id":"8042","abstract":[{"text":"We consider systems of N bosons in a box of volume one, interacting through a repulsive two-body potential of the form κN3β−1V(Nβx). For all 0<β<1, and for sufficiently small coupling constant κ>0, we establish the validity of Bogolyubov theory, identifying the ground state energy and the low-lying excitation spectrum up to errors that vanish in the limit of large N.","lang":"eng"}],"page":"2331-2403","publication":"Journal of the European Mathematical Society","title":"The excitation spectrum of Bose gases interacting through singular potentials","author":[{"id":"342E7E22-F248-11E8-B48F-1D18A9856A87","first_name":"Chiara","full_name":"Boccato, Chiara","last_name":"Boccato"},{"first_name":"Christian","full_name":"Brennecke, Christian","last_name":"Brennecke"},{"first_name":"Serena","full_name":"Cenatiempo, Serena","last_name":"Cenatiempo"},{"first_name":"Benjamin","last_name":"Schlein","full_name":"Schlein, Benjamin"}]},{"publication_status":"published","day":"19","article_processing_charge":"No","extern":"1","date_updated":"2021-01-12T08:19:41Z","doi":"10.4171/jems/642","publication":"Journal of the European Mathematical Society","author":[{"first_name":"Jacques","last_name":"Féjoz","full_name":"Féjoz, Jacques"},{"first_name":"Marcel","full_name":"Guàrdia, Marcel","last_name":"Guàrdia"},{"last_name":"Kaloshin","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim","orcid":"0000-0002-6051-2628"},{"first_name":"Pablo","full_name":"Roldán, Pablo","last_name":"Roldán"}],"title":"Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem","status":"public","abstract":[{"text":"We study the dynamics of the restricted planar three-body problem near mean motion resonances, i.e. a resonance involving the Keplerian periods of the two lighter bodies revolving around the most massive one. This problem is often used to model Sun–Jupiter–asteroid systems. For the primaries (Sun and Jupiter), we pick a realistic mass ratio μ=10−3 and a small eccentricity e0>0. The main result is a construction of a variety of non local diffusing orbits which show a drastic change of the osculating (instant) eccentricity of the asteroid, while the osculating semi major axis is kept almost constant. The proof relies on the careful analysis of the circular problem, which has a hyperbolic structure, but for which diffusion is prevented by KAM tori. In the proof we verify certain non-degeneracy conditions numerically.\r\n\r\nBased on the work of Treschev, it is natural to conjecture that the time of diffusion for this problem is ∼−ln(μe0)μ3/2e0. We expect our instability mechanism to apply to realistic values of e0 and we give heuristic arguments in its favor. If so, the applicability of Nekhoroshev theory to the three-body problem as well as the long time stability become questionable.\r\n\r\nIt is well known that, in the Asteroid Belt, located between the orbits of Mars and Jupiter, the distribution of asteroids has the so-called Kirkwood gaps exactly at mean motion resonances of low order. Our mechanism gives a possible explanation of their existence. To relate the existence of Kirkwood gaps with Arnol'd diffusion, we also state a conjecture on its existence for a typical ϵ-perturbation of the product of the pendulum and the rotator. Namely, we predict that a positive conditional measure of initial conditions concentrated in the main resonance exhibits Arnol’d diffusion on time scales −lnϵϵ2.","lang":"eng"}],"page":"2315-2403","year":"2016","_id":"8497","publication_identifier":{"issn":["1435-9855"]},"intvolume":"        18","date_published":"2016-09-19T00:00:00Z","type":"journal_article","oa_version":"None","citation":{"ieee":"J. Féjoz, M. Guàrdia, V. Kaloshin, and P. Roldán, “Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem,” <i>Journal of the European Mathematical Society</i>, vol. 18, no. 10. European Mathematical Society Publishing House, pp. 2315–2403, 2016.","apa":"Féjoz, J., Guàrdia, M., Kaloshin, V., &#38; Roldán, P. (2016). Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem. <i>Journal of the European Mathematical Society</i>. European Mathematical Society Publishing House. <a href=\"https://doi.org/10.4171/jems/642\">https://doi.org/10.4171/jems/642</a>","mla":"Féjoz, Jacques, et al. “Kirkwood Gaps and Diffusion along Mean Motion Resonances in the Restricted Planar Three-Body Problem.” <i>Journal of the European Mathematical Society</i>, vol. 18, no. 10, European Mathematical Society Publishing House, 2016, pp. 2315–403, doi:<a href=\"https://doi.org/10.4171/jems/642\">10.4171/jems/642</a>.","ama":"Féjoz J, Guàrdia M, Kaloshin V, Roldán P. Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem. <i>Journal of the European Mathematical Society</i>. 2016;18(10):2315-2403. doi:<a href=\"https://doi.org/10.4171/jems/642\">10.4171/jems/642</a>","ista":"Féjoz J, Guàrdia M, Kaloshin V, Roldán P. 2016. Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem. Journal of the European Mathematical Society. 18(10), 2315–2403.","short":"J. Féjoz, M. Guàrdia, V. Kaloshin, P. Roldán, Journal of the European Mathematical Society 18 (2016) 2315–2403.","chicago":"Féjoz, Jacques, Marcel Guàrdia, Vadim Kaloshin, and Pablo Roldán. “Kirkwood Gaps and Diffusion along Mean Motion Resonances in the Restricted Planar Three-Body Problem.” <i>Journal of the European Mathematical Society</i>. European Mathematical Society Publishing House, 2016. <a href=\"https://doi.org/10.4171/jems/642\">https://doi.org/10.4171/jems/642</a>."},"issue":"10","article_type":"original","volume":18,"language":[{"iso":"eng"}],"publisher":"European Mathematical Society Publishing House","month":"09","date_created":"2020-09-18T10:46:31Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","fulldoi":"https://doi.org/10.4171/jems/642"},{"fulldoi":"https://doi.org/10.4171/jems/499","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"02","publisher":"European Mathematical Society Publishing House","date_created":"2020-09-18T10:46:50Z","volume":17,"language":[{"iso":"eng"}],"issue":"1","article_type":"original","citation":{"ista":"Guardia M, Kaloshin V. 2015. Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation. Journal of the European Mathematical Society. 17(1), 71–149.","apa":"Guardia, M., &#38; Kaloshin, V. (2015). Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation. <i>Journal of the European Mathematical Society</i>. European Mathematical Society Publishing House. <a href=\"https://doi.org/10.4171/jems/499\">https://doi.org/10.4171/jems/499</a>","mla":"Guardia, Marcel, and Vadim Kaloshin. “Growth of Sobolev Norms in the Cubic Defocusing Nonlinear Schrödinger Equation.” <i>Journal of the European Mathematical Society</i>, vol. 17, no. 1, European Mathematical Society Publishing House, 2015, pp. 71–149, doi:<a href=\"https://doi.org/10.4171/jems/499\">10.4171/jems/499</a>.","ama":"Guardia M, Kaloshin V. Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation. <i>Journal of the European Mathematical Society</i>. 2015;17(1):71-149. doi:<a href=\"https://doi.org/10.4171/jems/499\">10.4171/jems/499</a>","ieee":"M. Guardia and V. Kaloshin, “Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation,” <i>Journal of the European Mathematical Society</i>, vol. 17, no. 1. European Mathematical Society Publishing House, pp. 71–149, 2015.","short":"M. Guardia, V. Kaloshin, Journal of the European Mathematical Society 17 (2015) 71–149.","chicago":"Guardia, Marcel, and Vadim Kaloshin. “Growth of Sobolev Norms in the Cubic Defocusing Nonlinear Schrödinger Equation.” <i>Journal of the European Mathematical Society</i>. European Mathematical Society Publishing House, 2015. <a href=\"https://doi.org/10.4171/jems/499\">https://doi.org/10.4171/jems/499</a>."},"oa_version":"None","intvolume":"        17","type":"journal_article","date_published":"2015-02-05T00:00:00Z","publication_identifier":{"issn":["1435-9855"]},"_id":"8499","year":"2015","status":"public","abstract":[{"lang":"eng","text":"We consider the cubic defocusing nonlinear Schrödinger equation in the two dimensional torus. Fix s>1. Recently Colliander, Keel, Staffilani, Tao and Takaoka proved the existence of solutions with s-Sobolev norm growing in time.\r\n\r\nWe establish the existence of solutions with polynomial time estimates. More exactly, there is c>0 such that for any K≫1 we find a solution u and a time T such that ∥u(T)∥Hs≥K∥u(0)∥Hs. Moreover, the time T satisfies the polynomial bound 0<T<Kc."}],"page":"71-149","title":"Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation","publication":"Journal of the European Mathematical Society","author":[{"full_name":"Guardia, Marcel","last_name":"Guardia","first_name":"Marcel"},{"first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","last_name":"Kaloshin"}],"date_updated":"2021-01-12T08:19:41Z","doi":"10.4171/jems/499","extern":"1","publication_status":"published","article_processing_charge":"No","day":"05"},{"OA_place":"repository","status":"public","doi":"10.4171/jems/180","scopus_import":"1","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.0707.3188","open_access":"1"}],"OA_type":"green","month":"12","volume":11,"external_id":{"arxiv":["0707.3188"]},"language":[{"iso":"eng"}],"intvolume":"        11","date_published":"2009-12-23T00:00:00Z","type":"journal_article","oa_version":"Preprint","year":"2009","_id":"22059","publication_identifier":{"eissn":["1435-9863"],"issn":["1435-9855"]},"publication":"Journal of the European Mathematical Society","author":[{"full_name":"Killip, Rowan","last_name":"Killip","first_name":"Rowan"},{"first_name":"Terence","full_name":"Tao, Terence","last_name":"Tao"},{"last_name":"Visan","full_name":"Visan, Monica","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"}],"title":"The cubic nonlinear Schrödinger equation in two dimensions with radial data","abstract":[{"text":"We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iut​ +Δu=±∣u∣ ^2 u for large spherically symmetric L 2/x (R^2) initial data; in the focusing case we require, of course, that the mass is strictly less than that of the ground state. As a consequence, we deduce that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time.\r\n\r\nWe also establish some partial results towards the analogous claims in other dimensions and without the assumption of spherical symmetry.","lang":"eng"}],"page":"1203-1258","mathsc":["35Q55"],"date_updated":"2026-06-29T10:38:29Z","arxiv":1,"publication_status":"published","day":"23","article_processing_charge":"No","extern":"1","fulldoi":"https://doi.org/10.4171/jems/180","publisher":"European Mathematical Society Press","date_created":"2026-06-19T08:06:10Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"6","article_type":"original","oa":1,"citation":{"ama":"Killip R, Tao T, Vişan M. The cubic nonlinear Schrödinger equation in two dimensions with radial data. <i>Journal of the European Mathematical Society</i>. 2009;11(6):1203-1258. doi:<a href=\"https://doi.org/10.4171/jems/180\">10.4171/jems/180</a>","mla":"Killip, Rowan, et al. “The Cubic Nonlinear Schrödinger Equation in Two Dimensions with Radial Data.” <i>Journal of the European Mathematical Society</i>, vol. 11, no. 6, European Mathematical Society Press, 2009, pp. 1203–58, doi:<a href=\"https://doi.org/10.4171/jems/180\">10.4171/jems/180</a>.","apa":"Killip, R., Tao, T., &#38; Vişan, M. (2009). The cubic nonlinear Schrödinger equation in two dimensions with radial data. <i>Journal of the European Mathematical Society</i>. European Mathematical Society Press. <a href=\"https://doi.org/10.4171/jems/180\">https://doi.org/10.4171/jems/180</a>","ista":"Killip R, Tao T, Vişan M. 2009. The cubic nonlinear Schrödinger equation in two dimensions with radial data. Journal of the European Mathematical Society. 11(6), 1203–1258.","ieee":"R. Killip, T. Tao, and M. Vişan, “The cubic nonlinear Schrödinger equation in two dimensions with radial data,” <i>Journal of the European Mathematical Society</i>, vol. 11, no. 6. European Mathematical Society Press, pp. 1203–1258, 2009.","short":"R. Killip, T. Tao, M. Vişan, Journal of the European Mathematical Society 11 (2009) 1203–1258.","chicago":"Killip, Rowan, Terence Tao, and Monica Vişan. “The Cubic Nonlinear Schrödinger Equation in Two Dimensions with Radial Data.” <i>Journal of the European Mathematical Society</i>. European Mathematical Society Press, 2009. <a href=\"https://doi.org/10.4171/jems/180\">https://doi.org/10.4171/jems/180</a>."},"das_tickbox":"1"},{"article_processing_charge":"No","day":"23","publication_status":"published","extern":"1","arxiv":1,"date_updated":"2026-07-01T12:57:57Z","author":[{"first_name":"Rowan","full_name":"Killip, Rowan","last_name":"Killip"},{"last_name":"Tao","full_name":"Tao, Terence","first_name":"Terence"},{"full_name":"Visan, Monica","last_name":"Visan","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","first_name":"Monica"}],"publication":"Journal of the European Mathematical Society","title":"The cubic nonlinear Schrödinger equation in two dimensions with radial data","page":"1203-1258","abstract":[{"lang":"eng","text":"We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iu \r\nt\r\n​\r\n +Δu=±∣u∣ \r\n2\r\n u for large spherically symmetric L \r\nx\r\n2\r\n​\r\n (R \r\n2\r\n ) initial data; in the focusing case we require, of course, that the mass is strictly less than that of the ground state. As a consequence, we deduce that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time.\r\n\r\nWe also establish some partial results towards the analogous claims in other dimensions and without the assumption of spherical symmetry."}],"_id":"22090","year":"2009","publication_identifier":{"issn":["1435-9855"],"eissn":["1435-9863"]},"oa":1,"das_tickbox":"1","citation":{"chicago":"Killip, Rowan, Terence Tao, and Monica Vişan. “The Cubic Nonlinear Schrödinger Equation in Two Dimensions with Radial Data.” <i>Journal of the European Mathematical Society</i>. European Mathematical Society Press, 2009. <a href=\"https://doi.org/10.4171/jems/180\">https://doi.org/10.4171/jems/180</a>.","short":"R. Killip, T. Tao, M. Vişan, Journal of the European Mathematical Society 11 (2009) 1203–1258.","ieee":"R. Killip, T. Tao, and M. Vişan, “The cubic nonlinear Schrödinger equation in two dimensions with radial data,” <i>Journal of the European Mathematical Society</i>, vol. 11, no. 6. European Mathematical Society Press, pp. 1203–1258, 2009.","ista":"Killip R, Tao T, Vişan M. 2009. The cubic nonlinear Schrödinger equation in two dimensions with radial data. Journal of the European Mathematical Society. 11(6), 1203–1258.","apa":"Killip, R., Tao, T., &#38; Vişan, M. (2009). The cubic nonlinear Schrödinger equation in two dimensions with radial data. <i>Journal of the European Mathematical Society</i>. European Mathematical Society Press. <a href=\"https://doi.org/10.4171/jems/180\">https://doi.org/10.4171/jems/180</a>","ama":"Killip R, Tao T, Vişan M. The cubic nonlinear Schrödinger equation in two dimensions with radial data. <i>Journal of the European Mathematical Society</i>. 2009;11(6):1203-1258. doi:<a href=\"https://doi.org/10.4171/jems/180\">10.4171/jems/180</a>","mla":"Killip, Rowan, et al. “The Cubic Nonlinear Schrödinger Equation in Two Dimensions with Radial Data.” <i>Journal of the European Mathematical Society</i>, vol. 11, no. 6, European Mathematical Society Press, 2009, pp. 1203–58, doi:<a href=\"https://doi.org/10.4171/jems/180\">10.4171/jems/180</a>."},"article_type":"original","issue":"6","date_created":"2026-06-19T08:49:58Z","publisher":"European Mathematical Society Press","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","fulldoi":"https://doi.org/10.4171/jems/180","scopus_import":"1","doi":"10.4171/jems/180","OA_place":"repository","status":"public","date_published":"2009-12-23T00:00:00Z","type":"journal_article","intvolume":"        11","oa_version":"Preprint","language":[{"iso":"eng"}],"external_id":{"arxiv":["0707.3188"]},"volume":11,"month":"12","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.0707.3188","open_access":"1"}],"OA_type":"green"}]