[{"isi":1,"file_date_updated":"2026-01-05T13:15:44Z","publication_status":"published","abstract":[{"text":"We prove upper and lower bounds on the number of pairs of commuting n x n matrices with integer entries in [-T, T], as T -> . Our work uses Fourier analysis and leads to an analysis of exponential sums involving matrices over finite fields. These are bounded by combining a stratification result of Fouvry and Katz with a new result about the flatness of the commutator Lie bracket.","lang":"eng"}],"arxiv":1,"PlanS_conform":"1","quality_controlled":"1","ddc":["510"],"publisher":"Springer Nature","language":[{"iso":"eng"}],"publication":"Mathematische Annalen","corr_author":"1","date_updated":"2026-07-17T12:01:12Z","file":[{"access_level":"open_access","success":1,"checksum":"1e94da1a67306e03c8e0086518faf4bc","file_name":"2025_MathAnnalen_Browning.pdf","date_updated":"2026-01-05T13:15:44Z","date_created":"2026-01-05T13:15:44Z","file_size":337505,"creator":"dernst","relation":"main_file","file_id":"20950","content_type":"application/pdf"}],"oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","das_tickbox":"0","OA_type":"hybrid","doi":"10.1007/s00208-025-03285-5","date_created":"2025-09-21T22:01:31Z","has_accepted_license":"1","_id":"20367","ec_funded":1,"year":"2025","article_type":"original","supplementarymaterial":"no","month":"10","researchdata_availability":"no","day":"01","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","date_published":"2025-10-01T00:00:00Z","status":"public","volume":393,"department":[{"_id":"TiBr"}],"citation":{"apa":"Browning, T. D., Sawin, W., &#38; Wang, V. (2025). Pairs of commuting integer matrices. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-025-03285-5\">https://doi.org/10.1007/s00208-025-03285-5</a>","ista":"Browning TD, Sawin W, Wang V. 2025. Pairs of commuting integer matrices. Mathematische Annalen. 393, 1863–1880.","chicago":"Browning, Timothy D, Will Sawin, and Victor Wang. “Pairs of Commuting Integer Matrices.” <i>Mathematische Annalen</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00208-025-03285-5\">https://doi.org/10.1007/s00208-025-03285-5</a>.","short":"T.D. Browning, W. Sawin, V. Wang, Mathematische Annalen 393 (2025) 1863–1880.","ieee":"T. D. Browning, W. Sawin, and V. Wang, “Pairs of commuting integer matrices,” <i>Mathematische Annalen</i>, vol. 393. Springer Nature, pp. 1863–1880, 2025.","mla":"Browning, Timothy D., et al. “Pairs of Commuting Integer Matrices.” <i>Mathematische Annalen</i>, vol. 393, Springer Nature, 2025, pp. 1863–1880, doi:<a href=\"https://doi.org/10.1007/s00208-025-03285-5\">10.1007/s00208-025-03285-5</a>.","ama":"Browning TD, Sawin W, Wang V. Pairs of commuting integer matrices. <i>Mathematische Annalen</i>. 2025;393:1863–1880. doi:<a href=\"https://doi.org/10.1007/s00208-025-03285-5\">10.1007/s00208-025-03285-5</a>"},"type":"journal_article","author":[{"last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177"},{"last_name":"Sawin","first_name":"Will","full_name":"Sawin, Will"},{"last_name":"Wang","first_name":"Victor","id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","full_name":"Wang, Victor","orcid":"0000-0002-0704-7026"}],"page":"1863–1880","OA_place":"publisher","project":[{"name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","grant_number":"P36278"},{"grant_number":"101034413","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"external_id":{"arxiv":["2409.01920"],"isi":["001567740200001"]},"publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"title":"Pairs of commuting integer matrices","intvolume":"       393","acknowledgement":"The authors are very grateful to Alina Ostafe, Matthew Satriano and Igor Shparlinski for drawing their attention to this problem and for useful comments, and to Michael Larsen and Peter Sarnak for their helpful correspondence. We also thank the referee for their valuable input. While working on this paper the first author was supported by a FWF grant (DOI 10.55776/P36278), the second author by a Sloan Research Fellowship, and the third author by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413. Open access funding provided by Institute of Science and Technology (IST Austria).","scopus_import":"1","license":"https://creativecommons.org/licenses/by/4.0/","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"}},{"_id":"18705","article_type":"original","supplementarymaterial":"no","year":"2025","das_tickbox":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"has_accepted_license":"1","date_created":"2024-12-22T23:01:48Z","doi":"10.1007/s00208-024-03035-z","OA_type":"hybrid","publication":"Mathematische Annalen","language":[{"iso":"eng"}],"publisher":"Springer Nature","file":[{"date_updated":"2025-04-16T09:38:55Z","success":1,"access_level":"open_access","checksum":"dcf57a8b01332c36e0cf2b0d1aeecb36","file_name":"2025_MathAnnalen_Glas.pdf","date_created":"2025-04-16T09:38:55Z","file_size":650021,"creator":"dernst","file_id":"19579","content_type":"application/pdf","relation":"main_file"}],"date_updated":"2026-08-06T10:33:33Z","corr_author":"1","abstract":[{"text":"Given a non-singular diagonal cubic hypersurface X⊂Pn−1 over Fq(t) with char(Fq)≠3, we show that the number of rational points of height at most |P| is O(|P|3+ε) for n=6 and O(|P|2+ε) for n=4. In fact, if n=4 and char(Fq)>3 we prove that the number of rational points away from any rational line contained in X is bounded by O(|P|3/2+ε). From the result in 6 variables we deduce weak approximation for diagonal cubic hypersurfaces for n≥7 over Fq(t) when char(Fq)>3 and handle Waring's problem for cubes in 7 variables over Fq(t) when char(Fq)≠3. Our results answer a question of Davenport regarding the number of solutions of bounded height to x31+x32+x33=x34+x35+x36 with xi∈Fq[t].","lang":"eng"}],"publication_status":"published","file_date_updated":"2025-04-16T09:38:55Z","isi":1,"quality_controlled":"1","ddc":["510"],"arxiv":1,"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"},"scopus_import":"1","acknowledgement":"Open Access funding enabled and organized by Projekt DEAL.\r\nThe authors would like to thank Tim Browning for suggesting this project. Further they are grateful for his and Damaris Schindler’s helpful comments. We would also like to thank Efthymios Sofos for bringing Davenport’s question to our attention and Keith Matthews for providing us with scanned copies of the original correspondence. Finally we would like to thank the reviewer for helpful comments.","external_id":{"isi":["001376740400001"],"arxiv":["2208.05422"]},"page":"5485-5533","OA_place":"publisher","intvolume":"       391","title":"On a question of Davenport and diagonal cubic forms over Fq(t)","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"volume":391,"author":[{"id":"d6423cba-dc74-11ea-a0a7-ee61689ff5fb","first_name":"Jakob","last_name":"Glas","full_name":"Glas, Jakob"},{"first_name":"Leonhard","last_name":"Hochfilzer","full_name":"Hochfilzer, Leonhard"}],"type":"journal_article","citation":{"chicago":"Glas, Jakob, and Leonhard Hochfilzer. “On a Question of Davenport and Diagonal Cubic Forms over Fq(T).” <i>Mathematische Annalen</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00208-024-03035-z\">https://doi.org/10.1007/s00208-024-03035-z</a>.","short":"J. Glas, L. Hochfilzer, Mathematische Annalen 391 (2025) 5485–5533.","ista":"Glas J, Hochfilzer L. 2025. On a question of Davenport and diagonal cubic forms over Fq(t). Mathematische Annalen. 391, 5485–5533.","apa":"Glas, J., &#38; Hochfilzer, L. (2025). On a question of Davenport and diagonal cubic forms over Fq(t). <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-024-03035-z\">https://doi.org/10.1007/s00208-024-03035-z</a>","ama":"Glas J, Hochfilzer L. On a question of Davenport and diagonal cubic forms over Fq(t). <i>Mathematische Annalen</i>. 2025;391:5485-5533. doi:<a href=\"https://doi.org/10.1007/s00208-024-03035-z\">10.1007/s00208-024-03035-z</a>","mla":"Glas, Jakob, and Leonhard Hochfilzer. “On a Question of Davenport and Diagonal Cubic Forms over Fq(T).” <i>Mathematische Annalen</i>, vol. 391, Springer Nature, 2025, pp. 5485–533, doi:<a href=\"https://doi.org/10.1007/s00208-024-03035-z\">10.1007/s00208-024-03035-z</a>.","ieee":"J. Glas and L. Hochfilzer, “On a question of Davenport and diagonal cubic forms over Fq(t),” <i>Mathematische Annalen</i>, vol. 391. Springer Nature, pp. 5485–5533, 2025."},"department":[{"_id":"TiBr"}],"dataavailabilitystatement":"Data sharing is not applicable to this article as no datasets were generated or analysed\r\nduring the current study.","day":"01","related_material":{"record":[{"id":"18293","relation":"earlier_version","status":"public"}]},"researchdata_availability":"no","month":"04","status":"public","date_published":"2025-04-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version"},{"volume":389,"department":[{"_id":"JaMa"}],"citation":{"short":"A. Volberg, H. Zhang, Mathematische Annalen 389 (2024) 1657–1676.","chicago":"Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.” <i>Mathematische Annalen</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00208-023-02680-0\">https://doi.org/10.1007/s00208-023-02680-0</a>.","ista":"Volberg A, Zhang H. 2024. Noncommutative Bohnenblust–Hille inequalities. Mathematische Annalen. 389, 1657–1676.","apa":"Volberg, A., &#38; Zhang, H. (2024). Noncommutative Bohnenblust–Hille inequalities. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-023-02680-0\">https://doi.org/10.1007/s00208-023-02680-0</a>","ama":"Volberg A, Zhang H. Noncommutative Bohnenblust–Hille inequalities. <i>Mathematische Annalen</i>. 2024;389:1657-1676. doi:<a href=\"https://doi.org/10.1007/s00208-023-02680-0\">10.1007/s00208-023-02680-0</a>","mla":"Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.” <i>Mathematische Annalen</i>, vol. 389, Springer Nature, 2024, pp. 1657–76, doi:<a href=\"https://doi.org/10.1007/s00208-023-02680-0\">10.1007/s00208-023-02680-0</a>.","ieee":"A. Volberg and H. Zhang, “Noncommutative Bohnenblust–Hille inequalities,” <i>Mathematische Annalen</i>, vol. 389. Springer Nature, pp. 1657–1676, 2024."},"author":[{"full_name":"Volberg, Alexander","last_name":"Volberg","first_name":"Alexander"},{"full_name":"Zhang, Haonan","last_name":"Zhang","first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425"}],"type":"journal_article","month":"06","day":"01","oa_version":"Published Version","article_processing_charge":"Yes (in subscription journal)","date_published":"2024-06-01T00:00:00Z","status":"public","acknowledgement":"The research of A.V. is supported by NSF DMS-1900286, DMS-2154402 and by Hausdorff Center for Mathematics. H.Z. is supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. This work is partially supported by NSF DMS-1929284 while both authors were in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Harmonic Analysis and Convexity program.","scopus_import":"1","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"},"page":"1657-1676","project":[{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337"}],"external_id":{"pmid":["38751410"],"arxiv":["2210.14468"],"isi":["001035665500001"]},"publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"title":"Noncommutative Bohnenblust–Hille inequalities","intvolume":"       389","publisher":"Springer Nature","language":[{"iso":"eng"}],"publication":"Mathematische Annalen","corr_author":"1","date_updated":"2025-04-23T07:50:55Z","file":[{"file_name":"2024_MathAnnalen_Volberg.pdf","checksum":"56e67756e4c6c97589a8385e15ea2d2a","access_level":"open_access","success":1,"date_updated":"2024-07-22T09:38:15Z","creator":"dernst","date_created":"2024-07-22T09:38:15Z","file_size":351796,"relation":"main_file","content_type":"application/pdf","file_id":"17299"}],"isi":1,"file_date_updated":"2024-07-22T09:38:15Z","publication_status":"published","abstract":[{"lang":"eng","text":"Bohnenblust–Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow subexponentially in the degree (Defant et al. in Math Ann 374(1):653–680, 2019). Such inequalities have found great applications in learning low-degree Boolean functions (Eskenazis and Ivanisvili in Proceedings of the 54th annual ACM SIGACT symposium on theory of computing, pp 203–207, 2022). Motivated by learning quantum observables, a qubit analogue of Bohnenblust–Hille inequality for Boolean cubes was recently conjectured in Rouzé et al. (Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions, 2022. arXiv preprint arXiv:2209.07279). The conjecture was resolved in Huang et al. (Learning to predict arbitrary quantum processes, 2022. arXiv preprint arXiv:2210.14894). In this paper, we give a new proof of these Bohnenblust–Hille inequalities for qubit system with constants that are dimension-free and of exponential growth in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials. Using similar ideas, we also study learning problems of low degree quantum observables and Bohr’s radius phenomenon on quantum Boolean cubes."}],"arxiv":1,"quality_controlled":"1","ddc":["510"],"_id":"13318","pmid":1,"year":"2024","article_type":"original","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1007/s00208-023-02680-0","date_created":"2023-07-30T22:01:03Z","has_accepted_license":"1"},{"volume":390,"author":[{"full_name":"Agresti, Antonio","orcid":"0000-0002-9573-2962","last_name":"Agresti","first_name":"Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"last_name":"Luongo","first_name":"Eliseo","full_name":"Luongo, Eliseo"}],"type":"journal_article","department":[{"_id":"JuFi"}],"citation":{"ama":"Agresti A, Luongo E. Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions. <i>Mathematische Annalen</i>. 2024;390:2727-2766. doi:<a href=\"https://doi.org/10.1007/s00208-024-02812-0\">10.1007/s00208-024-02812-0</a>","mla":"Agresti, Antonio, and Eliseo Luongo. “Global Well-Posedness and Interior Regularity of 2D Navier-Stokes Equations with Stochastic Boundary Conditions.” <i>Mathematische Annalen</i>, vol. 390, Springer Nature, 2024, pp. 2727–66, doi:<a href=\"https://doi.org/10.1007/s00208-024-02812-0\">10.1007/s00208-024-02812-0</a>.","ieee":"A. Agresti and E. Luongo, “Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions,” <i>Mathematische Annalen</i>, vol. 390. Springer Nature, pp. 2727–2766, 2024.","short":"A. Agresti, E. Luongo, Mathematische Annalen 390 (2024) 2727–2766.","chicago":"Agresti, Antonio, and Eliseo Luongo. “Global Well-Posedness and Interior Regularity of 2D Navier-Stokes Equations with Stochastic Boundary Conditions.” <i>Mathematische Annalen</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00208-024-02812-0\">https://doi.org/10.1007/s00208-024-02812-0</a>.","ista":"Agresti A, Luongo E. 2024. Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions. Mathematische Annalen. 390, 2727–2766.","apa":"Agresti, A., &#38; Luongo, E. (2024). Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-024-02812-0\">https://doi.org/10.1007/s00208-024-02812-0</a>"},"month":"10","day":"01","article_processing_charge":"Yes (via OA deal)","date_published":"2024-10-01T00:00:00Z","status":"public","oa_version":"Published Version","scopus_import":"1","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"},"acknowledgement":"The authors thank Professor Franco Flandoli for useful discussions and valuable insight into the subject. In particular, A.A. would like to thank professor Franco Flandoli for hosting and financially contributing to his research visit at Scuola Normale di Pisa in January 2023, where this work started. E.L. would like to express sincere gratitude to Professor Marco Fuhrman for igniting his interest in this particular field of research. E.L. want to thank Professor Matthias Hieber and Dr. Martin Saal for useful discussions. Finally, the authors thank the anonymous referee for helpful comments which improved the paper from its initial version.Open access funding provided by Scuola Normale Superiore within the CRUI-CARE Agreement. A. Agresti has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 948819).","project":[{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials","call_identifier":"H2020","grant_number":"948819"}],"external_id":{"isi":["001172711400002"],"pmid":["39351582"],"arxiv":["2306.11081"]},"page":"2727-2766","OA_place":"publisher","intvolume":"       390","title":"Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"publication":"Mathematische Annalen","publisher":"Springer Nature","language":[{"iso":"eng"}],"date_updated":"2025-09-04T12:19:59Z","file":[{"date_updated":"2025-01-09T08:23:36Z","checksum":"d55cac8bddea09a97f06612825c4f229","file_name":"2024_MathAnnalen_Agresti.pdf","access_level":"open_access","success":1,"creator":"dernst","date_created":"2025-01-09T08:23:36Z","file_size":661557,"content_type":"application/pdf","file_id":"18790","relation":"main_file"}],"file_date_updated":"2025-01-09T08:23:36Z","isi":1,"abstract":[{"text":"The paper is devoted to the analysis of the global well-posedness and the interior regularity of the 2D Navier–Stokes equations with inhomogeneous stochastic boundary conditions. The noise, white in time and coloured in space, can be interpreted as the physical law describing the driving mechanism on the atmosphere–ocean interface, i.e. as a balance of the shear stress of the ocean and the horizontal wind force.","lang":"eng"}],"publication_status":"published","quality_controlled":"1","ddc":["510"],"arxiv":1,"_id":"15098","ec_funded":1,"article_type":"original","pmid":1,"year":"2024","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"has_accepted_license":"1","date_created":"2024-03-10T23:00:54Z","OA_type":"hybrid","doi":"10.1007/s00208-024-02812-0"},{"author":[{"first_name":"Dante","id":"6A459894-5FDD-11E9-AF35-BB24E6697425","last_name":"Bonolis","full_name":"Bonolis, Dante"},{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning"},{"full_name":"Huang, Zhizhong","id":"21f1b52f-2fd1-11eb-a347-a4cdb9b18a51","first_name":"Zhizhong","last_name":"Huang"}],"type":"journal_article","citation":{"ama":"Bonolis D, Browning TD, Huang Z. Density of rational points on some quadric bundle threefolds. <i>Mathematische Annalen</i>. 2024;390:4123-4207. doi:<a href=\"https://doi.org/10.1007/s00208-024-02854-4\">10.1007/s00208-024-02854-4</a>","ieee":"D. Bonolis, T. D. Browning, and Z. Huang, “Density of rational points on some quadric bundle threefolds,” <i>Mathematische Annalen</i>, vol. 390. Springer Nature, pp. 4123–4207, 2024.","mla":"Bonolis, Dante, et al. “Density of Rational Points on Some Quadric Bundle Threefolds.” <i>Mathematische Annalen</i>, vol. 390, Springer Nature, 2024, pp. 4123–207, doi:<a href=\"https://doi.org/10.1007/s00208-024-02854-4\">10.1007/s00208-024-02854-4</a>.","short":"D. Bonolis, T.D. Browning, Z. Huang, Mathematische Annalen 390 (2024) 4123–4207.","chicago":"Bonolis, Dante, Timothy D Browning, and Zhizhong Huang. “Density of Rational Points on Some Quadric Bundle Threefolds.” <i>Mathematische Annalen</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00208-024-02854-4\">https://doi.org/10.1007/s00208-024-02854-4</a>.","apa":"Bonolis, D., Browning, T. D., &#38; Huang, Z. (2024). Density of rational points on some quadric bundle threefolds. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-024-02854-4\">https://doi.org/10.1007/s00208-024-02854-4</a>","ista":"Bonolis D, Browning TD, Huang Z. 2024. Density of rational points on some quadric bundle threefolds. Mathematische Annalen. 390, 4123–4207."},"department":[{"_id":"TiBr"}],"volume":390,"date_published":"2024-11-01T00:00:00Z","status":"public","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","day":"01","month":"11","researchdata_availability":"no","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"},"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).The authors are grateful to Florian Wilsch for useful comments. While working on this paper the authors were supported by FWF grant P 32428.","intvolume":"       390","publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"title":"Density of rational points on some quadric bundle threefolds","external_id":{"isi":["001204670500001"],"arxiv":["2204.09322"]},"project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","name":"New frontiers of the Manin conjecture","call_identifier":"FWF","grant_number":"P32428"}],"page":"4123-4207","OA_place":"publisher","file":[{"date_updated":"2025-01-09T09:08:14Z","checksum":"5dd51531deb1e4760c38c3c0c7d5aedc","file_name":"2024_MathAnnalen_Bonolis.pdf","access_level":"open_access","success":1,"content_type":"application/pdf","file_id":"18796","relation":"main_file","creator":"dernst","date_created":"2025-01-09T09:08:14Z","file_size":1019116}],"date_updated":"2026-07-29T09:56:42Z","corr_author":"1","publication":"Mathematische Annalen","language":[{"iso":"eng"}],"publisher":"Springer Nature","quality_controlled":"1","ddc":["510"],"arxiv":1,"abstract":[{"lang":"eng","text":"We prove the Manin–Peyre conjecture for the number of rational points of bounded height outside of a thin subset on a family of Fano threefolds of bidegree (1, 2)."}],"publication_status":"published","isi":1,"file_date_updated":"2025-01-09T09:08:14Z","supplementarymaterial":"no","article_type":"original","year":"2024","_id":"15337","has_accepted_license":"1","date_created":"2024-04-21T22:00:53Z","doi":"10.1007/s00208-024-02854-4","OA_type":"hybrid","das_tickbox":"0","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1},{"date_updated":"2025-07-10T11:51:45Z","publisher":"Springer Nature","language":[{"iso":"eng"}],"publication":"Mathematische Annalen","arxiv":1,"quality_controlled":"1","abstract":[{"lang":"eng","text":"Fix a non-square integer 𝑘≠0. We show that the number of curves 𝐸𝐵:𝑦^2=𝑥^3+𝑘𝐵^2 containing an integral point, where B ranges over positive integers less than N, is bounded by ≪𝑘𝑁(log𝑁)−1/2+𝜖. In particular, this implies that the number of positive integers 𝐵≤𝑁 such that −3𝑘𝐵^2 is the discriminant of an elliptic curve over 𝑄 is o(N). The proof involves a discriminant-lowering procedure on integral binary cubic forms."}],"publication_status":"published","year":"2023","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2203.11366","open_access":"1"}],"article_type":"original","_id":"19487","doi":"10.1007/s00208-023-02578-x","OA_type":"green","date_created":"2025-04-05T10:50:37Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"S. Chan, “Integral points on cubic twists of Mordell curves,” <i>Mathematische Annalen</i>, vol. 388, no. 3. Springer Nature, pp. 2275–2288, 2023.","mla":"Chan, Stephanie. “Integral Points on Cubic Twists of Mordell Curves.” <i>Mathematische Annalen</i>, vol. 388, no. 3, Springer Nature, 2023, pp. 2275–88, doi:<a href=\"https://doi.org/10.1007/s00208-023-02578-x\">10.1007/s00208-023-02578-x</a>.","ama":"Chan S. Integral points on cubic twists of Mordell curves. <i>Mathematische Annalen</i>. 2023;388(3):2275-2288. doi:<a href=\"https://doi.org/10.1007/s00208-023-02578-x\">10.1007/s00208-023-02578-x</a>","apa":"Chan, S. (2023). Integral points on cubic twists of Mordell curves. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-023-02578-x\">https://doi.org/10.1007/s00208-023-02578-x</a>","ista":"Chan S. 2023. Integral points on cubic twists of Mordell curves. Mathematische Annalen. 388(3), 2275–2288.","short":"S. Chan, Mathematische Annalen 388 (2023) 2275–2288.","chicago":"Chan, Stephanie. “Integral Points on Cubic Twists of Mordell Curves.” <i>Mathematische Annalen</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00208-023-02578-x\">https://doi.org/10.1007/s00208-023-02578-x</a>."},"type":"journal_article","author":[{"last_name":"Chan","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","first_name":"Yik Tung","full_name":"Chan, Yik Tung","orcid":"0000-0001-8467-4106"}],"volume":388,"oa_version":"Preprint","article_processing_charge":"No","status":"public","date_published":"2023-02-07T00:00:00Z","month":"02","day":"07","scopus_import":"1","issue":"3","title":"Integral points on cubic twists of Mordell curves","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"intvolume":"       388","OA_place":"repository","page":"2275-2288","extern":"1","external_id":{"arxiv":["2203.11366"]}},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"has_accepted_license":"1","date_created":"2022-01-02T23:01:35Z","doi":"10.1007/s00208-021-02331-2","ec_funded":1,"_id":"10588","article_type":"original","keyword":["quasi curvature-dimension condition","sub-riemannian geometry","Sobolev-to-Lipschitz property","Varadhan short-time asymptotics"],"year":"2022","publication_status":"published","abstract":[{"text":"We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds.","lang":"eng"}],"isi":1,"file_date_updated":"2022-01-03T11:08:31Z","quality_controlled":"1","ddc":["510"],"arxiv":1,"publication":"Mathematische Annalen","language":[{"iso":"eng"}],"publisher":"Springer Nature","file":[{"relation":"main_file","content_type":"application/pdf","file_id":"10596","creator":"alisjak","date_created":"2022-01-03T11:08:31Z","file_size":410090,"file_name":"2021_MathAnn_DelloSchiavo.pdf","checksum":"2593abbf195e38efa93b6006b1e90eb1","success":1,"access_level":"open_access","date_updated":"2022-01-03T11:08:31Z"}],"corr_author":"1","date_updated":"2025-04-14T07:27:46Z","external_id":{"arxiv":["2110.05137"],"isi":["000734150200001"]},"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"page":"1815-1832","intvolume":"       384","title":"Sobolev-to-Lipschitz property on QCD- spaces and applications","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"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"},"scopus_import":"1","acknowledgement":"The authors are grateful to Dr. Bang-Xian Han for helpful discussions on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino Antonelli for reading a preliminary version of this work and for their valuable comments and suggestions. Finally, they wish to express their gratitude to two anonymous Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S. gratefully acknowledges funding of his position by the Austrian Science Fund (FWF) grant F65, and by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number 17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium.","day":"01","month":"12","status":"public","date_published":"2022-12-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","volume":384,"type":"journal_article","author":[{"first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo"},{"full_name":"Suzuki, Kohei","first_name":"Kohei","last_name":"Suzuki"}],"citation":{"ama":"Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and applications. <i>Mathematische Annalen</i>. 2022;384:1815-1832. doi:<a href=\"https://doi.org/10.1007/s00208-021-02331-2\">10.1007/s00208-021-02331-2</a>","ieee":"L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces and applications,” <i>Mathematische Annalen</i>, vol. 384. Springer Nature, pp. 1815–1832, 2022.","mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” <i>Mathematische Annalen</i>, vol. 384, Springer Nature, 2022, pp. 1815–32, doi:<a href=\"https://doi.org/10.1007/s00208-021-02331-2\">10.1007/s00208-021-02331-2</a>.","short":"L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832.","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” <i>Mathematische Annalen</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00208-021-02331-2\">https://doi.org/10.1007/s00208-021-02331-2</a>.","apa":"Dello Schiavo, L., &#38; Suzuki, K. (2022). Sobolev-to-Lipschitz property on QCD- spaces and applications. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-021-02331-2\">https://doi.org/10.1007/s00208-021-02331-2</a>","ista":"Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 384, 1815–1832."},"department":[{"_id":"JaMa"}]},{"volume":379,"citation":{"ista":"Chen X, Zinger A. 2021. WDVV-type relations for disk Gromov–Witten invariants in dimension 6. Mathematische Annalen. 379(3–4), 1231–1313.","apa":"Chen, X., &#38; Zinger, A. (2021). WDVV-type relations for disk Gromov–Witten invariants in dimension 6. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-020-02130-1\">https://doi.org/10.1007/s00208-020-02130-1</a>","chicago":"Chen, Xujia, and Aleksey Zinger. “WDVV-Type Relations for Disk Gromov–Witten Invariants in Dimension 6.” <i>Mathematische Annalen</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00208-020-02130-1\">https://doi.org/10.1007/s00208-020-02130-1</a>.","short":"X. Chen, A. Zinger, Mathematische Annalen 379 (2021) 1231–1313.","mla":"Chen, Xujia, and Aleksey Zinger. “WDVV-Type Relations for Disk Gromov–Witten Invariants in Dimension 6.” <i>Mathematische Annalen</i>, vol. 379, no. 3–4, Springer Nature, 2021, pp. 1231–313, doi:<a href=\"https://doi.org/10.1007/s00208-020-02130-1\">10.1007/s00208-020-02130-1</a>.","ieee":"X. Chen and A. Zinger, “WDVV-type relations for disk Gromov–Witten invariants in dimension 6,” <i>Mathematische Annalen</i>, vol. 379, no. 3–4. Springer Nature, pp. 1231–1313, 2021.","ama":"Chen X, Zinger A. WDVV-type relations for disk Gromov–Witten invariants in dimension 6. <i>Mathematische Annalen</i>. 2021;379(3-4):1231-1313. doi:<a href=\"https://doi.org/10.1007/s00208-020-02130-1\">10.1007/s00208-020-02130-1</a>"},"type":"journal_article","author":[{"full_name":"Chen, Xujia","last_name":"Chen","id":"968ad14a-fd86-11ee-a420-ea29715511a3","first_name":"Xujia"},{"full_name":"Zinger, Aleksey","first_name":"Aleksey","last_name":"Zinger"}],"day":"25","month":"01","oa_version":"Preprint","date_published":"2021-01-25T00:00:00Z","status":"public","article_processing_charge":"No","issue":"3-4","scopus_import":"1","OA_place":"repository","page":"1231-1313","external_id":{"arxiv":["1904.04254"]},"extern":"1","publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"title":"WDVV-type relations for disk Gromov–Witten invariants in dimension 6","intvolume":"       379","language":[{"iso":"eng"}],"publisher":"Springer Nature","publication":"Mathematische Annalen","date_updated":"2025-11-10T15:11:29Z","abstract":[{"lang":"eng","text":"The first author’s previous work established Solomon’s WDVV-type relations for Welschinger’s invariant curve counts in real symplectic fourfolds by lifting geometric relations over possibly unorientable morphisms. We apply her framework to obtain WDVV-style relations for the disk invariants of real symplectic sixfolds with some symmetry, in particular confirming Alcolado’s prediction for P^3 and extending it to other spaces. These relations reduce the computation of Welschinger’s invariants of many real symplectic sixfolds to invariants in small degrees and provide lower bounds for counts of real rational curves with positive-dimensional insertions in some cases. In the case of P^3, our lower bounds fit perfectly with Kollár’s vanishing results."}],"publication_status":"published","arxiv":1,"quality_controlled":"1","_id":"20619","year":"2021","article_type":"original","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1904.04254"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1007/s00208-020-02130-1","OA_type":"green","date_created":"2025-11-10T08:41:40Z"},{"year":"2014","article_type":"original","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1203.4886"}],"_id":"22031","doi":"10.1007/s00208-013-0960-z","OA_type":"green","date_created":"2026-06-19T07:42:09Z","oa":1,"das_tickbox":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-06-22T11:16:03Z","language":[{"iso":"eng"}],"publisher":"Springer Nature","publication":"Mathematische Annalen","arxiv":1,"quality_controlled":"1","publication_status":"published","abstract":[{"text":"We analyze the blowup behaviour of solutions to the focusing nonlinear Klein–Gordon equation in spatial dimensions d>=2. We obtain upper bounds on the blowup rate, both globally in space and in light cones. The results are sharp in the conformal and sub-conformal cases. The argument relies on Lyapunov functionals derived from the dilation identity. We also prove that the critical Sobolev norm diverges near the blowup time.","lang":"eng"}],"scopus_import":"1","issue":"1-2","title":"Blowup behaviour for the nonlinear Klein-Gordon equation","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"intvolume":"       358","page":"289-350","OA_place":"repository","external_id":{"arxiv":["1203.4886"]},"extern":"1","citation":{"ieee":"R. Killip, B. Stovall, and M. Vişan, “Blowup behaviour for the nonlinear Klein-Gordon equation,” <i>Mathematische Annalen</i>, vol. 358, no. 1–2. Springer Nature, pp. 289–350, 2014.","mla":"Killip, Rowan, et al. “Blowup Behaviour for the Nonlinear Klein-Gordon Equation.” <i>Mathematische Annalen</i>, vol. 358, no. 1–2, Springer Nature, 2014, pp. 289–350, doi:<a href=\"https://doi.org/10.1007/s00208-013-0960-z\">10.1007/s00208-013-0960-z</a>.","ama":"Killip R, Stovall B, Vişan M. Blowup behaviour for the nonlinear Klein-Gordon equation. <i>Mathematische Annalen</i>. 2014;358(1-2):289-350. doi:<a href=\"https://doi.org/10.1007/s00208-013-0960-z\">10.1007/s00208-013-0960-z</a>","apa":"Killip, R., Stovall, B., &#38; Vişan, M. (2014). Blowup behaviour for the nonlinear Klein-Gordon equation. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-013-0960-z\">https://doi.org/10.1007/s00208-013-0960-z</a>","ista":"Killip R, Stovall B, Vişan M. 2014. Blowup behaviour for the nonlinear Klein-Gordon equation. Mathematische Annalen. 358(1–2), 289–350.","short":"R. Killip, B. Stovall, M. Vişan, Mathematische Annalen 358 (2014) 289–350.","chicago":"Killip, Rowan, Betsy Stovall, and Monica Vişan. “Blowup Behaviour for the Nonlinear Klein-Gordon Equation.” <i>Mathematische Annalen</i>. Springer Nature, 2014. <a href=\"https://doi.org/10.1007/s00208-013-0960-z\">https://doi.org/10.1007/s00208-013-0960-z</a>."},"author":[{"full_name":"Killip, Rowan","first_name":"Rowan","last_name":"Killip"},{"full_name":"Stovall, Betsy","first_name":"Betsy","last_name":"Stovall"},{"full_name":"Visan, Monica","last_name":"Visan","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","first_name":"Monica"}],"type":"journal_article","volume":358,"oa_version":"Preprint","status":"public","date_published":"2014-02-01T00:00:00Z","article_processing_charge":"No","day":"01","month":"02"}]