[{"external_id":{"arxiv":["2408.16848"]},"month":"08","title":"Anomalous multi-gap topological phases in periodically driven quantum  rotors","type":"preprint","status":"public","publication_status":"draft","OA_type":"green","date_created":"2025-03-20T07:48:23Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2024-08-29T00:00:00Z","OA_place":"repository","publication":"arXiv","_id":"19425","day":"29","related_material":{"record":[{"status":"public","id":"19393","relation":"dissertation_contains"},{"id":"21009","status":"public","relation":"later_version"}]},"oa":1,"language":[{"iso":"eng"}],"author":[{"full_name":"Karle, Volker","orcid":"0000-0002-6963-0129","first_name":"Volker","id":"D7C012AE-D7ED-11E9-95E8-1EC5E5697425","last_name":"Karle"},{"full_name":"Lemeshko, Mikhail","orcid":"0000-0002-6990-7802","first_name":"Mikhail","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","last_name":"Lemeshko"},{"first_name":"Adrien","last_name":"Bouhon","full_name":"Bouhon, Adrien"},{"full_name":"Slager, Robert-Jan","first_name":"Robert-Jan","last_name":"Slager"},{"last_name":"Ünal","first_name":"F. Nur","full_name":"Ünal, F. Nur"}],"date_updated":"2026-07-29T08:59:31Z","fulldoi":"https://doi.org/10.48550/arXiv.2408.16848","oa_version":"Preprint","ec_funded":1,"article_number":"2408.16848","project":[{"grant_number":"801770","_id":"2688CF98-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Angulon: physics and applications of a new quasiparticle"}],"department":[{"_id":"MiLe"}],"article_processing_charge":"No","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2408.16848","open_access":"1"}],"citation":{"ieee":"V. Karle, M. Lemeshko, A. Bouhon, R.-J. Slager, and F. N. Ünal, “Anomalous multi-gap topological phases in periodically driven quantum  rotors,” <i>arXiv</i>. .","apa":"Karle, V., Lemeshko, M., Bouhon, A., Slager, R.-J., &#38; Ünal, F. N. (n.d.). Anomalous multi-gap topological phases in periodically driven quantum  rotors. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2408.16848\">https://doi.org/10.48550/arXiv.2408.16848</a>","ama":"Karle V, Lemeshko M, Bouhon A, Slager R-J, Ünal FN. Anomalous multi-gap topological phases in periodically driven quantum  rotors. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2408.16848\">10.48550/arXiv.2408.16848</a>","ista":"Karle V, Lemeshko M, Bouhon A, Slager R-J, Ünal FN. Anomalous multi-gap topological phases in periodically driven quantum  rotors. arXiv, 2408.16848.","chicago":"Karle, Volker, Mikhail Lemeshko, Adrien Bouhon, Robert-Jan Slager, and F. Nur Ünal. “Anomalous Multi-Gap Topological Phases in Periodically Driven Quantum  Rotors.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2408.16848\">https://doi.org/10.48550/arXiv.2408.16848</a>.","short":"V. Karle, M. Lemeshko, A. Bouhon, R.-J. Slager, F.N. Ünal, ArXiv (n.d.).","mla":"Karle, Volker, et al. “Anomalous Multi-Gap Topological Phases in Periodically Driven Quantum  Rotors.” <i>ArXiv</i>, 2408.16848, doi:<a href=\"https://doi.org/10.48550/arXiv.2408.16848\">10.48550/arXiv.2408.16848</a>."},"arxiv":1,"abstract":[{"lang":"eng","text":"We demonstrate that periodically driven quantum rotors provide a promising and broadly applicable platform to implement multi-gap topological phases, where groups of bands can acquire topological invariants due to non-Abelian braiding of band degeneracies. By adiabatically varying the periodic kicks to the rotor we find nodal-line braiding, which causes sign flips of topological charges of band nodes and can prevent them from annihilating, indicated by non-zero values of the %non-Abelian patch Euler class. In particular, we report\r\non the emergence of an anomalous Dirac string phase arising in the strongly driven regime, a truly out-of-equilibrium phase of the quantum rotor. This phase emanates from braiding processes involving all (quasienergy) gaps and manifests itself with edge states at zero angular momentum. Our results reveal direct applications in state-of-the-art experiments of quantum rotors, such as linear molecules driven by periodic far-off-resonant laser pulses or artificial\r\nquantum rotors in optical lattices, whose extensive versatility offers precise modification and observation of novel non-Abelian topological properties. "}],"year":"2024","acknowledgement":"We thank G. M. Koutentakis, S. Wimberger, J. G. E. Harris, T. Enss and A. Ghazaryan for fruitful discussions. M.L. acknowledges support by the European Research Council (ERC) Starting Grant No. 801770 (ANGULON). R.-J. S. acknowledges funding from a EPSRC ERC underwrite grant EP/X025829/1, a EPSRC New Investigator Award grant EP/W00187X/1, as well as Trinity College, Cambridge. F.N.U. acknowledges support from the Marie ¨Sk lodowska-Curie programme of the European Commission [Grant No. 893915], Simons Investigator Award\r\n[Grant No. 511029] and Trinity College Cambridge.","doi":"10.48550/arXiv.2408.16848"},{"language":[{"iso":"eng"}],"supplementarymaterial":"no","author":[{"full_name":"Wang, Victor","orcid":"0000-0002-0704-7026","first_name":"Victor","last_name":"Wang","id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9"},{"full_name":"Xu, Max Wenqiang","last_name":"Xu","first_name":"Max Wenqiang"}],"date_updated":"2026-07-29T09:57:59Z","oa":1,"ec_funded":1,"file":[{"content_type":"application/pdf","file_id":"17446","file_name":"Paucity_phenomena_for_polynomial_products__Wang_Xu_ (7).pdf","access_level":"open_access","date_created":"2024-08-20T08:36:32Z","date_updated":"2024-08-20T08:36:32Z","checksum":"ae386a4031856efac23c7cdcb53b559b","file_size":331775,"creator":"vwang","relation":"main_file","success":1}],"publication_identifier":{"issn":["0024-6093"],"eissn":["1469-2120"]},"isi":1,"fulldoi":"https://doi.org/10.1112/blms.13095","oa_version":"Submitted Version","researchdata_availability":"no","issue":"8","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2211.02908"}],"article_processing_charge":"No","project":[{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"article_type":"original","volume":56,"department":[{"_id":"TiBr"}],"acknowledgement":"We thank Oleksiy Klurman, Ilya Shkredov, and Igor Shparlinski for helpful comments on earlier versions of the paper, and thank Yotam Hendel for providing a reference for Lemma 2.1. We also thank the anonymous referee for their generous corrections and comments. The first author has received funding from the European Union's Horizon 2020 Research and Innovation Program under the Marie Skłodowska-Curie Grant Agreement Number: 101034413. The second author is partially supported by the Cuthbert C. Hurd Graduate Fellowship in the Mathematical Sciences, Stanford.","abstract":[{"lang":"eng","text":"Let  P(x)∈Z[x] be a polynomial with at least two distinct complex roots. We prove that the number of solutions  (x1,…,xk,y1,…,yk)∈[N]2k to the equation\r\n∏1≤i≤kP(xi)=∏1≤j≤kP(yj)≠0\r\n(for any  k≥1 ) is asymptotically  k!Nk  as  N→+∞. This solves a question first proposed and studied by Najnudel. The result can also be interpreted as saying that all even moments of random partial sums  1N√∑n≤Nf(P(n)) match standard complex Gaussian moments as  N→+∞\r\n , where  f is the Steinhaus random multiplicative function."}],"year":"2024","scopus_import":"1","arxiv":1,"ddc":["512"],"doi":"10.1112/blms.13095","citation":{"chicago":"Wang, Victor, and Max Wenqiang Xu. “Paucity Phenomena for Polynomial Products.” <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society, 2024. <a href=\"https://doi.org/10.1112/blms.13095\">https://doi.org/10.1112/blms.13095</a>.","mla":"Wang, Victor, and Max Wenqiang Xu. “Paucity Phenomena for Polynomial Products.” <i>Bulletin of the London Mathematical Society</i>, vol. 56, no. 8, London Mathematical Society, 2024, pp. 2718–26, doi:<a href=\"https://doi.org/10.1112/blms.13095\">10.1112/blms.13095</a>.","short":"V. Wang, M.W. Xu, Bulletin of the London Mathematical Society 56 (2024) 2718–2726.","ieee":"V. Wang and M. W. Xu, “Paucity phenomena for polynomial products,” <i>Bulletin of the London Mathematical Society</i>, vol. 56, no. 8. London Mathematical Society, pp. 2718–2726, 2024.","ama":"Wang V, Xu MW. Paucity phenomena for polynomial products. <i>Bulletin of the London Mathematical Society</i>. 2024;56(8):2718-2726. doi:<a href=\"https://doi.org/10.1112/blms.13095\">10.1112/blms.13095</a>","ista":"Wang V, Xu MW. 2024. Paucity phenomena for polynomial products. Bulletin of the London Mathematical Society. 56(8), 2718–2726.","apa":"Wang, V., &#38; Xu, M. W. (2024). Paucity phenomena for polynomial products. <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/blms.13095\">https://doi.org/10.1112/blms.13095</a>"},"external_id":{"arxiv":["2211.02908"],"isi":["001235729900001"]},"has_accepted_license":"1","intvolume":"        56","type":"journal_article","file_date_updated":"2024-08-20T08:36:32Z","das_tickbox":"0","title":"Paucity phenomena for polynomial products","status":"public","month":"08","quality_controlled":"1","date_published":"2024-08-01T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2024-06-09T22:01:03Z","publisher":"London Mathematical Society","publication_status":"published","day":"01","page":"2718-2726","_id":"17127","publication":"Bulletin of the London Mathematical Society"},{"day":"01","page":"2859-2912","OA_place":"publisher","publication":"Journal of the Institute of Mathematics of Jussieu","_id":"15338","OA_type":"hybrid","date_created":"2024-04-21T22:00:53Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2024-11-01T00:00:00Z","publication_status":"published","publisher":"Cambridge University Press","title":"Generalised quadratic forms over totally real number fields","file_date_updated":"2025-01-09T08:56:33Z","das_tickbox":"0","type":"journal_article","status":"public","quality_controlled":"1","month":"11","has_accepted_license":"1","external_id":{"arxiv":["2212.11038"],"isi":["001200337400001"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"        23","scopus_import":"1","arxiv":1,"abstract":[{"lang":"eng","text":"We introduce a new class of generalised quadratic forms over totally real number fields, which is rich enough to capture the arithmetic of arbitrary systems of quadrics over the rational numbers. We explore this connection through a version of the Hardy–Littlewood circle method over number fields."}],"acknowledgement":"The authors are grateful to Jayce Getz for asking questions that set this project in motion and to the anonymous referee for useful comments. T.B. was supported by a FWF grant (DOI 10.55776/P32428) and by a grant from the Institute for Advanced Study School of Mathematics. L.B.P. was partially supported by NSF DMS-2200470 and DMS-1652173, and thanks the Hausdorff Centre for Mathematics for hosting research visits.","year":"2024","doi":"10.1017/S1474748024000161","ddc":["510"],"citation":{"ieee":"T. D. Browning, L. B. Pierce, and D. Schindler, “Generalised quadratic forms over totally real number fields,” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 23, no. 6. Cambridge University Press, pp. 2859–2912, 2024.","ama":"Browning TD, Pierce LB, Schindler D. Generalised quadratic forms over totally real number fields. <i>Journal of the Institute of Mathematics of Jussieu</i>. 2024;23(6):2859-2912. doi:<a href=\"https://doi.org/10.1017/S1474748024000161\">10.1017/S1474748024000161</a>","ista":"Browning TD, Pierce LB, Schindler D. 2024. Generalised quadratic forms over totally real number fields. Journal of the Institute of Mathematics of Jussieu. 23(6), 2859–2912.","apa":"Browning, T. D., Pierce, L. B., &#38; Schindler, D. (2024). Generalised quadratic forms over totally real number fields. <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/S1474748024000161\">https://doi.org/10.1017/S1474748024000161</a>","chicago":"Browning, Timothy D, Lillian B. Pierce, and Damaris Schindler. “Generalised Quadratic Forms over Totally Real Number Fields.” <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press, 2024. <a href=\"https://doi.org/10.1017/S1474748024000161\">https://doi.org/10.1017/S1474748024000161</a>.","mla":"Browning, Timothy D., et al. “Generalised Quadratic Forms over Totally Real Number Fields.” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 23, no. 6, Cambridge University Press, 2024, pp. 2859–912, doi:<a href=\"https://doi.org/10.1017/S1474748024000161\">10.1017/S1474748024000161</a>.","short":"T.D. Browning, L.B. Pierce, D. Schindler, Journal of the Institute of Mathematics of Jussieu 23 (2024) 2859–2912."},"issue":"6","article_processing_charge":"Yes (via OA deal)","article_type":"original","volume":23,"project":[{"grant_number":"P32428","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"New frontiers of the Manin conjecture"}],"department":[{"_id":"TiBr"}],"file":[{"content_type":"application/pdf","file_name":"2024_JournInstMathJussieu_Browning.pdf","file_id":"18793","date_updated":"2025-01-09T08:56:33Z","date_created":"2025-01-09T08:56:33Z","creator":"dernst","checksum":"b300541d581a71d92314df5ae8c4cc09","access_level":"open_access","file_size":690974,"relation":"main_file","success":1}],"publication_identifier":{"issn":["1474-7480"],"eissn":["1475-3030"]},"isi":1,"researchdata_availability":"no","fulldoi":"https://doi.org/10.1017/S1474748024000161","corr_author":"1","oa_version":"Published Version","language":[{"iso":"eng"}],"date_updated":"2026-07-29T09:57:08Z","author":[{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pierce","first_name":"Lillian B.","full_name":"Pierce, Lillian B."},{"last_name":"Schindler","first_name":"Damaris","full_name":"Schindler, Damaris"}],"supplementarymaterial":"no","oa":1},{"project":[{"call_identifier":"FWF","name":"New frontiers of the Manin conjecture","grant_number":"P32428","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425"}],"volume":390,"article_type":"original","department":[{"_id":"TiBr"}],"article_processing_charge":"Yes (via OA deal)","citation":{"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.","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>","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>","ista":"Bonolis D, Browning TD, Huang Z. 2024. Density of rational points on some quadric bundle threefolds. Mathematische Annalen. 390, 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>.","short":"D. Bonolis, T.D. Browning, Z. Huang, Mathematische Annalen 390 (2024) 4123–4207.","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>."},"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.","year":"2024","abstract":[{"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).","lang":"eng"}],"arxiv":1,"ddc":["510"],"doi":"10.1007/s00208-024-02854-4","oa":1,"language":[{"iso":"eng"}],"supplementarymaterial":"no","author":[{"full_name":"Bonolis, Dante","id":"6A459894-5FDD-11E9-AF35-BB24E6697425","last_name":"Bonolis","first_name":"Dante"},{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","first_name":"Timothy D"},{"full_name":"Huang, Zhizhong","last_name":"Huang","id":"21f1b52f-2fd1-11eb-a347-a4cdb9b18a51","first_name":"Zhizhong"}],"date_updated":"2026-07-29T09:56:42Z","fulldoi":"https://doi.org/10.1007/s00208-024-02854-4","researchdata_availability":"no","corr_author":"1","oa_version":"Published Version","file":[{"success":1,"relation":"main_file","date_updated":"2025-01-09T09:08:14Z","date_created":"2025-01-09T09:08:14Z","access_level":"open_access","file_size":1019116,"creator":"dernst","checksum":"5dd51531deb1e4760c38c3c0c7d5aedc","content_type":"application/pdf","file_name":"2024_MathAnnalen_Bonolis.pdf","file_id":"18796"}],"isi":1,"publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"publisher":"Springer Nature","publication_status":"published","OA_type":"hybrid","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2024-11-01T00:00:00Z","date_created":"2024-04-21T22:00:53Z","OA_place":"publisher","_id":"15337","publication":"Mathematische Annalen","day":"01","page":"4123-4207","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"       390","external_id":{"isi":["001204670500001"],"arxiv":["2204.09322"]},"has_accepted_license":"1","month":"11","quality_controlled":"1","das_tickbox":"0","type":"journal_article","file_date_updated":"2025-01-09T09:08:14Z","title":"Density of rational points on some quadric bundle threefolds","status":"public"},{"fulldoi":"https://doi.org/10.1093/qmath/haae044","researchdata_availability":"no","corr_author":"1","oa_version":"Published Version","isi":1,"publication_identifier":{"eissn":["1464-3847"],"issn":["0033-5606"]},"file":[{"relation":"main_file","success":1,"content_type":"application/pdf","file_id":"18931","file_name":"2024_QuarterlyJourMath_Elsholtz.pdf","date_created":"2025-01-28T07:03:51Z","access_level":"open_access","date_updated":"2025-01-28T07:03:51Z","file_size":424645,"creator":"dernst","checksum":"1a06e052761d3f1e873463d6f529dd82"}],"PlanS_conform":"1","oa":1,"date_updated":"2026-07-29T09:58:28Z","author":[{"last_name":"Elsholtz","first_name":"Christian","full_name":"Elsholtz, Christian"},{"orcid":"0009-0004-5360-0074","full_name":"Wurzinger, Lena","first_name":"Lena","id":"50c57d72-32a8-11ee-aeea-d652094d2ccd","last_name":"Wurzinger"}],"supplementarymaterial":"no","language":[{"iso":"eng"}],"citation":{"ama":"Elsholtz C, Wurzinger L. Sumsets in the set of squares. <i>The Quarterly Journal of Mathematics</i>. 2024;75(4):1243-1254. doi:<a href=\"https://doi.org/10.1093/qmath/haae044\">10.1093/qmath/haae044</a>","ista":"Elsholtz C, Wurzinger L. 2024. Sumsets in the set of squares. The Quarterly Journal of Mathematics. 75(4), 1243–1254.","apa":"Elsholtz, C., &#38; Wurzinger, L. (2024). Sumsets in the set of squares. <i>The Quarterly Journal of Mathematics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/qmath/haae044\">https://doi.org/10.1093/qmath/haae044</a>","ieee":"C. Elsholtz and L. Wurzinger, “Sumsets in the set of squares,” <i>The Quarterly Journal of Mathematics</i>, vol. 75, no. 4. Oxford University Press, pp. 1243–1254, 2024.","mla":"Elsholtz, Christian, and Lena Wurzinger. “Sumsets in the Set of Squares.” <i>The Quarterly Journal of Mathematics</i>, vol. 75, no. 4, Oxford University Press, 2024, pp. 1243–54, doi:<a href=\"https://doi.org/10.1093/qmath/haae044\">10.1093/qmath/haae044</a>.","short":"C. Elsholtz, L. Wurzinger, The Quarterly Journal of Mathematics 75 (2024) 1243–1254.","chicago":"Elsholtz, Christian, and Lena Wurzinger. “Sumsets in the Set of Squares.” <i>The Quarterly Journal of Mathematics</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/qmath/haae044\">https://doi.org/10.1093/qmath/haae044</a>."},"doi":"10.1093/qmath/haae044","ddc":["510"],"scopus_import":"1","year":"2024","acknowledgement":"This manuscript grew out of the second author’s MSc Thesis at Graz University of Technology [34]. C. Elsholtz is supported by a joint FWF-ANR project ArithRand, grant numbers FWF I 4945-N and ANR-20-CE91-0006. Both authors would like to thank Igor Shparlinski for drawing our attention to related character sum estimates. Furthermore, we would like to thank the referee for a careful reading of the paper.","abstract":[{"lang":"eng","text":"We study sumsets 𝒜 + ℬ in the set of squares 𝒮 (and, more generally, in the set of kth powers 𝒮k, where k ≥2 is an integer). It is known by a result of Gyarmati that 𝒜 + ℬ ⊂ 𝒮k ∩[1,N] implies that min(|𝒜|,|ℬ|) =Ok(logN). Here, we study how the upper bound on |ℬ| decreases, when the size of |𝒜| increases (or vice versa). In particular, if |𝒜| ≥ Ck1m m(logN)1m , then |ℬ| = Ok(m2logN), for sufficiently large N, a positive integer m and an explicit constant C > 0. For example, with m ∼ loglogN this gives: If |𝒜| ≥ CkloglogN,then |ℬ| = Ok(logN(loglogN)2)."}],"department":[{"_id":"TiBr"}],"volume":75,"article_type":"original","article_processing_charge":"Yes (via OA deal)","issue":"4","month":"12","quality_controlled":"1","status":"public","title":"Sumsets in the set of squares","type":"journal_article","file_date_updated":"2025-01-28T07:03:51Z","das_tickbox":"0","intvolume":"        75","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","external_id":{"isi":["001304396600001"]},"publication":"The Quarterly Journal of Mathematics","_id":"18930","OA_place":"publisher","page":"1243-1254","day":"01","publication_status":"published","publisher":"Oxford University Press","date_created":"2025-01-28T06:55:31Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2024-12-01T00:00:00Z","OA_type":"hybrid"},{"intvolume":"       261","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","external_id":{"arxiv":["2305.15493"],"isi":["001220725000001"]},"quality_controlled":"1","month":"08","status":"public","type":"journal_article","file_date_updated":"2025-01-09T09:00:02Z","das_tickbox":"0","title":"Square-free values of random polynomials","publisher":"Elsevier","publication_status":"published","date_published":"2024-08-01T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2024-04-14T22:01:00Z","OA_type":"hybrid","_id":"15312","publication":"Journal of Number Theory","OA_place":"publisher","day":"01","page":"220-240","oa":1,"supplementarymaterial":"no","date_updated":"2026-07-29T09:55:38Z","author":[{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D"},{"first_name":"Igor E.","last_name":"Shparlinski","full_name":"Shparlinski, Igor E."}],"language":[{"iso":"eng"}],"corr_author":"1","fulldoi":"https://doi.org/10.1016/j.jnt.2024.02.013","oa_version":"Published Version","researchdata_availability":"no","isi":1,"publication_identifier":{"issn":["0022-314X"]},"file":[{"file_name":"2024_JourNumberTheory_Browning.pdf","file_id":"18794","content_type":"application/pdf","file_size":394850,"checksum":"614032802febde0aa8e904e9a8ef99ab","creator":"dernst","access_level":"open_access","date_updated":"2025-01-09T09:00:02Z","date_created":"2025-01-09T09:00:02Z","relation":"main_file","success":1}],"department":[{"_id":"TiBr"}],"article_type":"original","volume":261,"article_processing_charge":"No","citation":{"chicago":"Browning, Timothy D, and Igor E. Shparlinski. “Square-Free Values of Random Polynomials.” <i>Journal of Number Theory</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jnt.2024.02.013\">https://doi.org/10.1016/j.jnt.2024.02.013</a>.","mla":"Browning, Timothy D., and Igor E. Shparlinski. “Square-Free Values of Random Polynomials.” <i>Journal of Number Theory</i>, vol. 261, Elsevier, 2024, pp. 220–40, doi:<a href=\"https://doi.org/10.1016/j.jnt.2024.02.013\">10.1016/j.jnt.2024.02.013</a>.","short":"T.D. Browning, I.E. Shparlinski, Journal of Number Theory 261 (2024) 220–240.","ieee":"T. D. Browning and I. E. Shparlinski, “Square-free values of random polynomials,” <i>Journal of Number Theory</i>, vol. 261. Elsevier, pp. 220–240, 2024.","ama":"Browning TD, Shparlinski IE. Square-free values of random polynomials. <i>Journal of Number Theory</i>. 2024;261:220-240. doi:<a href=\"https://doi.org/10.1016/j.jnt.2024.02.013\">10.1016/j.jnt.2024.02.013</a>","ista":"Browning TD, Shparlinski IE. 2024. Square-free values of random polynomials. Journal of Number Theory. 261, 220–240.","apa":"Browning, T. D., &#38; Shparlinski, I. E. (2024). Square-free values of random polynomials. <i>Journal of Number Theory</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jnt.2024.02.013\">https://doi.org/10.1016/j.jnt.2024.02.013</a>"},"ddc":["510"],"doi":"10.1016/j.jnt.2024.02.013","abstract":[{"lang":"eng","text":"The question of whether or not a given integral polynomial takes infinitely many square-free values has only been addressed unconditionally for polynomials of degree at most 3. We address this question, on average, for polynomials of arbitrary degree."}],"year":"2024","arxiv":1,"scopus_import":"1"},{"corr_author":"1","fulldoi":"https://doi.org/10.1093/imrn/rnae066","researchdata_availability":"no","oa_version":"Published Version","file":[{"date_created":"2025-02-18T07:56:36Z","date_updated":"2025-02-18T07:56:36Z","creator":"dernst","access_level":"open_access","checksum":"b625b8adf018d2a97591813c1fc17b96","file_size":205750,"content_type":"application/pdf","file_id":"19052","file_name":"2024_IMRN_Browning.pdf","success":1,"relation":"main_file"}],"publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"isi":1,"oa":1,"language":[{"iso":"eng"}],"supplementarymaterial":"no","author":[{"full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning"}],"date_updated":"2026-07-29T09:59:57Z","citation":{"chicago":"Browning, Timothy D. “The Polynomial Sieve and Equal Sums of like Polynomials.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/imrn/rnae066\">https://doi.org/10.1093/imrn/rnae066</a>.","short":"T.D. Browning, International Mathematics Research Notices 2024 (2024) 10165–10168.","mla":"Browning, Timothy D. “The Polynomial Sieve and Equal Sums of like Polynomials.” <i>International Mathematics Research Notices</i>, vol. 2024, no. 13, Oxford University Press, 2024, pp. 10165–68, doi:<a href=\"https://doi.org/10.1093/imrn/rnae066\">10.1093/imrn/rnae066</a>.","ieee":"T. D. Browning, “The polynomial sieve and equal sums of like polynomials,” <i>International Mathematics Research Notices</i>, vol. 2024, no. 13. Oxford University Press, pp. 10165–10168, 2024.","apa":"Browning, T. D. (2024). The polynomial sieve and equal sums of like polynomials. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnae066\">https://doi.org/10.1093/imrn/rnae066</a>","ista":"Browning TD. 2024. The polynomial sieve and equal sums of like polynomials. International Mathematics Research Notices. 2024(13), 10165–10168.","ama":"Browning TD. The polynomial sieve and equal sums of like polynomials. <i>International Mathematics Research Notices</i>. 2024;2024(13):10165-10168. doi:<a href=\"https://doi.org/10.1093/imrn/rnae066\">10.1093/imrn/rnae066</a>"},"year":"2024","abstract":[{"text":"This paper corrects an error in an earlier work of the author.","lang":"eng"}],"scopus_import":"1","doi":"10.1093/imrn/rnae066","ddc":["510"],"article_type":"original","volume":2024,"department":[{"_id":"TiBr"}],"issue":"13","article_processing_charge":"Yes (via OA deal)","month":"07","quality_controlled":"1","type":"journal_article","file_date_updated":"2025-02-18T07:56:36Z","das_tickbox":"0","title":"The polynomial sieve and equal sums of like polynomials","status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"      2024","has_accepted_license":"1","external_id":{"isi":["001196957300001"]},"OA_place":"publisher","_id":"19051","publication":"International Mathematics Research Notices","related_material":{"record":[{"status":"public","id":"254","relation":"earlier_version"}]},"day":"01","page":"10165-10168","publisher":"Oxford University Press","publication_status":"published","OA_type":"hybrid","date_published":"2024-07-01T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2025-02-18T07:15:50Z"},{"author":[{"first_name":"Ulrich","last_name":"Derenthal","full_name":"Derenthal, Ulrich"},{"full_name":"Wilsch, Florian Alexander","orcid":"0000-0001-7302-8256","first_name":"Florian Alexander","last_name":"Wilsch","id":"560601DA-8D36-11E9-A136-7AC1E5697425"}],"date_updated":"2026-07-29T10:00:51Z","supplementarymaterial":"no","language":[{"iso":"eng"}],"oa":1,"publication_identifier":{"issn":["1474-7480"],"eissn":["1475-3030 "]},"isi":1,"file":[{"success":1,"relation":"main_file","file_size":592305,"access_level":"open_access","creator":"dernst","checksum":"c4698ea12cfe10ef2c6c79880290c7ac","date_updated":"2024-06-03T08:33:29Z","date_created":"2024-06-03T08:33:29Z","file_id":"17102","file_name":"2024_JourMathJussieu_Derenthal.pdf","content_type":"application/pdf"}],"corr_author":"1","fulldoi":"https://doi.org/10.1017/S1474748022000482","oa_version":"Published Version","researchdata_availability":"no","article_processing_charge":"Yes (via OA deal)","issue":"3","department":[{"_id":"TiBr"}],"volume":23,"article_type":"original","project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","name":"New frontiers of the Manin conjecture","call_identifier":"FWF"}],"ddc":["510"],"doi":"10.1017/S1474748022000482","scopus_import":"1","arxiv":1,"acknowledgement":"The first author was partly supported by grant DE 1646/4-2 of the Deutsche Forschungsgemeinschaft. The second author was partly supported by FWF grant P 32428-N35 and conducted part of this work as a guest at the Institut de Mathématiques de Jussieu–Paris Rive Gauche invited by Antoine Chambert-Loir and funded by DAAD.","abstract":[{"lang":"eng","text":"In order to study integral points of bounded log-anticanonical height on weak del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a quartic del Pezzo surface of singularity type A1 + A3 and prove an analogue of Manin's conjecture for integral points with respect to its singularities and its lines."}],"year":"2024","citation":{"short":"U. Derenthal, F.A. Wilsch, Journal of the Institute of Mathematics of Jussieu 23 (2024) 1259–1294.","mla":"Derenthal, Ulrich, and Florian Alexander Wilsch. “Integral Points on Singular Del Pezzo Surfaces.” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 23, no. 3, Cambridge University Press, 2024, pp. 1259–94, doi:<a href=\"https://doi.org/10.1017/S1474748022000482\">10.1017/S1474748022000482</a>.","chicago":"Derenthal, Ulrich, and Florian Alexander Wilsch. “Integral Points on Singular Del Pezzo Surfaces.” <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press, 2024. <a href=\"https://doi.org/10.1017/S1474748022000482\">https://doi.org/10.1017/S1474748022000482</a>.","apa":"Derenthal, U., &#38; Wilsch, F. A. (2024). Integral points on singular del Pezzo surfaces. <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/S1474748022000482\">https://doi.org/10.1017/S1474748022000482</a>","ama":"Derenthal U, Wilsch FA. Integral points on singular del Pezzo surfaces. <i>Journal of the Institute of Mathematics of Jussieu</i>. 2024;23(3):1259-1294. doi:<a href=\"https://doi.org/10.1017/S1474748022000482\">10.1017/S1474748022000482</a>","ista":"Derenthal U, Wilsch FA. 2024. Integral points on singular del Pezzo surfaces. Journal of the Institute of Mathematics of Jussieu. 23(3), 1259–1294.","ieee":"U. Derenthal and F. A. Wilsch, “Integral points on singular del Pezzo surfaces,” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 23, no. 3. Cambridge University Press, pp. 1259–1294, 2024."},"has_accepted_license":"1","external_id":{"isi":["000881319200001"],"arxiv":["2109.06778"]},"intvolume":"        23","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"status":"public","title":"Integral points on singular del Pezzo surfaces","das_tickbox":"0","type":"journal_article","file_date_updated":"2024-06-03T08:33:29Z","quality_controlled":"1","month":"05","date_created":"2021-09-15T10:06:48Z","date_published":"2024-05-10T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","publisher":"Cambridge University Press","page":"1259-1294","day":"10","keyword":["Integral points","del Pezzo surface","universal torsor","Manin’s conjecture"],"publication":"Journal of the Institute of Mathematics of Jussieu","_id":"10018"},{"article_processing_charge":"Yes (via OA deal)","issue":"3","department":[{"_id":"TiBr"}],"project":[{"grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"article_type":"original","volume":110,"doi":"10.1112/jlms.12975","ddc":["512"],"arxiv":1,"scopus_import":"1","acknowledgement":"This paper is an important component of the thesis work described in [25]; many of my acknowledgements there apply here as well. I also thank my advisor, Peter Sarnak, for many helpful suggestions and questions on the exposition, references, assumptions, and scope of (various drafts of) the present work. I am also grateful to Trevor Wooley for providing some helpful general comments on special subvarieties and the reference [24]. I thank Tim Browning for inspiring part of the current title of the paper. Finally, thanks are due to the referee for providing many helpful suggestions. This work was partially supported by NSF grant DMS-1802211, and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant AgreementNo. 101034413.","abstract":[{"text":"Let  F be a diagonal cubic form over Z in six variables. From the dual variety in the delta method of Duke–Friedlander–Iwaniec and Heath‐Brown, we unconditionally extract a weighted count of certain special integral zeros of F in regions of diameter X - 8 . Heath‐Brown did the same in four variables, but our analysis differs and captures some novel features. We also put forth an axiomatic framework for more general F.","lang":"eng"}],"year":"2024","citation":{"short":"V. Wang, Journal of the London Mathematical Society 110 (2024).","mla":"Wang, Victor. “Special Cubic Zeros and the Dual Variety.” <i>Journal of the London Mathematical Society</i>, vol. 110, no. 3, e12975, Wiley, 2024, doi:<a href=\"https://doi.org/10.1112/jlms.12975\">10.1112/jlms.12975</a>.","chicago":"Wang, Victor. “Special Cubic Zeros and the Dual Variety.” <i>Journal of the London Mathematical Society</i>. Wiley, 2024. <a href=\"https://doi.org/10.1112/jlms.12975\">https://doi.org/10.1112/jlms.12975</a>.","apa":"Wang, V. (2024). Special cubic zeros and the dual variety. <i>Journal of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/jlms.12975\">https://doi.org/10.1112/jlms.12975</a>","ista":"Wang V. 2024. Special cubic zeros and the dual variety. Journal of the London Mathematical Society. 110(3), e12975.","ama":"Wang V. Special cubic zeros and the dual variety. <i>Journal of the London Mathematical Society</i>. 2024;110(3). doi:<a href=\"https://doi.org/10.1112/jlms.12975\">10.1112/jlms.12975</a>","ieee":"V. Wang, “Special cubic zeros and the dual variety,” <i>Journal of the London Mathematical Society</i>, vol. 110, no. 3. Wiley, 2024."},"date_updated":"2026-07-29T10:02:22Z","author":[{"last_name":"Wang","id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","first_name":"Victor","full_name":"Wang, Victor","orcid":"0000-0002-0704-7026"}],"supplementarymaterial":"no","language":[{"iso":"eng"}],"oa":1,"isi":1,"publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"article_number":"e12975","file":[{"relation":"main_file","success":1,"content_type":"application/pdf","file_name":"2024_JourLondonMathSoc_Wang.pdf","file_id":"17454","access_level":"open_access","file_size":438751,"creator":"dernst","checksum":"90437e19f57520b4d66ca62408f6c81e","date_created":"2024-08-21T06:36:40Z","date_updated":"2024-08-21T06:36:40Z"}],"ec_funded":1,"fulldoi":"https://doi.org/10.1112/jlms.12975","oa_version":"Published Version","corr_author":"1","researchdata_availability":"no","date_created":"2024-08-20T08:41:40Z","date_published":"2024-08-14T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","publisher":"Wiley","day":"14","publication":"Journal of the London Mathematical Society","_id":"17447","has_accepted_license":"1","external_id":{"isi":["001310529600001"],"arxiv":["2108.03396"]},"intvolume":"       110","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"status":"public","title":"Special cubic zeros and the dual variety","das_tickbox":"0","type":"journal_article","file_date_updated":"2024-08-21T06:36:40Z","quality_controlled":"1","month":"08"},{"ec_funded":1,"file":[{"relation":"main_file","success":1,"content_type":"application/pdf","file_name":"2024_Mathematika_Browning.pdf","file_id":"18842","file_size":273006,"access_level":"open_access","creator":"dernst","date_created":"2025-01-13T11:06:25Z","checksum":"0b1518bdc1a901413005c19202cfa497","date_updated":"2025-01-13T11:06:25Z"}],"isi":1,"article_number":"e12269","publication_identifier":{"eissn":["2041-7942"],"issn":["0025-5793"]},"fulldoi":"https://doi.org/10.1112/mtk.12269","oa_version":"Published Version","corr_author":"1","researchdata_availability":"no","language":[{"iso":"eng"}],"supplementarymaterial":"no","date_updated":"2026-07-29T10:01:24Z","author":[{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D"},{"orcid":"0000-0002-0854-0306","full_name":"Verzobio, Matteo","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","last_name":"Verzobio","first_name":"Matteo"}],"oa":1,"year":"2024","abstract":[{"lang":"eng","text":"We investigate strong divisibility sequences and produce lower and upper bounds for the density of integers in the sequence that only have (somewhat) large prime factors. We focus on the special cases of Fibonacci numbers and elliptic divisibility sequences, discussing the limitations of our methods. At the end of the paper, there is an appendix by Sandro Bettin on divisor closed sets that we use to study the density of prime terms that appear in strong divisibility sequences."}],"acknowledgement":"The authors are very grateful to Andrew Granville, Dimitris Koukoulopoulos, Davide Lombardo,Florian Luca, Igor Shparlinski and Joni Teräväinen for useful comments. While working on thispaper, the first author was supported by a FWF Grant (DOI 10.55776/P36278) and the secondauthor was supported by the European Union’s Horizon 2020 research and innovation programunder the Marie Skłodowska-Curie Grant Agreement Number 101034413.","scopus_import":"1","doi":"10.1112/mtk.12269","ddc":["510"],"citation":{"ieee":"T. D. Browning and M. Verzobio, “Strong divisibility sequences and sieve methods,” <i>Mathematika</i>, vol. 70, no. 4. London Mathematical Society, 2024.","ama":"Browning TD, Verzobio M. Strong divisibility sequences and sieve methods. <i>Mathematika</i>. 2024;70(4). doi:<a href=\"https://doi.org/10.1112/mtk.12269\">10.1112/mtk.12269</a>","ista":"Browning TD, Verzobio M. 2024. Strong divisibility sequences and sieve methods. Mathematika. 70(4), e12269.","apa":"Browning, T. D., &#38; Verzobio, M. (2024). Strong divisibility sequences and sieve methods. <i>Mathematika</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/mtk.12269\">https://doi.org/10.1112/mtk.12269</a>","chicago":"Browning, Timothy D, and Matteo Verzobio. “Strong Divisibility Sequences and Sieve Methods.” <i>Mathematika</i>. London Mathematical Society, 2024. <a href=\"https://doi.org/10.1112/mtk.12269\">https://doi.org/10.1112/mtk.12269</a>.","mla":"Browning, Timothy D., and Matteo Verzobio. “Strong Divisibility Sequences and Sieve Methods.” <i>Mathematika</i>, vol. 70, no. 4, e12269, London Mathematical Society, 2024, doi:<a href=\"https://doi.org/10.1112/mtk.12269\">10.1112/mtk.12269</a>.","short":"T.D. Browning, M. Verzobio, Mathematika 70 (2024)."},"issue":"4","article_processing_charge":"Yes (via OA deal)","project":[{"_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","grant_number":"P36278","name":"Rational curves via function field analytic number theory"},{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413"}],"volume":70,"article_type":"original","department":[{"_id":"TiBr"}],"type":"journal_article","das_tickbox":"0","file_date_updated":"2025-01-13T11:06:25Z","title":"Strong divisibility sequences and sieve methods","status":"public","month":"10","quality_controlled":"1","external_id":{"isi":["001273912800001"]},"has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"        70","day":"01","OA_place":"publisher","_id":"17323","publication":"Mathematika","OA_type":"hybrid","date_published":"2024-10-01T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2024-07-28T22:01:08Z","publisher":"London Mathematical Society","publication_status":"published"},{"language":[{"iso":"eng"}],"author":[{"orcid":"0000-0001-8467-4106","full_name":"Chan, Yik Tung","last_name":"Chan","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","first_name":"Yik Tung"}],"date_updated":"2026-07-29T10:03:09Z","supplementarymaterial":"no","oa":1,"file":[{"relation":"main_file","success":1,"file_id":"18829","file_name":"2024_AdvancesMath_Chan.pdf","content_type":"application/pdf","access_level":"open_access","date_created":"2025-01-13T08:54:09Z","date_updated":"2025-01-13T08:54:09Z","file_size":564386,"checksum":"f555742540ad91a3040aeafd68b1fcde","creator":"dernst"}],"publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"article_number":"109946","oa_version":"Published Version","fulldoi":"https://doi.org/10.1016/j.aim.2024.109946","researchdata_availability":"no","corr_author":"1","issue":"11","article_processing_charge":"Yes (via OA deal)","volume":457,"article_type":"original","department":[{"_id":"TiBr"}],"arxiv":1,"scopus_import":"1","year":"2024","abstract":[{"text":" We show that the total number of non-torsion integral points on the elliptic curves ED : y\r\n2 = x3 − D2x, where D ranges over positive squarefree integers less than N, is O(N(log N)\r\n−1/4+ǫ). The proof involves a discriminant-lowering procedure on integral binary quartic forms and an application of Heath-Brown’s method on estimating the average size of the 2-Selmer group of the curves in this family.","lang":"eng"}],"ddc":["510"],"doi":"10.1016/j.aim.2024.109946","citation":{"ieee":"S. Chan, “The average number of integral points on the congruent number curves,” <i>Advances in Mathematics</i>, vol. 457, no. 11. Elsevier, 2024.","apa":"Chan, S. (2024). The average number of integral points on the congruent number curves. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2024.109946\">https://doi.org/10.1016/j.aim.2024.109946</a>","ista":"Chan S. 2024. The average number of integral points on the congruent number curves. Advances in Mathematics. 457(11), 109946.","ama":"Chan S. The average number of integral points on the congruent number curves. <i>Advances in Mathematics</i>. 2024;457(11). doi:<a href=\"https://doi.org/10.1016/j.aim.2024.109946\">10.1016/j.aim.2024.109946</a>","chicago":"Chan, Stephanie. “The Average Number of Integral Points on the Congruent Number Curves.” <i>Advances in Mathematics</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.aim.2024.109946\">https://doi.org/10.1016/j.aim.2024.109946</a>.","short":"S. Chan, Advances in Mathematics 457 (2024).","mla":"Chan, Stephanie. “The Average Number of Integral Points on the Congruent Number Curves.” <i>Advances in Mathematics</i>, vol. 457, no. 11, 109946, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.aim.2024.109946\">10.1016/j.aim.2024.109946</a>."},"has_accepted_license":"1","external_id":{"arxiv":["2112.01615"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"       457","title":"The average number of integral points on the congruent number curves","das_tickbox":"0","type":"journal_article","file_date_updated":"2025-01-13T08:54:09Z","status":"public","quality_controlled":"1","month":"11","OA_type":"hybrid","date_created":"2024-09-15T22:01:39Z","date_published":"2024-11-01T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","publisher":"Elsevier","day":"01","OA_place":"publisher","publication":"Advances in Mathematics","_id":"18064"},{"external_id":{"arxiv":["2306.02718"]},"has_accepted_license":"1","intvolume":"       110","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"status":"public","title":"Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t)","file_date_updated":"2024-10-07T08:51:01Z","das_tickbox":"0","type":"journal_article","quality_controlled":"1","month":"10","date_created":"2024-10-06T22:01:11Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2024-10-01T00:00:00Z","publication_status":"published","publisher":"London Mathematical Society","day":"01","related_material":{"record":[{"relation":"dissertation_contains","id":"18132","status":"public"}]},"publication":"Journal of the London Mathematical Society","_id":"18173","date_updated":"2026-07-29T10:04:55Z","author":[{"full_name":"Glas, Jakob","first_name":"Jakob","id":"d6423cba-dc74-11ea-a0a7-ee61689ff5fb","last_name":"Glas"}],"supplementarymaterial":"no","language":[{"iso":"eng"}],"oa":1,"publication_identifier":{"issn":["0024-6107"],"eissn":["1469-7750"]},"article_number":"e12991","file":[{"relation":"main_file","success":1,"content_type":"application/pdf","file_id":"18181","file_name":"2024_JLondonMathSoc_Glas.pdf","date_updated":"2024-10-07T08:51:01Z","file_size":579601,"date_created":"2024-10-07T08:51:01Z","checksum":"11ebf690363151026ce81f91f2220855","creator":"dernst","access_level":"open_access"}],"fulldoi":"https://doi.org/10.1112/jlms.12991","corr_author":"1","researchdata_availability":"no","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","issue":"4","department":[{"_id":"TiBr"}],"project":[{"name":"Rational curves via function field analytic number theory","grant_number":"P36278","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3"}],"article_type":"original","volume":110,"doi":"10.1112/jlms.12991","ddc":["510"],"scopus_import":"1","arxiv":1,"acknowledgement":"The author would like to thank his supervisor Tim Browning for suggesting this project and many helpful conversations and Pankaj Vishe for useful comments. Moreover, he is grateful to Dante Bonolis and Julian Lyczak for sharing their expertise in exponential sums and geometry. While working on this paper, the author was supported by FWF grant (DOI 10.55776/P36278).","abstract":[{"lang":"eng","text":"Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least 23 over Fq(t), provided char (Fq)>3. Under the same hypotheses, we also verify weak approximation."}],"year":"2024","citation":{"apa":"Glas, J. (2024). Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). <i>Journal of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/jlms.12991\">https://doi.org/10.1112/jlms.12991</a>","ista":"Glas J. 2024. Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). Journal of the London Mathematical Society. 110(4), e12991.","ama":"Glas J. Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). <i>Journal of the London Mathematical Society</i>. 2024;110(4). doi:<a href=\"https://doi.org/10.1112/jlms.12991\">10.1112/jlms.12991</a>","ieee":"J. Glas, “Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t),” <i>Journal of the London Mathematical Society</i>, vol. 110, no. 4. London Mathematical Society, 2024.","short":"J. Glas, Journal of the London Mathematical Society 110 (2024).","mla":"Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric Hypersurfaces over Fq(T).” <i>Journal of the London Mathematical Society</i>, vol. 110, no. 4, e12991, London Mathematical Society, 2024, doi:<a href=\"https://doi.org/10.1112/jlms.12991\">10.1112/jlms.12991</a>.","chicago":"Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric Hypersurfaces over Fq(T).” <i>Journal of the London Mathematical Society</i>. London Mathematical Society, 2024. <a href=\"https://doi.org/10.1112/jlms.12991\">https://doi.org/10.1112/jlms.12991</a>."}},{"department":[{"_id":"TiBr"}],"project":[{"name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","grant_number":"P36278"}],"article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2405.16648"}],"citation":{"ieee":"J. Glas, “Canonical singularities on moduli spaces of rational curves via the  circle method,” <i>arXiv</i>. .","apa":"Glas, J. (n.d.). Canonical singularities on moduli spaces of rational curves via the  circle method. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2405.16648\">https://doi.org/10.48550/arXiv.2405.16648</a>","ista":"Glas J. Canonical singularities on moduli spaces of rational curves via the  circle method. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2405.16648\">10.48550/arXiv.2405.16648</a>.","ama":"Glas J. Canonical singularities on moduli spaces of rational curves via the  circle method. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2405.16648\">10.48550/arXiv.2405.16648</a>","chicago":"Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves via the  Circle Method.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2405.16648\">https://doi.org/10.48550/arXiv.2405.16648</a>.","short":"J. Glas, ArXiv (n.d.).","mla":"Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves via the  Circle Method.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2405.16648\">10.48550/arXiv.2405.16648</a>."},"doi":"10.48550/arXiv.2405.16648","arxiv":1,"year":"2024","abstract":[{"text":"By developing a suitable version of the circle method, we show that the space of degree e rational curves on a smooth hypersurface of degree d has only canonical singularities provided its dimension is sufficiently large with respect to e and d.","lang":"eng"}],"oa":1,"date_updated":"2026-07-29T10:05:58Z","author":[{"full_name":"Glas, Jakob","id":"d6423cba-dc74-11ea-a0a7-ee61689ff5fb","last_name":"Glas","first_name":"Jakob"}],"supplementarymaterial":"no","language":[{"iso":"eng"}],"corr_author":"1","fulldoi":"https://doi.org/10.48550/arXiv.2405.16648","oa_version":"Preprint","researchdata_availability":"no","publication_status":"submitted","date_created":"2024-10-10T13:15:43Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2024-05-26T00:00:00Z","publication":"arXiv","_id":"18295","OA_place":"repository","day":"26","related_material":{"record":[{"relation":"later_version","id":"19013","status":"public"},{"relation":"dissertation_contains","status":"public","id":"18132"}]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"arxiv":["2405.16648"]},"month":"05","status":"public","title":"Canonical singularities on moduli spaces of rational curves via the  circle method","das_tickbox":"0","type":"preprint"},{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"arxiv":["2412.14923"]},"month":"12","status":"public","title":"Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method","type":"preprint","das_tickbox":"0","publication_status":"draft","date_created":"2025-02-07T12:04:11Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2024-12-19T00:00:00Z","publication":"arXiv","_id":"19013","OA_place":"repository","day":"19","related_material":{"record":[{"relation":"earlier_version","id":"18295","status":"public"}]},"oa":1,"date_updated":"2026-07-29T10:05:58Z","author":[{"first_name":"Jakob","id":"d6423cba-dc74-11ea-a0a7-ee61689ff5fb","last_name":"Glas","full_name":"Glas, Jakob"},{"full_name":"Hase-Liu, Matthew ","first_name":"Matthew ","last_name":"Hase-Liu"}],"supplementarymaterial":"no","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.48550/arXiv.2412.14923","corr_author":"1","oa_version":"Preprint","researchdata_availability":"no","department":[{"_id":"TiBr"}],"article_processing_charge":"No","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2412.14923","open_access":"1"}],"citation":{"ista":"Glas J, Hase-Liu M. Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2412.14923\">10.48550/arXiv.2412.14923</a>.","ama":"Glas J, Hase-Liu M. Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2412.14923\">10.48550/arXiv.2412.14923</a>","apa":"Glas, J., &#38; Hase-Liu, M. (n.d.). Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2412.14923\">https://doi.org/10.48550/arXiv.2412.14923</a>","ieee":"J. Glas and M. Hase-Liu, “Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method,” <i>arXiv</i>. .","mla":"Glas, Jakob, and Matthew Hase-Liu. “Terminal Singularities of the Moduli Space of Curves on Low Degree Hypersurfaces and the Circle Method.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2412.14923\">10.48550/arXiv.2412.14923</a>.","short":"J. Glas, M. Hase-Liu, ArXiv (n.d.).","chicago":"Glas, Jakob, and Matthew  Hase-Liu. “Terminal Singularities of the Moduli Space of Curves on Low Degree Hypersurfaces and the Circle Method.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2412.14923\">https://doi.org/10.48550/arXiv.2412.14923</a>."},"doi":"10.48550/arXiv.2412.14923","arxiv":1,"year":"2024","abstract":[{"lang":"eng","text":"We study the singularities of the moduli space of degree e maps from smooth genus g curves to an arbitrary smooth hypersurface of low degree. For e large compared to g, we show that these moduli spaces have at worst terminal singularities. Our main approach is to study the jet schemes of these moduli spaces by developing a suitable form of the circle method."}]},{"publication_status":"draft","OA_type":"green","date_created":"2025-07-23T11:21:52Z","date_published":"2024-09-12T00:00:00Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","OA_place":"repository","publication":"arXiv","_id":"20071","day":"12","keyword":["Farkas lemma","linear programming","extended reals","calculus of inductive constructions"],"related_material":{"link":[{"url":"https://github.com/madvorak/duality/tree/v3.2","relation":"software","description":"full version of all definitions, statement, and proofs"}],"record":[{"relation":"later_version","id":"22607","status":"public"},{"status":"public","id":"21393","relation":"dissertation_contains"}]},"external_id":{"arxiv":["2409.08119"]},"month":"09","title":"Duality theory in linear optimization and its extensions -- formally  verified","type":"preprint","status":"public","department":[{"_id":"GradSch"},{"_id":"VlKo"}],"article_processing_charge":"No","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2409.08119","open_access":"1"}],"citation":{"chicago":"Dvorak, Martin, and Vladimir Kolmogorov. “Duality Theory in Linear Optimization and Its Extensions -- Formally  Verified.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2409.08119\">https://doi.org/10.48550/arXiv.2409.08119</a>.","mla":"Dvorak, Martin, and Vladimir Kolmogorov. “Duality Theory in Linear Optimization and Its Extensions -- Formally  Verified.” <i>ArXiv</i>, 2409.08119, doi:<a href=\"https://doi.org/10.48550/arXiv.2409.08119\">10.48550/arXiv.2409.08119</a>.","short":"M. Dvorak, V. Kolmogorov, ArXiv (n.d.).","ieee":"M. Dvorak and V. Kolmogorov, “Duality theory in linear optimization and its extensions -- formally  verified,” <i>arXiv</i>. .","ama":"Dvorak M, Kolmogorov V. Duality theory in linear optimization and its extensions -- formally  verified. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2409.08119\">10.48550/arXiv.2409.08119</a>","ista":"Dvorak M, Kolmogorov V. Duality theory in linear optimization and its extensions -- formally  verified. arXiv, 2409.08119.","apa":"Dvorak, M., &#38; Kolmogorov, V. (n.d.). Duality theory in linear optimization and its extensions -- formally  verified. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2409.08119\">https://doi.org/10.48550/arXiv.2409.08119</a>"},"arxiv":1,"year":"2024","acknowledgement":"We would like to thank David Bartl and Jasmin Blanchette for frequent consultations. We would also like to express gratitude to Andrew Yang for the proof of Finset.univ sum of zero when not and to Henrik B¨oving for a help with generalization from extended rationals to extended linearly ordered fields. We would also like to acknowledge Antoine Chambert-Loir, Apurva Nakade, Ya¨el Dillies, Richard Copley, Edward van de Meent, Markus Himmel, Mario Carneiro, and Kevin Buzzard.","abstract":[{"text":"Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over linearly ordered fields in Lean 4. Furthermore, we extend duality theory to the case when some coefficients are allowed to take \"infinite values\".","lang":"eng"}],"doi":"10.48550/arXiv.2409.08119","oa":1,"language":[{"iso":"eng"}],"date_updated":"2026-07-29T12:56:51Z","author":[{"last_name":"Dvorak","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","first_name":"Martin","orcid":"0000-0001-5293-214X","full_name":"Dvorak, Martin"},{"full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","first_name":"Vladimir"}],"fulldoi":"https://doi.org/10.48550/arXiv.2409.08119","corr_author":"1","oa_version":"Preprint","article_number":"2409.08119"},{"related_material":{"record":[{"status":"public","id":"14862","relation":"research_data"},{"status":"public","id":"20811","relation":"dissertation_contains"}],"link":[{"url":"https://github.com/Simon-Re/complex-vaccination","relation":"software"}]},"day":"01","page":"1722-1738","_id":"18307","publication":"Evolution: International journal of organic evolution","OA_place":"publisher","date_published":"2024-10-01T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2024-10-13T22:01:50Z","OA_type":"hybrid","publisher":"Oxford University Press","publication_status":"published","status":"public","file_date_updated":"2024-10-21T09:34:50Z","type":"journal_article","title":"Complex vaccination strategies prevent the emergence of vaccine resistance","month":"10","quality_controlled":"1","external_id":{"pmid":["38990788"],"isi":["001286581900001"]},"has_accepted_license":"1","intvolume":"        78","tmp":{"image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"doi":"10.1093/evolut/qpae106","ddc":["570"],"abstract":[{"text":"Vaccination is the most effective tool to control infectious diseases. However, the evolution of vaccine resistance, exemplified by vaccine resistance in SARS-CoV-2, remains a concern. Here, we model complex vaccination strategies against a pathogen with multiple epitopes—molecules targeted by the vaccine. We found that a vaccine targeting one epitope was ineffective in preventing vaccine escape. Vaccine resistance in highly infectious pathogens was prevented by the full-epitope vaccine, that is, one targeting all available epitopes, but only when the rate of pathogen evolution was low. Strikingly, a bet-hedging strategy of random administration of vaccines targeting different epitopes was the most effective in preventing vaccine resistance in pathogens with the low rate of infection and high rate of evolution. Thus, complex vaccination strategies, when biologically feasible, may be preferable to the currently used single-vaccine approaches for long-term control of disease outbreaks, especially when applied to livestock with near 100% vaccination rates.","lang":"eng"}],"year":"2024","acknowledgement":"We thank Raimundo Julian Saona Urmeneta, Maike Morrison, Sergey Kryazhimskiy, Hiroki Ishikawa, Simone Pigolotti, and Shingo Miyauchi for fruitful discussions. We also thank the participants of the FRISBI seminar at ISTA for useful comments.","scopus_import":"1","citation":{"short":"S. Rella, Y.A. Kulikova, A. Minnegalieva, F. Kondrashov, Evolution: International Journal of Organic Evolution 78 (2024) 1722–1738.","mla":"Rella, Simon, et al. “Complex Vaccination Strategies Prevent the Emergence of Vaccine Resistance.” <i>Evolution: International Journal of Organic Evolution</i>, vol. 78, no. 10, Oxford University Press, 2024, pp. 1722–38, doi:<a href=\"https://doi.org/10.1093/evolut/qpae106\">10.1093/evolut/qpae106</a>.","chicago":"Rella, Simon, Yuliya A. Kulikova, Aygul Minnegalieva, and Fyodor Kondrashov. “Complex Vaccination Strategies Prevent the Emergence of Vaccine Resistance.” <i>Evolution: International Journal of Organic Evolution</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/evolut/qpae106\">https://doi.org/10.1093/evolut/qpae106</a>.","apa":"Rella, S., Kulikova, Y. A., Minnegalieva, A., &#38; Kondrashov, F. (2024). Complex vaccination strategies prevent the emergence of vaccine resistance. <i>Evolution: International Journal of Organic Evolution</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/evolut/qpae106\">https://doi.org/10.1093/evolut/qpae106</a>","ista":"Rella S, Kulikova YA, Minnegalieva A, Kondrashov F. 2024. Complex vaccination strategies prevent the emergence of vaccine resistance. Evolution: International journal of organic evolution. 78(10), 1722–1738.","ama":"Rella S, Kulikova YA, Minnegalieva A, Kondrashov F. Complex vaccination strategies prevent the emergence of vaccine resistance. <i>Evolution: International journal of organic evolution</i>. 2024;78(10):1722-1738. doi:<a href=\"https://doi.org/10.1093/evolut/qpae106\">10.1093/evolut/qpae106</a>","ieee":"S. Rella, Y. A. Kulikova, A. Minnegalieva, and F. Kondrashov, “Complex vaccination strategies prevent the emergence of vaccine resistance,” <i>Evolution: International journal of organic evolution</i>, vol. 78, no. 10. Oxford University Press, pp. 1722–1738, 2024."},"article_processing_charge":"Yes (via OA deal)","issue":"10","department":[{"_id":"GaTk"}],"article_type":"original","volume":78,"publication_identifier":{"eissn":["1558-5646"]},"isi":1,"file":[{"relation":"main_file","success":1,"file_id":"18453","file_name":"2024_Evolution_Rella.pdf","content_type":"application/pdf","checksum":"5c6e8475bb88b07d424a5130d5e91e74","creator":"dernst","file_size":29360811,"date_updated":"2024-10-21T09:34:50Z","access_level":"open_access","date_created":"2024-10-21T09:34:50Z"}],"oa_version":"Published Version","fulldoi":"https://doi.org/10.1093/evolut/qpae106","corr_author":"1","author":[{"first_name":"Simon","id":"B4765ACA-AA38-11E9-AC9A-0930E6697425","last_name":"Rella","full_name":"Rella, Simon"},{"full_name":"Kulikova, Yuliya A.","first_name":"Yuliya A.","last_name":"Kulikova"},{"full_name":"Minnegalieva, Aygul","id":"87DF77F0-1D9A-11EA-B6AE-CE443DDC885E","last_name":"Minnegalieva","first_name":"Aygul"},{"full_name":"Kondrashov, Fyodor","orcid":"0000-0001-8243-4694","last_name":"Kondrashov","id":"44FDEF62-F248-11E8-B48F-1D18A9856A87","first_name":"Fyodor"}],"date_updated":"2026-07-29T12:57:48Z","language":[{"iso":"eng"}],"oa":1,"pmid":1},{"publication":"41st International Symposium on Theoretical Aspects of Computer Science","_id":"15168","day":"01","related_material":{"record":[{"id":"22247","status":"public","relation":"later_version"},{"relation":"dissertation_contains","status":"public","id":"20339"}]},"publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","date_created":"2024-03-24T23:00:59Z","date_published":"2024-03-01T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","quality_controlled":"1","month":"03","status":"public","title":"Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs","file_date_updated":"2024-03-25T07:44:30Z","type":"conference","intvolume":"       289","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","external_id":{"arxiv":["2312.12981"],"isi":["001300393400034"]},"citation":{"mla":"Filakovský, Marek, et al. “Hardness of Linearly Ordered 4-Colouring of 3-Colourable 3-Uniform Hypergraphs.” <i>41st International Symposium on Theoretical Aspects of Computer Science</i>, vol. 289, 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.STACS.2024.34\">10.4230/LIPIcs.STACS.2024.34</a>.","short":"M. Filakovský, T.V. Nakajima, J. Opršal, G. Tasinato, U. Wagner, in:, 41st International Symposium on Theoretical Aspects of Computer Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","chicago":"Filakovský, Marek, Tamio Vesa Nakajima, Jakub Opršal, Gianluca Tasinato, and Uli Wagner. “Hardness of Linearly Ordered 4-Colouring of 3-Colourable 3-Uniform Hypergraphs.” In <i>41st International Symposium on Theoretical Aspects of Computer Science</i>, Vol. 289. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.STACS.2024.34\">https://doi.org/10.4230/LIPIcs.STACS.2024.34</a>.","ista":"Filakovský M, Nakajima TV, Opršal J, Tasinato G, Wagner U. 2024. Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs. 41st International Symposium on Theoretical Aspects of Computer Science. STACS: Symposium on Theoretical Aspects of Computer Science, LIPIcs, vol. 289, 34.","ama":"Filakovský M, Nakajima TV, Opršal J, Tasinato G, Wagner U. Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs. In: <i>41st International Symposium on Theoretical Aspects of Computer Science</i>. Vol 289. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.STACS.2024.34\">10.4230/LIPIcs.STACS.2024.34</a>","apa":"Filakovský, M., Nakajima, T. V., Opršal, J., Tasinato, G., &#38; Wagner, U. (2024). Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs. In <i>41st International Symposium on Theoretical Aspects of Computer Science</i> (Vol. 289). Clermont-Ferrand, France: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.STACS.2024.34\">https://doi.org/10.4230/LIPIcs.STACS.2024.34</a>","ieee":"M. Filakovský, T. V. Nakajima, J. Opršal, G. Tasinato, and U. Wagner, “Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs,” in <i>41st International Symposium on Theoretical Aspects of Computer Science</i>, Clermont-Ferrand, France, 2024, vol. 289."},"alternative_title":["LIPIcs"],"ddc":["510"],"doi":"10.4230/LIPIcs.STACS.2024.34","arxiv":1,"scopus_import":"1","year":"2024","acknowledgement":"Marek Filakovský: This research was supported by Charles University (project PRIMUS/\r\n21/SCI/014), the Austrian Science Fund (FWF project P31312-N35), and MSCAfellow5_MUNI\r\n(CZ.02.01.01/00/22_010/0003229). Tamio-Vesa Nakajima: This research was funded by UKRI EP/X024431/1 and by a Clarendon Fund Scholarship. All data is provided in full in the results section of this paper. Jakub Opršal: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 101034413. Uli Wagner: This research was supported by the Austrian Science Fund (FWF project P31312-N35).","abstract":[{"text":"A linearly ordered (LO) k-colouring of a hypergraph is a colouring of its vertices with colours 1, … , k such that each edge contains a unique maximal colour. Deciding whether an input hypergraph admits LO k-colouring with a fixed number of colours is NP-complete (and in the special case of graphs, LO colouring coincides with the usual graph colouring). Here, we investigate the complexity of approximating the \"linearly ordered chromatic number\" of a hypergraph. We prove that the following promise problem is NP-complete: Given a 3-uniform hypergraph, distinguish between the case that it is LO 3-colourable, and the case that it is not even LO 4-colourable. We prove this result by a combination of algebraic, topological, and combinatorial methods, building on and extending a topological approach for studying approximate graph colouring introduced by Krokhin, Opršal, Wrochna, and Živný (2023).","lang":"eng"}],"department":[{"_id":"UlWa"}],"volume":289,"project":[{"_id":"26611F5C-B435-11E9-9278-68D0E5697425","grant_number":"P31312","name":"Algorithms for Embeddings and Homotopy Theory","call_identifier":"FWF"},{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"article_processing_charge":"No","fulldoi":"https://doi.org/10.4230/LIPIcs.STACS.2024.34","corr_author":"1","oa_version":"Published Version","publication_identifier":{"eissn":["1868-8969"],"isbn":["9783959773119"]},"article_number":"34","isi":1,"file":[{"creator":"dernst","date_updated":"2024-03-25T07:44:30Z","date_created":"2024-03-25T07:44:30Z","checksum":"0524d4189fd1ed08989546511343edf3","file_size":927290,"access_level":"open_access","content_type":"application/pdf","file_id":"15175","file_name":"2024_LIPICs_Filakovsky.pdf","success":1,"relation":"main_file"}],"ec_funded":1,"oa":1,"author":[{"first_name":"Marek","last_name":"Filakovský","id":"3E8AF77E-F248-11E8-B48F-1D18A9856A87","full_name":"Filakovský, Marek"},{"first_name":"Tamio Vesa","last_name":"Nakajima","full_name":"Nakajima, Tamio Vesa"},{"orcid":"0000-0003-1245-3456","full_name":"Opršal, Jakub","first_name":"Jakub","last_name":"Opršal","id":"ec596741-c539-11ec-b829-c79322a91242"},{"full_name":"Tasinato, Gianluca","first_name":"Gianluca","id":"0433290C-AF8F-11E9-A4C7-F729E6697425","last_name":"Tasinato"},{"full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2026-07-29T13:13:17Z","language":[{"iso":"eng"}],"conference":{"name":"STACS: Symposium on Theoretical Aspects of Computer Science","location":"Clermont-Ferrand, France","end_date":"2024-03-14","start_date":"2024-03-12"}},{"department":[{"_id":"LaEr"}],"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2309.05488","open_access":"1"}],"article_processing_charge":"No","citation":{"short":"G. Cipolloni, L. Erdös, S.J. Henheik, ArXiv (n.d.).","mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2309.05488\">10.48550/arXiv.2309.05488</a>.","chicago":"Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2309.05488\">https://doi.org/10.48550/arXiv.2309.05488</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Henheik, S. J. (n.d.). Eigenstate thermalisation at the edge for Wigner matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2309.05488\">https://doi.org/10.48550/arXiv.2309.05488</a>","ama":"Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2309.05488\">10.48550/arXiv.2309.05488</a>","ista":"Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2309.05488\">10.48550/arXiv.2309.05488</a>.","ieee":"G. Cipolloni, L. Erdös, and S. J. Henheik, “Eigenstate thermalisation at the edge for Wigner matrices,” <i>arXiv</i>. ."},"doi":"10.48550/arXiv.2309.05488","abstract":[{"lang":"eng","text":"We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices\r\nuniformly in the entire spectrum, in particular near the spectral edges, with a\r\nbound on the fluctuation that is optimal for any observable. This complements\r\nearlier works of Cipolloni et. al. (Comm. Math. Phys. 388, 2021; Forum Math.,\r\nSigma 10, 2022) and Benigni et. al. (Comm. Math. Phys. 391, 2022; arXiv:\r\n2303.11142) that were restricted either to the bulk of the spectrum or to\r\nspecial observables. As a main ingredient, we prove a new multi-resolvent local\r\nlaw that optimally accounts for the edge scaling."}],"acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","year":"2024","arxiv":1,"oa":1,"date_updated":"2026-07-29T13:18:16Z","author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni"},{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","first_name":"Sven Joscha"}],"language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.48550/arXiv.2309.05488","oa_version":"Preprint","corr_author":"1","ec_funded":1,"publication_status":"draft","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_published":"2024-12-17T00:00:00Z","date_created":"2025-04-11T08:19:22Z","_id":"19545","publication":"arXiv","OA_place":"repository","related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"}]},"day":"17","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"arxiv":["2309.05488"]},"month":"12","status":"public","type":"preprint","title":"Eigenstate thermalisation at the edge for Wigner matrices"},{"article_processing_charge":"No","date_created":"2025-04-11T11:43:58Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_published":"2024-10-21T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2409.17297","open_access":"1"}],"department":[{"_id":"LaEr"},{"_id":"RoSe"}],"publication_status":"draft","arxiv":1,"year":"2024","abstract":[{"text":"We introduce a multi-band BCS free energy functional and prove that for a\r\nmulti-band superconductor the effect of inter-band coupling can only increase\r\nthe critical temperature, irrespective of its attractive or repulsive nature\r\nand its strength. Further, for weak coupling and weaker inter-band coupling, we\r\nprove that the dependence of the increase in critical temperature on the\r\ninter-band coupling is (1) linear, if there are two or more equally strongly\r\nsuperconducting bands, or (2) quadratic, if there is only one dominating band.","lang":"eng"}],"doi":"10.48550/arXiv.2409.17297","day":"21","related_material":{"record":[{"relation":"later_version","status":"public","id":"22290"},{"id":"19540","status":"public","relation":"dissertation_contains"}]},"citation":{"ama":"Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2409.17297\">10.48550/arXiv.2409.17297</a>","ista":"Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2409.17297\">10.48550/arXiv.2409.17297</a>.","apa":"Henheik, S. J., Langmann, E., &#38; Lauritsen, A. B. (n.d.). Multi-band superconductors have enhanced critical temperatures. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2409.17297\">https://doi.org/10.48550/arXiv.2409.17297</a>","ieee":"S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors have enhanced critical temperatures,” <i>arXiv</i>. .","mla":"Henheik, Sven Joscha, et al. “Multi-Band Superconductors Have Enhanced Critical Temperatures.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2409.17297\">10.48550/arXiv.2409.17297</a>.","short":"S.J. Henheik, E. Langmann, A.B. Lauritsen, ArXiv (n.d.).","chicago":"Henheik, Sven Joscha, Edwin Langmann, and Asbjørn Bækgaard Lauritsen. “Multi-Band Superconductors Have Enhanced Critical Temperatures.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2409.17297\">https://doi.org/10.48550/arXiv.2409.17297</a>."},"OA_place":"repository","publication":"arXiv","_id":"19550","external_id":{"arxiv":["2409.17297"]},"language":[{"iso":"eng"}],"date_updated":"2026-07-29T13:18:16Z","author":[{"last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha"},{"first_name":"Edwin","last_name":"Langmann","full_name":"Langmann, Edwin"},{"orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"oa":1,"title":"Multi-band superconductors have enhanced critical temperatures","type":"preprint","status":"public","month":"10","fulldoi":"https://doi.org/10.48550/arXiv.2409.17297","oa_version":"Preprint","corr_author":"1"},{"month":"08","quality_controlled":"1","status":"public","title":"Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices","type":"journal_article","file_date_updated":"2025-06-24T13:14:21Z","intvolume":"       287","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","external_id":{"isi":["001325502400001"]},"publication":"Journal of Functional Analysis","_id":"17049","OA_place":"publisher","day":"15","related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"}]},"publication_status":"published","publisher":"Elsevier","date_created":"2024-05-26T22:00:57Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2024-08-15T00:00:00Z","OA_type":"hybrid","oa_version":"Published Version","fulldoi":"https://doi.org/10.1016/j.jfa.2024.110495","corr_author":"1","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"isi":1,"article_number":"110495","ec_funded":1,"file":[{"relation":"main_file","success":1,"content_type":"application/pdf","file_name":"2025_JourFunctionalAnalysis_Cipolloni.pdf","file_id":"19891","date_created":"2025-06-24T13:14:21Z","date_updated":"2025-06-24T13:14:21Z","checksum":"07d3f73e0c56e68eb110851842c22ee0","access_level":"open_access","file_size":1374854,"creator":"dernst"}],"oa":1,"date_updated":"2026-07-29T13:18:17Z","author":[{"orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","first_name":"Sven Joscha"},{"first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"language":[{"iso":"eng"}],"citation":{"ama":"Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>. 2024;287(4). doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">10.1016/j.jfa.2024.110495</a>","ista":"Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. 2024. Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. Journal of Functional Analysis. 287(4), 110495.","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Schröder, D. J. (2024). Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">https://doi.org/10.1016/j.jfa.2024.110495</a>","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and D. J. Schröder, “Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices,” <i>Journal of Functional Analysis</i>, vol. 287, no. 4. Elsevier, 2024.","mla":"Cipolloni, Giorgio, et al. “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>, vol. 287, no. 4, 110495, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">10.1016/j.jfa.2024.110495</a>.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, D.J. Schröder, Journal of Functional Analysis 287 (2024).","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Dominik J Schröder. “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">https://doi.org/10.1016/j.jfa.2024.110495</a>."},"doi":"10.1016/j.jfa.2024.110495","ddc":["510"],"scopus_import":"1","abstract":[{"lang":"eng","text":"We consider large non-Hermitian NxN matrices with an additive independent, identically distributed (i.i.d.) noise for each matrix elements. We show that already a small noise of variance 1/N completely thermalises the bulk singular vectors, in particular they satisfy the strong form of Quantum Unique Ergodicity (QUE) with an optimal speed of convergence. In physics terms, we thus extend the Eigenstate Thermalisation Hypothesis, formulated originally by Deutsch [34] and proven for Wigner matrices in [23], to arbitrary non-Hermitian matrices with an i.i.d. noise. As a consequence we obtain an optimal lower bound on the diagonal overlaps of the corresponding non-Hermitian eigenvectors. This quantity, also known as the (square of the) eigenvalue condition number measuring the sensitivity of the eigenvalue to small perturbations, has notoriously escaped rigorous treatment beyond the explicitly computable Ginibre ensemble apart from the very recent upper bounds given in [7] and [45]. As a key tool, we develop a new systematic decomposition of general observables in random matrix theory that governs the size of products of resolvents with deterministic matrices in between."}],"year":"2024","acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nSupported by the SNSF Ambizione Grant PZ00P2_209089.","department":[{"_id":"LaEr"}],"volume":287,"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"article_type":"original","article_processing_charge":"Yes (via OA deal)","issue":"4"}]