[{"volume":461,"article_processing_charge":"No","doi":"10.1016/j.aim.2024.110055","date_published":"2025-02-01T00:00:00Z","OA_type":"green","language":[{"iso":"eng"}],"publication":"Advances in Mathematics","status":"public","abstract":[{"lang":"eng","text":"The local angle property of the (order-1) Delaunay triangulations of a generic set in R2\r\n asserts that the sum of two angles opposite a common edge is less than π. This paper extends this property to higher order and uses it to generalize two classic properties from order-1 to order-2: (1) among the complete level-2 hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation lexicographically maximizes the sorted angle vector; (2) among the maximal level-2 hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation is the only one that has the local angle property. We also use our method of establishing (2) to give a new short proof of the angle vector optimality for the (order-1) Delaunay triangulation. For order-1, both properties have been instrumental in numerous applications of Delaunay triangulations, and we expect that their generalization will make order-2 Delaunay triangulations more attractive to applications as well."}],"corr_author":"1","oa_version":"Preprint","type":"journal_article","author":[{"orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"full_name":"Garber, Alexey","last_name":"Garber","first_name":"Alexey"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"publisher":"Elsevier","day":"01","isi":1,"project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"date_updated":"2025-04-15T07:16:53Z","intvolume":"       461","year":"2025","arxiv":1,"external_id":{"arxiv":["2310.18238"],"isi":["001370682500001"]},"oa":1,"scopus_import":"1","article_type":"original","acknowledgement":"Work by the first and third authors is partially supported by the European Research Council (ERC), grant no. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant no. I 02979-N35. Work by the second author is partially supported by the Alexander von Humboldt Foundation.","publication_status":"published","month":"02","department":[{"_id":"HeEd"}],"quality_controlled":"1","title":"Order-2 Delaunay triangulations optimize angles","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2310.18238"}],"date_created":"2024-12-08T23:01:54Z","citation":{"ista":"Edelsbrunner H, Garber A, Saghafian M. 2025. Order-2 Delaunay triangulations optimize angles. Advances in Mathematics. 461, 110055.","short":"H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).","apa":"Edelsbrunner, H., Garber, A., &#38; Saghafian, M. (2025). Order-2 Delaunay triangulations optimize angles. <i>Advances in Mathematics</i>. 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Elsevier, 2025.","mla":"Edelsbrunner, Herbert, et al. “Order-2 Delaunay Triangulations Optimize Angles.” <i>Advances in Mathematics</i>, vol. 461, 110055, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.aim.2024.110055\">10.1016/j.aim.2024.110055</a>."},"ec_funded":1,"article_number":"110055","publication_identifier":{"issn":["0001-8708"],"eissn":["1090-2082"]},"OA_place":"repository","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"18626"},{"day":"01","isi":1,"project":[{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"date_updated":"2026-07-16T10:45:31Z","type":"journal_article","publisher":"Elsevier","author":[{"id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","first_name":"Victor","orcid":"0000-0002-0704-7026","full_name":"Wang, Victor","last_name":"Wang"}],"file":[{"checksum":"01f2589b678ba840d6a4066c1d8d7642","date_created":"2025-12-30T08:30:17Z","relation":"main_file","success":1,"content_type":"application/pdf","access_level":"open_access","file_id":"20895","date_updated":"2025-12-30T08:30:17Z","file_name":"2025_AdvMathematics_Wang.pdf","creator":"dernst","file_size":1592341}],"supplementarymaterial":"no","publication":"Advances in Mathematics","status":"public","abstract":[{"lang":"eng","text":"By studying some Clausen-like multiple Dirichlet series, we complete the proof of Manin's conjecture for sufficiently split smooth equivariant compactifications of the translation-dilation group over the rationals. Secondary terms remain elusive in general."}],"corr_author":"1","oa_version":"Published Version","volume":475,"article_processing_charge":"Yes (via OA deal)","doi":"10.1016/j.aim.2025.110341","file_date_updated":"2025-12-30T08:30:17Z","date_published":"2025-07-01T00:00:00Z","language":[{"iso":"eng"}],"OA_type":"hybrid","ec_funded":1,"article_number":"110341","publication_identifier":{"issn":["0001-8708"],"eissn":["1090-2082"]},"OA_place":"publisher","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"19727","department":[{"_id":"TiBr"}],"quality_controlled":"1","title":"Asymptotic growth of translation-dilation orbits","researchdata_availability":"no","date_created":"2025-05-25T22:16:41Z","has_accepted_license":"1","citation":{"ama":"Wang V. Asymptotic growth of translation-dilation orbits. <i>Advances in Mathematics</i>. 2025;475. doi:<a href=\"https://doi.org/10.1016/j.aim.2025.110341\">10.1016/j.aim.2025.110341</a>","apa":"Wang, V. (2025). Asymptotic growth of translation-dilation orbits. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2025.110341\">https://doi.org/10.1016/j.aim.2025.110341</a>","ista":"Wang V. 2025. Asymptotic growth of translation-dilation orbits. Advances in Mathematics. 475, 110341.","short":"V. Wang, Advances in Mathematics 475 (2025).","mla":"Wang, Victor. “Asymptotic Growth of Translation-Dilation Orbits.” <i>Advances in Mathematics</i>, vol. 475, 110341, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.aim.2025.110341\">10.1016/j.aim.2025.110341</a>.","chicago":"Wang, Victor. “Asymptotic Growth of Translation-Dilation Orbits.” <i>Advances in Mathematics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.aim.2025.110341\">https://doi.org/10.1016/j.aim.2025.110341</a>.","ieee":"V. Wang, “Asymptotic growth of translation-dilation orbits,” <i>Advances in Mathematics</i>, vol. 475. Elsevier, 2025."},"PlanS_conform":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"scopus_import":"1","article_type":"original","oa":1,"ddc":["510"],"acknowledgement":"I thank Yuri Tschinkel for introducing me to the beautiful paper [53] and associated open questions, and thank him as well as Ramin Takloo-Bighash and Sho Tanimoto for their encouragement and comments. Also, I thank Tim Browning and Dan Loughran for comments and suggestions concerning Manin–Peyre, homogeneous spaces, and splitness. Thanks also to Anshul Adve, Peter Sarnak, Philip Tosteson, Katy Woo, and Nina Zubrilina for some interesting discussions. I thank the Browning Group and Andy O'Desky for many conversations. This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101034413. Finally, I thank the editors and referees for their detailed input, which substantially improved the paper.","publication_status":"published","month":"07","das_tickbox":"0","intvolume":"       475","year":"2025","arxiv":1,"external_id":{"arxiv":["2309.07626"],"isi":["001495142300002"]}},{"year":"2024","arxiv":1,"external_id":{"arxiv":["2302.02817"],"isi":["001216128200001"]},"intvolume":"       443","month":"05","acknowledgement":"Shiyu Shen has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 101034413.","publication_status":"published","ddc":["510"],"oa":1,"scopus_import":"1","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"has_accepted_license":"1","citation":{"ieee":"S. Shen, “Mirror symmetry for parabolic Higgs bundles via p-adic integration,” <i>Advances in Mathematics</i>, vol. 443, no. 5. Elsevier, 2024.","chicago":"Shen, Shiyu. “Mirror Symmetry for Parabolic Higgs Bundles via P-Adic Integration.” <i>Advances in Mathematics</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.aim.2024.109616\">https://doi.org/10.1016/j.aim.2024.109616</a>.","mla":"Shen, Shiyu. “Mirror Symmetry for Parabolic Higgs Bundles via P-Adic Integration.” <i>Advances in Mathematics</i>, vol. 443, no. 5, 109616, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.aim.2024.109616\">10.1016/j.aim.2024.109616</a>.","short":"S. Shen, Advances in Mathematics 443 (2024).","ista":"Shen S. 2024. Mirror symmetry for parabolic Higgs bundles via p-adic integration. Advances in Mathematics. 443(5), 109616.","apa":"Shen, S. (2024). Mirror symmetry for parabolic Higgs bundles via p-adic integration. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2024.109616\">https://doi.org/10.1016/j.aim.2024.109616</a>","ama":"Shen S. Mirror symmetry for parabolic Higgs bundles via p-adic integration. <i>Advances in Mathematics</i>. 2024;443(5). doi:<a href=\"https://doi.org/10.1016/j.aim.2024.109616\">10.1016/j.aim.2024.109616</a>"},"date_created":"2024-03-31T22:01:11Z","department":[{"_id":"TaHa"}],"quality_controlled":"1","title":"Mirror symmetry for parabolic Higgs bundles via p-adic integration","_id":"15248","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","OA_place":"publisher","publication_identifier":{"issn":["0001-8708"],"eissn":["1090-2082"]},"ec_funded":1,"article_number":"109616","file_date_updated":"2024-07-22T12:10:03Z","OA_type":"hybrid","date_published":"2024-05-01T00:00:00Z","language":[{"iso":"eng"}],"article_processing_charge":"Yes (via OA deal)","doi":"10.1016/j.aim.2024.109616","volume":443,"oa_version":"Published Version","status":"public","corr_author":"1","abstract":[{"lang":"eng","text":"Applying the technique of p-adic integration, we prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli spaces of (strongly) parabolic Higgs bundles for the structure groups SLn and PGLn, building on previous work of Groechenig-Wyss-Ziegler on the non-parabolic case. We also prove the E-polynomial of the smooth moduli space of parabolic GLn-Higgs bundles is independent of the degree of the underlying vector bundles."}],"publication":"Advances in Mathematics","file":[{"content_type":"application/pdf","creator":"dernst","file_size":702889,"date_updated":"2024-07-22T12:10:03Z","file_name":"2024_AdvancesMath_Shen.pdf","file_id":"17315","access_level":"open_access","relation":"main_file","date_created":"2024-07-22T12:10:03Z","checksum":"68f2f08136ccf547891a16a2c0621e97","success":1}],"issue":"5","author":[{"last_name":"Shen","full_name":"Shen, Shiyu","orcid":"0000-0002-4444-8718","id":"544cccd3-9005-11ec-87bc-94aef1c5b814","first_name":"Shiyu"}],"publisher":"Elsevier","type":"journal_article","date_updated":"2025-09-04T13:21:18Z","isi":1,"project":[{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"day":"01"},{"citation":{"mla":"Hou, Xuanji, et al. “Dynamical Classification of Analytic One-Frequency Quasi-Periodic SO(3,R)-Cocycles.” <i>Advances in Mathematics</i>, vol. 457, 109943, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.aim.2024.109943\">10.1016/j.aim.2024.109943</a>.","ieee":"X. Hou, Y. Pan, and Q. Zhou, “Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles,” <i>Advances in Mathematics</i>, vol. 457. Elsevier, 2024.","chicago":"Hou, Xuanji, Yi Pan, and Qi Zhou. “Dynamical Classification of Analytic One-Frequency Quasi-Periodic SO(3,R)-Cocycles.” <i>Advances in Mathematics</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.aim.2024.109943\">https://doi.org/10.1016/j.aim.2024.109943</a>.","apa":"Hou, X., Pan, Y., &#38; Zhou, Q. (2024). Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2024.109943\">https://doi.org/10.1016/j.aim.2024.109943</a>","ama":"Hou X, Pan Y, Zhou Q. Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles. <i>Advances in Mathematics</i>. 2024;457. doi:<a href=\"https://doi.org/10.1016/j.aim.2024.109943\">10.1016/j.aim.2024.109943</a>","short":"X. Hou, Y. Pan, Q. Zhou, Advances in Mathematics 457 (2024).","ista":"Hou X, Pan Y, Zhou Q. 2024. Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles. Advances in Mathematics. 457, 109943."},"has_accepted_license":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"title":"Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles","quality_controlled":"1","department":[{"_id":"VaKa"}],"date_created":"2024-09-15T22:01:39Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"18065","article_number":"109943","ec_funded":1,"publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"OA_place":"publisher","external_id":{"isi":["001315306500001"],"arxiv":["2311.17537"]},"arxiv":1,"year":"2024","intvolume":"       457","month":"11","article_type":"original","scopus_import":"1","oa":1,"acknowledgement":"X. Hou is partially supported by National Natural Science Foundation of China (Grant \r\n12071083) and Funds for Distinguished Youths of Hubei Province of China (\r\n2019CFA680). Y. Pan is supported by ERC Advanced Grant (#885707). Q. Zhou is partially supported by National Key R&D Program of China (2020YFA0713300), NSFC grant (\r\n12071232) and Nankai Zhide Foundation.","publication_status":"published","ddc":["510"],"author":[{"last_name":"Hou","full_name":"Hou, Xuanji","first_name":"Xuanji"},{"full_name":"Pan, Yi","last_name":"Pan","first_name":"Yi","id":"1e21c7f7-9070-11eb-847d-8b04c7169523"},{"full_name":"Zhou, Qi","last_name":"Zhou","first_name":"Qi"}],"publisher":"Elsevier","type":"journal_article","date_updated":"2025-09-08T09:44:19Z","day":"01","project":[{"call_identifier":"H2020","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","name":"Spectral rigidity and integrability for billiards and geodesic flows","grant_number":"885707"}],"isi":1,"language":[{"iso":"eng"}],"date_published":"2024-11-01T00:00:00Z","OA_type":"hybrid","file_date_updated":"2025-01-13T08:29:27Z","volume":457,"article_processing_charge":"Yes (via OA deal)","doi":"10.1016/j.aim.2024.109943","oa_version":"Published Version","file":[{"relation":"main_file","date_created":"2025-01-13T08:29:27Z","checksum":"1c80b844a91d93cf4799f4a65873b18d","success":1,"content_type":"application/pdf","file_name":"2024_AdvancesMath_Hou.pdf","date_updated":"2025-01-13T08:29:27Z","file_id":"18826","access_level":"open_access","file_size":713659,"creator":"dernst"}],"publication":"Advances in Mathematics","corr_author":"1","abstract":[{"text":"We establish a close connection between acceleration and dynamical degree for one-frequency quasi-periodic compact cocycles, by showing that two vectors derived separately from each coincide. Based on this, we provide a dynamical classification of one-frequency quasi-periodic  SO(3, R)-cocycles.","lang":"eng"}],"status":"public"},{"month":"11","publication_status":"published","ddc":["510"],"article_type":"original","scopus_import":"1","oa":1,"year":"2024","external_id":{"arxiv":["2112.01615"]},"arxiv":1,"das_tickbox":"0","intvolume":"       457","_id":"18064","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","OA_place":"publisher","publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"article_number":"109946","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"has_accepted_license":"1","citation":{"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>.","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.","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>.","ista":"Chan S. 2024. The average number of integral points on the congruent number curves. Advances in Mathematics. 457(11), 109946.","short":"S. Chan, Advances in Mathematics 457 (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>","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>"},"researchdata_availability":"no","date_created":"2024-09-15T22:01:39Z","quality_controlled":"1","department":[{"_id":"TiBr"}],"title":"The average number of integral points on the congruent number curves","oa_version":"Published Version","status":"public","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"}],"corr_author":"1","supplementarymaterial":"no","file":[{"content_type":"application/pdf","file_name":"2024_AdvancesMath_Chan.pdf","file_id":"18829","date_updated":"2025-01-13T08:54:09Z","access_level":"open_access","creator":"dernst","file_size":564386,"relation":"main_file","checksum":"f555742540ad91a3040aeafd68b1fcde","date_created":"2025-01-13T08:54:09Z","success":1}],"publication":"Advances in Mathematics","issue":"11","file_date_updated":"2025-01-13T08:54:09Z","language":[{"iso":"eng"}],"date_published":"2024-11-01T00:00:00Z","OA_type":"hybrid","article_processing_charge":"Yes (via OA deal)","doi":"10.1016/j.aim.2024.109946","volume":457,"date_updated":"2026-07-29T10:03:09Z","day":"01","publisher":"Elsevier","author":[{"orcid":"0000-0001-8467-4106","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","first_name":"Yik Tung","full_name":"Chan, Yik Tung","last_name":"Chan"}],"type":"journal_article"},{"researchdata_availability":"no","main_file_link":[{"url":"https://arxiv.org/abs/2003.07287","open_access":"1"}],"date_created":"2022-02-20T23:01:30Z","department":[{"_id":"TiBr"}],"quality_controlled":"1","title":"Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics","citation":{"ieee":"Y. Cao and Z. Huang, “Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics,” <i>Advances in Mathematics</i>, vol. 398, no. 3. Elsevier, 2022.","chicago":"Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood Property and Geometric Sieve for Affine Quadrics.” <i>Advances in Mathematics</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.aim.2022.108236\">https://doi.org/10.1016/j.aim.2022.108236</a>.","mla":"Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood Property and Geometric Sieve for Affine Quadrics.” <i>Advances in Mathematics</i>, vol. 398, no. 3, 108236, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.aim.2022.108236\">10.1016/j.aim.2022.108236</a>.","short":"Y. Cao, Z. Huang, Advances in Mathematics 398 (2022).","ista":"Cao Y, Huang Z. 2022. Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. Advances in Mathematics. 398(3), 108236.","apa":"Cao, Y., &#38; Huang, Z. (2022). Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2022.108236\">https://doi.org/10.1016/j.aim.2022.108236</a>","ama":"Cao Y, Huang Z. Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. <i>Advances in Mathematics</i>. 2022;398(3). doi:<a href=\"https://doi.org/10.1016/j.aim.2022.108236\">10.1016/j.aim.2022.108236</a>"},"publication_identifier":{"issn":["0001-8708"],"eissn":["1090-2082"]},"article_number":"108236","_id":"10765","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","das_tickbox":"0","intvolume":"       398","year":"2022","external_id":{"isi":["000792517300014"],"arxiv":["2003.07287"]},"arxiv":1,"acknowledgement":"We are grateful to Mikhail Borovoi, Zeev Rudnick and Olivier Wienberg for their interest in our\r\nwork. We would like to address our gratitude to Ulrich Derenthal for his generous support at Leibniz Universitat Hannover. We are in debt to Tim Browning for an enlightening discussion and to the anonymous referees for critical comments, which lead to overall improvements of various preliminary versions of this paper. Part of this work was carried out and reported during a visit to the University of Science and Technology of China. We thank Yongqi Liang for offering warm hospitality. The first author was supported by a Humboldt-Forschungsstipendium. The second author was supported by grant DE 1646/4-2 of the Deutsche Forschungsgemeinschaft.","publication_status":"published","oa":1,"scopus_import":"1","article_type":"original","month":"03","type":"journal_article","author":[{"first_name":"Yang","full_name":"Cao, Yang","last_name":"Cao"},{"full_name":"Huang, Zhizhong","last_name":"Huang","id":"21f1b52f-2fd1-11eb-a347-a4cdb9b18a51","first_name":"Zhizhong"}],"publisher":"Elsevier","isi":1,"day":"26","date_updated":"2026-08-19T13:00:41Z","article_processing_charge":"No","doi":"10.1016/j.aim.2022.108236","volume":398,"date_published":"2022-03-26T00:00:00Z","language":[{"iso":"eng"}],"status":"public","abstract":[{"text":"We establish the Hardy-Littlewood property (à la Borovoi-Rudnick) for Zariski open subsets in affine quadrics of the form q(x1,...,xn)=m, where q is a non-degenerate integral quadratic form in  n>3 variables and m is a non-zero integer. This gives asymptotic formulas for the density of integral points taking coprime polynomial values, which is a quantitative version of the arithmetic purity of strong approximation property off infinity for affine quadrics.","lang":"eng"}],"corr_author":"1","publication":"Advances in Mathematics","supplementarymaterial":"no","issue":"3","oa_version":"Preprint"},{"keyword":["Chiral algebras","Chiral homology","Factorization algebras","Koszul duality","Ran space"],"intvolume":"       392","year":"2021","arxiv":1,"external_id":{"isi":["000707040300031"],"arxiv":["1610.00212"]},"scopus_import":"1","article_type":"original","oa":1,"acknowledgement":"The author would like to express his gratitude to D. Gaitsgory, without whose tireless guidance and encouragement in pursuing this problem, this work would not have been possible. The author is grateful to his advisor B.C. Ngô for many years of patient guidance and support. This paper is revised while the author is a postdoc in Hausel group at IST Austria. We thank him and the group for providing a wonderful research environment. The author also gratefully acknowledges the support of the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization Homology,” Austrian Science Fund (FWF): M 2751.","ddc":["514"],"publication_status":"published","month":"09","department":[{"_id":"TaHa"}],"quality_controlled":"1","title":"The Atiyah-Bott formula and connectivity in chiral Koszul duality","date_created":"2021-09-21T15:58:59Z","has_accepted_license":"1","citation":{"mla":"Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” <i>Advances in Mathematics</i>, vol. 392, 107992, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107992\">10.1016/j.aim.2021.107992</a>.","chicago":"Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” <i>Advances in Mathematics</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.aim.2021.107992\">https://doi.org/10.1016/j.aim.2021.107992</a>.","ieee":"Q. P. Ho, “The Atiyah-Bott formula and connectivity in chiral Koszul duality,” <i>Advances in Mathematics</i>, vol. 392. Elsevier, 2021.","apa":"Ho, Q. P. (2021). The Atiyah-Bott formula and connectivity in chiral Koszul duality. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2021.107992\">https://doi.org/10.1016/j.aim.2021.107992</a>","ama":"Ho QP. The Atiyah-Bott formula and connectivity in chiral Koszul duality. <i>Advances in Mathematics</i>. 2021;392. doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107992\">10.1016/j.aim.2021.107992</a>","ista":"Ho QP. 2021. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. 392, 107992.","short":"Q.P. Ho, Advances in Mathematics 392 (2021)."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_number":"107992","publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10033","volume":392,"article_processing_charge":"Yes (via OA deal)","doi":"10.1016/j.aim.2021.107992","file_date_updated":"2021-09-21T15:58:52Z","language":[{"iso":"eng"}],"date_published":"2021-09-21T00:00:00Z","publication":"Advances in Mathematics","file":[{"relation":"main_file","date_created":"2021-09-21T15:58:52Z","checksum":"f3c0086d41af11db31c00014efb38072","date_updated":"2021-09-21T15:58:52Z","file_id":"10034","file_name":"1-s2.0-S000187082100431X-main.pdf","access_level":"open_access","file_size":840635,"creator":"qho","content_type":"application/pdf"}],"status":"public","corr_author":"1","abstract":[{"lang":"eng","text":"The ⊗*-monoidal structure on the category of sheaves on the Ran space is not pro-nilpotent in the sense of [3]. However, under some connectivity assumptions, we prove that Koszul duality induces an equivalence of categories and that this equivalence behaves nicely with respect to Verdier duality on the Ran space and integrating along the Ran space, i.e. taking factorization homology. Based on ideas sketched in [4], we show that these results also offer a simpler alternative to one of the two main steps in the proof of the Atiyah-Bott formula given in [7] and [5]."}],"oa_version":"Published Version","type":"journal_article","publisher":"Elsevier","author":[{"first_name":"Quoc P","id":"3DD82E3C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6889-1418","last_name":"Ho","full_name":"Ho, Quoc P"}],"day":"21","isi":1,"project":[{"name":"Algebro-Geometric Applications of Factorization Homology","grant_number":"M02751","call_identifier":"FWF","_id":"26B96266-B435-11E9-9278-68D0E5697425"}],"date_updated":"2025-04-14T09:09:35Z"},{"intvolume":"       349","das_tickbox":"0","arxiv":1,"external_id":{"arxiv":["1810.08426"],"isi":["000468857300025"]},"year":"2019","ddc":["512"],"publication_status":"published","scopus_import":"1","oa":1,"month":"06","date_created":"2019-04-16T09:13:25Z","researchdata_availability":"no","title":"Counting rational points on biquadratic hypersurfaces","quality_controlled":"1","department":[{"_id":"TiBr"}],"citation":{"chicago":"Browning, Timothy D, and L.Q. Hu. “Counting Rational Points on Biquadratic Hypersurfaces.” <i>Advances in Mathematics</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.aim.2019.04.031\">https://doi.org/10.1016/j.aim.2019.04.031</a>.","ieee":"T. D. Browning and L. Q. Hu, “Counting rational points on biquadratic hypersurfaces,” <i>Advances in Mathematics</i>, vol. 349. Elsevier, pp. 920–940, 2019.","mla":"Browning, Timothy D., and L. Q. Hu. “Counting Rational Points on Biquadratic Hypersurfaces.” <i>Advances in Mathematics</i>, vol. 349, Elsevier, 2019, pp. 920–40, doi:<a href=\"https://doi.org/10.1016/j.aim.2019.04.031\">10.1016/j.aim.2019.04.031</a>.","ista":"Browning TD, Hu LQ. 2019. Counting rational points on biquadratic hypersurfaces. Advances in Mathematics. 349, 920–940.","short":"T.D. Browning, L.Q. Hu, Advances in Mathematics 349 (2019) 920–940.","ama":"Browning TD, Hu LQ. Counting rational points on biquadratic hypersurfaces. <i>Advances in Mathematics</i>. 2019;349:920-940. doi:<a href=\"https://doi.org/10.1016/j.aim.2019.04.031\">10.1016/j.aim.2019.04.031</a>","apa":"Browning, T. D., &#38; Hu, L. Q. (2019). Counting rational points on biquadratic hypersurfaces. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2019.04.031\">https://doi.org/10.1016/j.aim.2019.04.031</a>"},"has_accepted_license":"1","publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"_id":"6310","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","page":"920-940","article_processing_charge":"No","doi":"10.1016/j.aim.2019.04.031","volume":349,"language":[{"iso":"eng"}],"date_published":"2019-06-20T00:00:00Z","file_date_updated":"2020-07-14T12:47:27Z","abstract":[{"lang":"eng","text":"An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariskiopen subset of an arbitrary smooth biquadratic hypersurface in sufficiently many variables. The proof uses the Hardy–Littlewood circle method."}],"status":"public","file":[{"date_updated":"2020-07-14T12:47:27Z","file_id":"6311","file_name":"wliqun.pdf","access_level":"open_access","creator":"tbrownin","file_size":379158,"content_type":"application/pdf","relation":"main_file","checksum":"a63594a3a91b4ba6e2a1b78b0720b3d0","date_created":"2019-04-16T09:12:20Z"}],"publication":"Advances in Mathematics","supplementarymaterial":"no","oa_version":"Submitted Version","type":"journal_article","author":[{"full_name":"Browning, Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D"},{"full_name":"Hu, L.Q.","last_name":"Hu","first_name":"L.Q."}],"publisher":"Elsevier","isi":1,"day":"20","date_updated":"2026-08-06T12:11:51Z"}]