[{"supervisor":[{"first_name":"Krzysztof Z","orcid":"0000-0002-9139-1654","last_name":"Pietrzak","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","full_name":"Pietrzak, Krzysztof Z"}],"file_date_updated":"2026-01-08T14:11:39Z","oa_version":"Published Version","year":"2025","author":[{"id":"0f78d746-dc7d-11ea-9b2f-83f92091afe7","full_name":"Hoffmann, Charlotte","orcid":"0000-0003-2027-5549","first_name":"Charlotte","last_name":"Hoffmann"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","department":[{"_id":"GradSch"},{"_id":"KrPi"}],"month":"10","degree_awarded":"PhD","citation":{"ieee":"C. Hoffmann, “Theory and applications of verifiable delay functions,” Institute of Science and Technology Austria, 2025.","ama":"Hoffmann C. Theory and applications of verifiable delay functions. 2025. doi:10.15479/AT-ISTA-20556","chicago":"Hoffmann, Charlotte. “Theory and Applications of Verifiable Delay Functions.” Institute of Science and Technology Austria, 2025. https://doi.org/10.15479/AT-ISTA-20556.","apa":"Hoffmann, C. (2025). Theory and applications of verifiable delay functions. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-20556","ista":"Hoffmann C. 2025. Theory and applications of verifiable delay functions. Institute of Science and Technology Austria.","mla":"Hoffmann, Charlotte. Theory and Applications of Verifiable Delay Functions. Institute of Science and Technology Austria, 2025, doi:10.15479/AT-ISTA-20556.","short":"C. Hoffmann, Theory and Applications of Verifiable Delay Functions, Institute of Science and Technology Austria, 2025."},"has_accepted_license":"1","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"13143"},{"id":"12176","relation":"part_of_dissertation","status":"public"},{"status":"public","id":"20920","relation":"later_version"},{"id":"19778","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"20701"}]},"tmp":{"short":"CC BY-NC-SA (4.0)","image":"/images/cc_by_nc_sa.png","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode"},"publisher":"Institute of Science and Technology Austria","file":[{"file_id":"20573","checksum":"1fffa4e2c33dd0b9f883d615504a2858","access_level":"closed","file_size":2259304,"creator":"choffman","file_name":"2025_Hoffmann_Charlotte_Thesis.pdf","date_updated":"2026-01-08T14:11:39Z","content_type":"application/pdf","date_created":"2025-10-28T14:33:03Z","relation":"main_file"},{"access_level":"closed","file_size":9987633,"checksum":"076ea98a1f0a86c3bbc990b6b9460dc2","file_id":"20574","file_name":"2025_Hoffmann_Charlotte_Source.zip","creator":"choffman","date_updated":"2025-11-11T09:34:54Z","date_created":"2025-10-28T14:35:06Z","content_type":"application/x-zip-compressed","relation":"source_file"}],"status":"public","day":"31","corr_author":"1","type":"dissertation","date_created":"2025-10-27T14:16:56Z","page":"116","ddc":["004"],"_id":"20556","article_processing_charge":"No","language":[{"iso":"eng"}],"OA_place":"publisher","publication_status":"published","alternative_title":["ISTA Thesis"],"date_updated":"2026-07-06T13:15:27Z","doi":"10.15479/AT-ISTA-20556","publication_identifier":{"issn":["2663-337X"]},"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","abstract":[{"text":"Verifiable Delay Functions (VDFs) introduced by Boneh et al. (CRYPTO'18) are functions that require a prescribed number of sequential steps T to evaluate, yet their output can be verified in time much faster than T. Since their introduction, VDFs have gained a lot of attention due to their applications in blockchain protocols, randomness beacons, timestamping and deniability. This thesis explores the theory and applications of VDFs, focusing on enhancing their soundness, efficiency and practicality.\r\n\r\nThe only practical VDFs known to date are based on repeated squaring in hidden order groups. Consider the function VDF(x,T)=x^(2^T).\r\nThe iterated squaring assumption states that, for a random group element x, the result of VDF cannot be computed significantly faster than performing T sequential squarings if the group order is unknown. To make the result verifiable a prover can compute a proof of exponentiation (PoE) \\pi. Given \\pi, the output of VDF can be verified in time much less than T.\r\n\r\nWe first present new constructions of statistically sound proofs of exponentiation, which are an important building block in the construction of SNARKs (Succinct Non-Interactive Argument of Knowledge). Statistical soundness means that the proofs remain secure against computationally unbounded adversaries, in particular, it remains secure even when the group order is known. We thereby address limitations in previous PoE protocols which either required (non-standard) hardness assumptions or a lot of parallel repetitions. Our construction significantly reduces the proof size of statistically sound PoEs that allow for a structured exponent, which leads to better efficiency of SNARKs and other applications.\r\n\r\nSecondly, we introduce improved batching techniques for PoEs, which allow multiple proofs to be aggregated and verified with minimal overhead. These protocols optimize communication and computation complexity in large-scale blockchain environments and enable scalable remote benchmarking of parallel computation resources.\r\n\r\nWe then construct VDFs with enhanced properties such as zero-knowledge and watermarkability. It was shown by Arun, Bonneau and Clark (ASIACRYPT'22) that these features enable new cryptographic primitives called short-lived proofs and signatures. The validity of such proofs and signatures expires after a predefined amount of time T, i.e., they are deniable after time T. Our constructions improve upon the constructions by Arun, Bonneau and Clark in several dimensions (faster forging times, arguably weaker assumptions).\r\n\r\nFinally, we apply PoEs in the realm of primality testing, providing cryptographically sound proofs of non-primality for large Proth numbers. This work gives a surprising application of VDFs in the area of computational number theory.\r\n\r\nTogether, our contributions advance both the theoretical foundations and the real-world usability of VDFs in general and in particular of PoEs, making them more adaptable and secure for current and emerging cryptographic applications.","lang":"eng"}],"date_published":"2025-10-31T00:00:00Z","title":"Theory and applications of verifiable delay functions"},{"publisher":"International Press of Boston","ec_funded":1,"status":"public","scopus_import":"1","article_type":"original","day":"01","department":[{"_id":"JuFi"}],"month":"05","external_id":{"arxiv":["2109.04233"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":130,"citation":{"apa":"Hensel, S., & Laux, T. (2025). A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness. Journal of Differential Geometry. International Press of Boston. https://doi.org/10.4310/jdg/1747065796","ama":"Hensel S, Laux T. A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness. Journal of Differential Geometry. 2025;130:209-268. doi:10.4310/jdg/1747065796","chicago":"Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for Mean Curvature Flow: Convergence of the Allen-Cahn Equation and Weak-Strong Uniqueness.” Journal of Differential Geometry. International Press of Boston, 2025. https://doi.org/10.4310/jdg/1747065796.","ieee":"S. Hensel and T. Laux, “A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness,” Journal of Differential Geometry, vol. 130. International Press of Boston, pp. 209–268, 2025.","ista":"Hensel S, Laux T. 2025. A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness. Journal of Differential Geometry. 130, 209–268.","mla":"Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for Mean Curvature Flow: Convergence of the Allen-Cahn Equation and Weak-Strong Uniqueness.” Journal of Differential Geometry, vol. 130, International Press of Boston, 2025, pp. 209–68, doi:10.4310/jdg/1747065796.","short":"S. Hensel, T. Laux, Journal of Differential Geometry 130 (2025) 209–268."},"project":[{"call_identifier":"H2020","grant_number":"948819","name":"Bridging Scales in Random Materials","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"author":[{"full_name":"Hensel, Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","last_name":"Hensel","orcid":"0000-0001-7252-8072","first_name":"Sebastian"},{"full_name":"Laux, Tim","first_name":"Tim","last_name":"Laux"}],"quality_controlled":"1","year":"2025","OA_type":"green","oa_version":"Preprint","doi":"10.4310/jdg/1747065796","publication_identifier":{"issn":["0022-040X"],"eissn":["1945-743X"]},"date_updated":"2026-07-06T13:37:21Z","date_published":"2025-05-01T00:00:00Z","title":"A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness","abstract":[{"text":"We propose a new weak solution concept for (two-phase) mean curvature flow which enjoys both (unconditional) existence and (weak-strong) uniqueness properties. These solutions are evolving varifolds, just as in Brakke's formulation, but are coupled to the phase volumes by a simple transport equation. First, we show that, in the exact same setup as in Ilmanen's proof [J. Differential Geom. 38, 417-461, (1993)], any limit point of solutions to the Allen-Cahn equation is a varifold solution in our sense. Second, we prove that any calibrated flow in the sense of Fischer et al. [arXiv:2003.05478] - and hence any classical solution to mean curvature flow-is unique in the class of our new varifold solutions. This is in sharp contrast to the case of Brakke flows, which a priori may disappear at any given time and are therefore fatally non-unique. Finally, we propose an extension of the solution concept to the multi-phase case which is at least guaranteed to satisfy a weak-strong uniqueness principle.","lang":"eng"}],"keyword":["Mean curvature flow","gradient flows","varifolds","weak solutions","weak-strong uniqueness","calibrated geometry","gradient-flow calibrations"],"acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819), and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813. The content of this paper was developed and parts of it were written during a visit of the first author to the Hausdorff Center of Mathematics (HCM), University of Bonn. The hospitality and the support of HCM are gratefully acknowledged.","main_file_link":[{"url":"https://arxiv.org/abs/2109.04233","open_access":"1"}],"publication_status":"published","publication":"Journal of Differential Geometry","oa":1,"language":[{"iso":"eng"}],"OA_place":"repository","date_created":"2021-09-13T12:17:10Z","page":"209-268","type":"journal_article","arxiv":1,"article_processing_charge":"No","das_tickbox":"1","_id":"10011","corr_author":"1","intvolume":" 130"},{"day":"20","scopus_import":"1","file":[{"relation":"main_file","success":1,"content_type":"application/pdf","date_created":"2025-07-14T07:11:04Z","date_updated":"2025-07-14T07:11:04Z","creator":"dernst","file_name":"2025_LIPIcs.SoCG_Streltsova.pdf","checksum":"a8f7feb1aa3b896e31195841a989d622","file_id":"20015","access_level":"open_access","file_size":952807}],"status":"public","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"has_accepted_license":"1","citation":{"ista":"Streltsova E, Wagner U. 2025. Levels in arrangements: Linear relations, the g-matrix, and applications to crossing numbers. 41st International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 332, 75.","apa":"Streltsova, E., & Wagner, U. (2025). Levels in arrangements: Linear relations, the g-matrix, and applications to crossing numbers. In 41st International Symposium on Computational Geometry (Vol. 332). Kanazawa, Japan: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2025.75","ama":"Streltsova E, Wagner U. Levels in arrangements: Linear relations, the g-matrix, and applications to crossing numbers. In: 41st International Symposium on Computational Geometry. Vol 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:10.4230/LIPIcs.SoCG.2025.75","chicago":"Streltsova, Elizaveta, and Uli Wagner. “Levels in Arrangements: Linear Relations, the g-Matrix, and Applications to Crossing Numbers.” In 41st International Symposium on Computational Geometry, Vol. 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. https://doi.org/10.4230/LIPIcs.SoCG.2025.75.","ieee":"E. Streltsova and U. Wagner, “Levels in arrangements: Linear relations, the g-matrix, and applications to crossing numbers,” in 41st International Symposium on Computational Geometry, Kanazawa, Japan, 2025, vol. 332.","short":"E. Streltsova, U. Wagner, in:, 41st International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.","mla":"Streltsova, Elizaveta, and Uli Wagner. “Levels in Arrangements: Linear Relations, the g-Matrix, and Applications to Crossing Numbers.” 41st International Symposium on Computational Geometry, vol. 332, 75, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:10.4230/LIPIcs.SoCG.2025.75."},"month":"06","department":[{"_id":"UlWa"}],"conference":{"name":"SoCG: Symposium on Computational Geometry","location":"Kanazawa, Japan","start_date":"2025-06-23","end_date":"2025-06-27"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2504.07752","2504.07770"]},"volume":332,"author":[{"last_name":"Streltsova","first_name":"Elizaveta","full_name":"Streltsova, Elizaveta","id":"57a170da-dc96-11ea-b7c8-ab3565071bf7"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli","first_name":"Uli","orcid":"0000-0002-1494-0568","last_name":"Wagner"}],"OA_type":"gold","year":"2025","article_number":"75","oa_version":"Published Version","file_date_updated":"2025-07-14T07:11:04Z","quality_controlled":"1","title":"Levels in arrangements: Linear relations, the g-matrix, and applications to crossing numbers","date_published":"2025-06-20T00:00:00Z","abstract":[{"text":"A long-standing conjecture of Eckhoff, Linhart, and Welzl, which would generalize McMullen’s Upper Bound Theorem for polytopes and refine asymptotic bounds due to Clarkson, asserts that for k ⩽ ⌊(n-d-2)/2⌋, the complexity of the (⩽ k)-level in a simple arrangement of n hemispheres in S^d is maximized for arrangements that are polar duals of neighborly d-polytopes. We prove this conjecture in the case n = d+4. By Gale duality, this implies the following result about crossing numbers: In every spherical arc drawing of K_n in S² (given by a set V ⊂ S² of n unit vectors connected by spherical arcs), the number of crossings is at least 1/4 ⌊n/2⌋ ⌊(n-1)/2⌋ ⌊(n-2)/2⌋ ⌊(n-3)/2⌋. This lower bound is attained if every open linear halfspace contains at least ⌊(n-2)/2⌋ of the vectors in V.\r\nMoreover, we determine the space of all linear and affine relations that hold between the face numbers of levels in simple arrangements of n hemispheres in S^d. This completes a long line of research on such relations, answers a question posed by Andrzejak and Welzl in 2003, and generalizes the classical fact that the Dehn-Sommerville relations generate all linear relations between the face numbers of simple polytopes (which correspond to the 0-level).\r\nTo prove these results, we introduce the notion of the g-matrix, which encodes the face numbers of levels in an arrangement and generalizes the classical g-vector of a polytope.","lang":"eng"}],"publication_identifier":{"isbn":["9783959773706"],"eissn":["1868-8969"]},"doi":"10.4230/LIPIcs.SoCG.2025.75","date_updated":"2026-07-07T13:03:16Z","alternative_title":["LIPIcs"],"oa":1,"publication":"41st International Symposium on Computational Geometry","publication_status":"published","OA_place":"publisher","language":[{"iso":"eng"}],"article_processing_charge":"Yes","arxiv":1,"_id":"20004","das_tickbox":"1","ddc":["510"],"date_created":"2025-07-13T22:01:22Z","type":"conference","corr_author":"1","intvolume":" 332"},{"article_type":"letter_note","day":"16","has_accepted_license":"1","related_material":{"record":[{"status":"public","id":"22142","relation":"research_data"}]},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"scopus_import":"1","publisher":"American Physical Society","file":[{"success":1,"relation":"main_file","file_size":571784,"access_level":"open_access","file_id":"19755","checksum":"b83295a8f597b7781d8e7bfa3b393b42","file_name":"2025_PhysReviewA_Kun.pdf","creator":"dernst","date_updated":"2025-05-28T09:16:03Z","date_created":"2025-05-28T09:16:03Z","content_type":"application/pdf"}],"status":"public","citation":{"chicago":"Kun, Daniel, Karl T Strömberg, Michele Spagnolo, Borivoje Dakić, Lee A. Rozema, and Philip Walther. “Direct and Efficient Detection of Quantum Superposition.” Physical Review A. American Physical Society, 2025. https://doi.org/10.1103/PhysRevA.111.L050402.","ama":"Kun D, Strömberg KT, Spagnolo M, Dakić B, Rozema LA, Walther P. Direct and efficient detection of quantum superposition. Physical Review A. 2025;111(5). doi:10.1103/PhysRevA.111.L050402","ieee":"D. Kun, K. T. Strömberg, M. Spagnolo, B. Dakić, L. A. Rozema, and P. Walther, “Direct and efficient detection of quantum superposition,” Physical Review A, vol. 111, no. 5. American Physical Society, 2025.","apa":"Kun, D., Strömberg, K. T., Spagnolo, M., Dakić, B., Rozema, L. A., & Walther, P. (2025). Direct and efficient detection of quantum superposition. Physical Review A. American Physical Society. https://doi.org/10.1103/PhysRevA.111.L050402","ista":"Kun D, Strömberg KT, Spagnolo M, Dakić B, Rozema LA, Walther P. 2025. Direct and efficient detection of quantum superposition. Physical Review A. 111(5), L050402.","mla":"Kun, Daniel, et al. “Direct and Efficient Detection of Quantum Superposition.” Physical Review A, vol. 111, no. 5, L050402, American Physical Society, 2025, doi:10.1103/PhysRevA.111.L050402.","short":"D. Kun, K.T. Strömberg, M. Spagnolo, B. Dakić, L.A. Rozema, P. Walther, Physical Review A 111 (2025)."},"volume":111,"user_id":"68b8ca59-c5b3-11ee-8790-cd641c68093d","external_id":{"arxiv":["2405.08065"],"isi":["001501941500006"]},"department":[{"_id":"OnHo"}],"month":"05","author":[{"last_name":"Kun","first_name":"Daniel","full_name":"Kun, Daniel"},{"last_name":"Strömberg","first_name":"Karl T","full_name":"Strömberg, Karl T","id":"68011cd2-da32-11ee-a930-b2774c7aba5f"},{"first_name":"Michele","last_name":"Spagnolo","full_name":"Spagnolo, Michele"},{"full_name":"Dakić, Borivoje","last_name":"Dakić","first_name":"Borivoje"},{"full_name":"Rozema, Lee A.","last_name":"Rozema","first_name":"Lee A."},{"first_name":"Philip","last_name":"Walther","full_name":"Walther, Philip"}],"isi":1,"file_date_updated":"2025-05-28T09:16:03Z","article_number":"L050402","oa_version":"Published Version","year":"2025","OA_type":"hybrid","quality_controlled":"1","abstract":[{"text":"One of the most striking quantum phenomena is superposition, where one particle simultaneously inhabits different states. Most methods to verify coherent superposition are indirect, in that they require the distinct states to be recombined. Here, we adapt an xor game, in which a “test” photon is placed in a superposition of two orthogonal spatial modes, and each mode is sent to separated parties who perform local measurements on their modes without reinterfering the original modes. We show that by using a second identical “measurement” photon the parties are nonetheless able to verify if the test photon was placed in coherent superposition of the two spatial modes. We then turn this game into a resource-efficient verification scheme, obtaining a confidence that the particle is superposed which approaches unity exponentially fast. We demonstrate our scheme using a single photon, obtaining a 99% confidence that the particle is superposed with only 37 copies. Our work shows the utility of xor games to verify quantum resources, allowing us to efficiently detect quantum superposition without reinterfering the superposed modes.","lang":"eng"}],"date_published":"2025-05-16T00:00:00Z","title":"Direct and efficient detection of quantum superposition","date_updated":"2026-07-07T14:05:51Z","doi":"10.1103/PhysRevA.111.L050402","publication_identifier":{"issn":["2469-9926"],"eissn":["2469-9934"]},"language":[{"iso":"eng"}],"OA_place":"publisher","publication":"Physical Review A","publication_status":"published","oa":1,"dataavailabilitystatement":"Data that support the findings of this study are openly available at Zenodo.","acknowledgement":"This project has received funding from the European Union's Horizon 2020 and Horizon Europe research and innovation programmes under Grant Agreements No. 899368 (EPIQUS) and No. 101135288 (EPIQUE), the Marie Skłodowska-Curie Grant Agreement No. 956071 (AppQInfo), and the QuantERA II Programme under Grant Agreement No. 101017733 (PhoMemtor). The financial support by the Austrian Federal Ministry of Labour and Economy, the National Foundation for Research, Technology and Development, and the Christian Doppler Research Association is gratefully acknowledged. L.A.R. acknowledges support from the Erwin Schrödinger Center for Quantum Science & Technology (ESQ Discovery). This research was funded in whole or in part from the Austrian Science Fund (FWF) through [Grant No. 10.55776/COE1] (Quantum Science Austria), [Grant No. 10.55776/F71] (BeyondC), [Grant No. 10.55776/FG5] (Research Group 5), [Grant No. 10.55776/I6002] (PhoMemtor), and [Grant No. 10.55776/P36994] (Quantum Interference).","ddc":["530"],"_id":"19733","das_tickbox":"1","arxiv":1,"article_processing_charge":"No","supplementarymaterial":"yes","type":"journal_article","date_created":"2025-05-25T22:16:54Z","issue":"5","researchdata_availability":"yes","intvolume":" 111"},{"related_material":{"record":[{"status":"public","id":"19733","relation":"used_in_publication"}]},"doi":"10.5281/zenodo.13375452","publisher":"Zenodo","status":"public","date_updated":"2026-07-07T14:05:51Z","date_published":"2025-04-24T00:00:00Z","title":"Direct And Efficient Detection of Quantum Superposition - Data and Figures","day":"24","abstract":[{"text":"Data to generate Figures from the Letter \"Direct and Efficient Detection of Quantum Superposition\" published in APS Physical Review A.\r\nThe code can be found on the provided GitLab repository.","lang":"eng"}],"department":[{"_id":"OnHo"}],"month":"4","main_file_link":[{"url":"https://doi.org/10.5281/zenodo.13375452","open_access":"1"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"apa":"Kun, D. (2025). Direct And Efficient Detection of Quantum Superposition - Data and Figures. Zenodo. https://doi.org/10.5281/zenodo.13375452","ieee":"D. Kun, “Direct And Efficient Detection of Quantum Superposition - Data and Figures.” Zenodo, 2025.","chicago":"Kun, Daniel. “Direct And Efficient Detection of Quantum Superposition - Data and Figures.” Zenodo, 2025. https://doi.org/10.5281/zenodo.13375452.","ama":"Kun D. Direct And Efficient Detection of Quantum Superposition - Data and Figures. 2025. doi:10.5281/zenodo.13375452","ista":"Kun D. 2025. Direct And Efficient Detection of Quantum Superposition - Data and Figures, Zenodo, 10.5281/zenodo.13375452.","mla":"Kun, Daniel. Direct And Efficient Detection of Quantum Superposition - Data and Figures. Zenodo, 2025, doi:10.5281/zenodo.13375452.","short":"D. Kun, (2025)."},"oa":1,"OA_place":"repository","date_created":"2026-06-25T11:08:53Z","type":"research_data_reference","author":[{"last_name":"Kun","first_name":"Daniel","full_name":"Kun, Daniel"}],"article_processing_charge":"No","_id":"22142","ddc":["530"],"contributor":[{"last_name":"Rozema","first_name":"Lee","contributor_type":"researcher"},{"last_name":"Stroemberg","first_name":"Teodor","contributor_type":"researcher"},{"last_name":"Walther","first_name":"Philip","contributor_type":"supervisor"},{"last_name":"Dakic","first_name":"Borivoje","contributor_type":"supervisor"}],"year":"2025","OA_type":"green","oa_version":"Published Version"},{"researchdata_availability":"no","intvolume":" 12","_id":"19636","ddc":["530"],"das_tickbox":"1","article_processing_charge":"Yes","arxiv":1,"type":"journal_article","supplementarymaterial":"no","date_created":"2025-05-04T22:02:30Z","OA_place":"publisher","language":[{"iso":"eng"}],"oa":1,"dataavailabilitystatement":"No datasets were generated or analysed during the current study.","DOAJ_listed":"1","publication_status":"published","publication":"EPJ Quantum Technology","acknowledgement":"We acknowledge the support of the CERN Physics Beyond Collider activity, the CERN Quantum Technology Initiative, the Long Range Broad Agency Announcement (BAA) for the Navy and Marine Corps Science and Technology programme, Hannover Leibniz University, and the Physics Department at Imperial College London, whose contributions were instrumental in supporting the workshop that laid the foundation for this paper.\r\nThe workshop was partially funded by contributions from the Long Range Broad Agency Announcement (BAA) for the Navy and Marine Corps Science and Technology programme, Hannover Leibniz University, and the Physics Department at Imperial College London.","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","abstract":[{"lang":"eng","text":"This summary of the second Terrestrial Very-Long-Baseline Atom Interferometry (TVLBAI) Workshop provides a comprehensive overview of our meeting held in London in April 2024 (Second Terrestrial Very-Long-Baseline Atom Interferometry Workshop, Imperial College, April 2024), building on the initial discussions during the inaugural workshop held at CERN in March 2023 (First Terrestrial Very-Long-Baseline Atom Interferometry Workshop, CERN, March 2023). Like the summary of the first workshop (Abend et al. in AVS Quantum Sci. 6:024701, 2024), this document records a critical milestone for the international atom interferometry community. It documents our concerted efforts to evaluate progress, address emerging challenges, and refine strategic directions for future large-scale atom interferometry projects. Our commitment to collaboration is manifested by the integration of diverse expertise and the coordination of international resources, all aimed at advancing the frontiers of atom interferometry physics and technology, as set out in a Memorandum of Understanding signed by over 50 institutions (Memorandum of Understanding for the Terrestrial Very Long Baseline Atom Interferometer Study)."}],"title":"Terrestrial Very-Long-Baseline Atom Interferometry: Summary of the second workshop","date_published":"2025-04-03T00:00:00Z","date_updated":"2026-07-08T09:29:52Z","publication_identifier":{"eissn":["2196-0763"]},"doi":"10.1140/epjqt/s40507-025-00344-3","article_number":"42","oa_version":"Published Version","file_date_updated":"2025-05-05T10:52:52Z","OA_type":"gold","year":"2025","quality_controlled":"1","author":[{"full_name":"Abdalla, Adam","last_name":"Abdalla","first_name":"Adam"},{"first_name":"Mahiro","last_name":"Abe","full_name":"Abe, Mahiro"},{"last_name":"Abend","first_name":"Sven","full_name":"Abend, Sven"},{"last_name":"Abidi","first_name":"Mouine","full_name":"Abidi, Mouine"},{"first_name":"Monika","last_name":"Aidelsburger","full_name":"Aidelsburger, Monika"},{"full_name":"Alibabaei, Ashkan","first_name":"Ashkan","last_name":"Alibabaei"},{"full_name":"Allard, Baptiste","first_name":"Baptiste","last_name":"Allard"},{"full_name":"Antoniadis, John","last_name":"Antoniadis","first_name":"John"},{"last_name":"Arduini","first_name":"Gianluigi","full_name":"Arduini, Gianluigi"},{"full_name":"Augst, Nadja","first_name":"Nadja","last_name":"Augst"},{"last_name":"Balamatsias","first_name":"Philippos","full_name":"Balamatsias, Philippos"},{"full_name":"Balaž, Antun","first_name":"Antun","last_name":"Balaž"},{"last_name":"Banks","first_name":"Hannah","full_name":"Banks, Hannah"},{"full_name":"Barcklay, Rachel L.","first_name":"Rachel L.","last_name":"Barcklay"},{"last_name":"Barone","first_name":"Michele","full_name":"Barone, Michele"},{"first_name":"Michele","last_name":"Barsanti","full_name":"Barsanti, Michele"},{"last_name":"Bason","first_name":"Mark G.","full_name":"Bason, Mark G."},{"full_name":"Bassi, Angelo","first_name":"Angelo","last_name":"Bassi"},{"full_name":"Bayle, Jean Baptiste","first_name":"Jean Baptiste","last_name":"Bayle"},{"full_name":"Baynham, Charles F.A.","last_name":"Baynham","first_name":"Charles F.A."},{"first_name":"Quentin","last_name":"Beaufils","full_name":"Beaufils, Quentin"},{"first_name":"Sélyan","last_name":"Beldjoudi","full_name":"Beldjoudi, Sélyan"},{"first_name":"Aleksandar","last_name":"Belić","full_name":"Belić, Aleksandar"},{"full_name":"Bennetts, Shayne","first_name":"Shayne","last_name":"Bennetts"},{"full_name":"Bernabeu, Jose","last_name":"Bernabeu","first_name":"Jose"},{"last_name":"Bertoldi","first_name":"Andrea","full_name":"Bertoldi, Andrea"},{"first_name":"Clara","last_name":"Bigard","full_name":"Bigard, Clara"},{"full_name":"Bigelow, N. 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Wörner, M.E. Yahia, E. Yazgan, E. Zambrini Cruzeiro, M. Zarei, M. Zhan, S. Zhang, L. Zhou, E. 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Cambridge University Press. https://doi.org/10.1017/prm.2024.7","ista":"Naskręcki B, Verzobio M. 2025. Common valuations of division polynomials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 155(5), 1646–1660."},"page":"1646-1660","date_created":"2023-01-16T11:45:22Z","type":"journal_article","supplementarymaterial":"no","article_processing_charge":"Yes (via OA deal)","arxiv":1,"_id":"12311","das_tickbox":"0","ddc":["510"],"PlanS_conform":"1","corr_author":"1","intvolume":" 155","researchdata_availability":"no","issue":"5","publication_identifier":{"eissn":["1473-7124"],"issn":["0308-2105"]},"doi":"10.1017/prm.2024.7","date_updated":"2026-07-16T08:43:40Z","title":"Common valuations of division polynomials","date_published":"2025-10-01T00:00:00Z","abstract":[{"lang":"eng","text":"In this note, we prove a formula for the cancellation exponent kv,n between division polynomials ψn and ϕn associated with a sequence {nP}n∈N of points on an elliptic curve E defined over a discrete valuation field K. The formula greatly generalizes the previously known special cases and treats also the case of non-standard Kodaira types for non-perfect residue fields."}],"acknowledgement":"Silverman, and Paul Voutier for the comments on the earlier version of this paper. The first author acknowledges the support by Dioscuri programme initiated by the Max Planck Society, jointly managed with the National Science Centre (Poland), and mutually funded by the Polish Ministry of Science and Higher Education and the German Federal Ministry of Education and Research. The second author has been supported by MIUR (Italy) through PRIN 2017 ‘Geometric, algebraic and analytic methods in arithmetic’ and has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.","keyword":["Elliptic curves","Néron models","division polynomials","height functions","discrete valuation rings"],"oa":1,"publication":"Proceedings of the Royal Society of Edinburgh Section A: Mathematics","publication_status":"published","OA_place":"publisher","language":[{"iso":"eng"}]},{"citation":{"ieee":"H. Seabrook, E. Lavie, K. T. Strömberg, M. P. Stafford, and G. Rubino, “Surpassing the loss-noise robustness trade-off in quantum key distribution,” Physical Review Applied, vol. 24, no. 2. American Physical Society, 2025.","chicago":"Seabrook, Hannah, Emilien Lavie, Karl T Strömberg, Matthew P. Stafford, and Giulia Rubino. “Surpassing the Loss-Noise Robustness Trade-off in Quantum Key Distribution.” Physical Review Applied. American Physical Society, 2025. https://doi.org/10.1103/xq2l-r4r7.","ama":"Seabrook H, Lavie E, Strömberg KT, Stafford MP, Rubino G. Surpassing the loss-noise robustness trade-off in quantum key distribution. Physical Review Applied. 2025;24(2). doi:10.1103/xq2l-r4r7","apa":"Seabrook, H., Lavie, E., Strömberg, K. T., Stafford, M. P., & Rubino, G. (2025). Surpassing the loss-noise robustness trade-off in quantum key distribution. Physical Review Applied. American Physical Society. https://doi.org/10.1103/xq2l-r4r7","ista":"Seabrook H, Lavie E, Strömberg KT, Stafford MP, Rubino G. 2025. Surpassing the loss-noise robustness trade-off in quantum key distribution. 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Rubino, Physical Review Applied 24 (2025)."},"department":[{"_id":"OnHo"}],"month":"08","volume":24,"external_id":{"arxiv":["2412.08694"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_type":"original","day":"29","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"publisher":"American Physical Society","scopus_import":"1","status":"public","file":[{"content_type":"application/pdf","date_created":"2025-12-15T09:39:12Z","date_updated":"2025-12-15T09:39:12Z","creator":"dernst","file_name":"2025_PhysReviewApplied_Seabrook.pdf","checksum":"12ddb0414780f65b8e690fe0e6cfb95e","file_id":"20824","access_level":"open_access","file_size":3028735,"relation":"main_file","success":1}],"has_accepted_license":"1","year":"2025","OA_type":"hybrid","file_date_updated":"2025-12-15T09:39:12Z","article_number":"024072","oa_version":"Published Version","quality_controlled":"1","author":[{"full_name":"Seabrook, Hannah","first_name":"Hannah","last_name":"Seabrook"},{"full_name":"Lavie, Emilien","last_name":"Lavie","first_name":"Emilien"},{"first_name":"Karl T","last_name":"Strömberg","id":"68011cd2-da32-11ee-a930-b2774c7aba5f","full_name":"Strömberg, Karl T"},{"last_name":"Stafford","first_name":"Matthew P.","full_name":"Stafford, Matthew P."},{"full_name":"Rubino, Giulia","last_name":"Rubino","first_name":"Giulia"}],"publication_status":"published","publication":"Physical Review Applied","oa":1,"dataavailabilitystatement":"The data that support the findings of this article are openly available at https://github.com/hmis4/SurpassingLNTradeOffQKD; https://github.com/hmis4/SurpassingLNTradeOffQKD/tree/main/DomainEngineering ","language":[{"iso":"eng"}],"OA_place":"publisher","acknowledgement":"We thank B. Baragiola, A. Boubriak, M. Clark, M. Jones, and P. Skrzypczyk for useful discussions. H.S. acknowledges financial support from EPSRC Quantum Engineering Centre for Doctoral Training Grant No. EP/SO23607/1. E.L. acknowledges support from the Engineering and Physical Sciences Research Council (EPSRC) Hub in Quantum Computing and Simulation (EP/T001062/1). T.S. acknowledges that they received no funding in support of this research. M.P.S. acknowledges support from the EPSRC Quantum Engineering Centre for Doctoral Training EP/SO23607/1 and the European Commission through Starting Grant No. ERC-2018-STG803665 (PEQEM). G.R. acknowledges support from the Royal Commission for the Exhibition of 1851 through a Research Fellowship, from the European Commission through Starting Grant No. ERC-2018-STG803665 (PEQEM) and Advanced Grant No. ERC-2020-ADG101021085 (FLQuant), and from EPSRC through Standard Proposal Grant No. EP/X016218/1 (Mono-Squeeze).","date_published":"2025-08-29T00:00:00Z","title":"Surpassing the loss-noise robustness trade-off in quantum key distribution","abstract":[{"lang":"eng","text":"Quantum key distribution (QKD) offers a theoretically secure method to share secret keys, yet practical implementations face challenges due to noise and loss over long-distance channels. Traditional QKD protocols require extensive noise compensation, hindering their industrial scalability and lowering the achievable key rates. Alternative protocols encode logical qubits in noise-resilient states but at the cost of using many physical qubits, increasing susceptibility to loss and limiting transmission distance. In this work, we introduce a logical-qubit encoding that uses antisymmetric Bell states in the continuous photonic degrees of freedom, frequency and time. By leveraging the continuous space, we overcome this noise-loss robustness trade-off by minimizing the number of photons per logical qubit while optimizing the encoding resilience over noise fluctuations. We analyze the security of our encoding and demonstrate its robustness compared to existing state-of-the-art protocols. This approach provides a path toward scalable, efficient QKD implementations under realistic noise conditions."}],"doi":"10.1103/xq2l-r4r7","publication_identifier":{"eissn":["2331-7019"]},"date_updated":"2026-07-16T08:27:32Z","researchdata_availability":"yes","issue":"2","PlanS_conform":"1","intvolume":" 24","arxiv":1,"article_processing_charge":"Yes (in subscription journal)","_id":"20797","ddc":["530"],"das_tickbox":"1","date_created":"2025-12-11T10:46:28Z","type":"journal_article","supplementarymaterial":"no"},{"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"success":1,"relation":"main_file","date_created":"2026-02-17T11:56:20Z","content_type":"application/pdf","date_updated":"2026-02-17T11:56:20Z","creator":"dernst","file_name":"2025_AlgebraNumberTheory_Browning.pdf","file_size":1505580,"access_level":"open_access","file_id":"21300","checksum":"e50a60a4303b81563f7adbcadbe2e986"}],"status":"public","publisher":"Mathematical Sciences Publishers","has_accepted_license":"1","article_type":"original","day":"05","department":[{"_id":"TiBr"}],"month":"09","volume":19,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","external_id":{"arxiv":["2310.01135"]},"citation":{"short":"T.D. Browning, J. Lyczak, A. Smeets, Algebra & Number Theory 19 (2025) 2049–2090.","mla":"Browning, Timothy D., et al. “Paucity of Rational Points on Fibrations with Multiple Fibres.” Algebra & Number Theory, vol. 19, no. 10, Mathematical Sciences Publishers, 2025, pp. 2049–90, doi:10.2140/ant.2025.19.2049.","ista":"Browning TD, Lyczak J, Smeets A. 2025. Paucity of rational points on fibrations with multiple fibres. Algebra & Number Theory. 19(10), 2049–2090.","chicago":"Browning, Timothy D, Julian Lyczak, and Arne Smeets. “Paucity of Rational Points on Fibrations with Multiple Fibres.” Algebra & Number Theory. Mathematical Sciences Publishers, 2025. https://doi.org/10.2140/ant.2025.19.2049.","ieee":"T. D. Browning, J. Lyczak, and A. Smeets, “Paucity of rational points on fibrations with multiple fibres,” Algebra & Number Theory, vol. 19, no. 10. Mathematical Sciences Publishers, pp. 2049–2090, 2025.","ama":"Browning TD, Lyczak J, Smeets A. Paucity of rational points on fibrations with multiple fibres. Algebra & Number Theory. 2025;19(10):2049-2090. doi:10.2140/ant.2025.19.2049","apa":"Browning, T. D., Lyczak, J., & Smeets, A. (2025). Paucity of rational points on fibrations with multiple fibres. Algebra & Number Theory. Mathematical Sciences Publishers. https://doi.org/10.2140/ant.2025.19.2049"},"project":[{"call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","name":"New frontiers of the Manin conjecture","grant_number":"P32428"}],"author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","first_name":"Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning"},{"first_name":"Julian","last_name":"Lyczak","full_name":"Lyczak, Julian"},{"first_name":"Arne","last_name":"Smeets","full_name":"Smeets, Arne"}],"quality_controlled":"1","year":"2025","OA_type":"diamond","file_date_updated":"2026-02-17T11:56:20Z","oa_version":"Published Version","doi":"10.2140/ant.2025.19.2049","publication_identifier":{"eissn":["1944-7833"],"issn":["1937-0652"]},"date_updated":"2026-07-16T08:52:36Z","date_published":"2025-09-05T00:00:00Z","title":"Paucity of rational points on fibrations with multiple fibres","abstract":[{"text":"Given a family of varieties over the projective line, we study the density of fibres that are everywhere locally soluble in the case that components of higher multiplicity are allowed. We use log geometry to formulate a new sparsity criterion for the existence of everywhere locally soluble fibres and formulate new conjectures that generalise previous work of Loughran and Smeets. These conjectures involve geometric invariants of the associated multiplicity orbifolds on the base of the fibration in the spirit of Campana. We give evidence for the conjectures by providing an assortment of bounds using Chebotarev’s theorem and sieve methods, with most of the evidence involving upper bounds. ","lang":"eng"}],"acknowledgement":"We are very grateful to Tim Santens for useful conversations and to the anonymous referees for numerous pertinent remarks. While working on this paper, Browning was supported by a FWF grant (DOI 10.55776/P32428), Lyczak was supported by UKRI MR/V021362/1, and Smeets was supported by grant G0B1721N of the Fund for Scientific Research – Flanders.","publication":"Algebra & Number Theory","publication_status":"published","oa":1,"language":[{"iso":"eng"}],"OA_place":"publisher","date_created":"2026-02-16T15:22:19Z","page":"2049-2090","supplementarymaterial":"no","type":"journal_article","arxiv":1,"article_processing_charge":"No","das_tickbox":"0","_id":"21244","ddc":["510"],"corr_author":"1","PlanS_conform":"1","intvolume":" 19","researchdata_availability":"no","issue":"10"},{"researchdata_availability":"no","issue":"3","corr_author":"1","intvolume":" 37","arxiv":1,"article_processing_charge":"Yes (in subscription journal)","ddc":["510"],"_id":"20850","das_tickbox":"0","date_created":"2025-12-21T23:01:35Z","page":"973-988","supplementarymaterial":"no","type":"journal_article","publication":"Journal de theorie des nombres de Bordeaux","publication_status":"published","oa":1,"language":[{"iso":"eng"}],"OA_place":"publisher","acknowledgement":"The author would like to thank his supervisor Tim Browning for suggesting this project and many helpful conversations and useful comments. Moreover, he is grateful to Jakob Glas, Damaris Schindler, Igor Shparlinski, Matteo Verzobio, Victor Wang, Florian Wilsch and Shuntaro Yamagishi for taking their time to answer his questions and their valuable suggestions.","date_published":"2025-11-27T00:00:00Z","title":"Class numbers and integer points on some Pellian surfaces","license":"https://creativecommons.org/licenses/by-nd/4.0/","abstract":[{"text":"We provide an estimate for the number of nontrivial integer points on the Pellian surface t^2 - du^2 = 1 in a bounded region. We give a lower bound on the size of fundamental solutions for almost all d in a certain class, based on a recent conjecture of Browning and Wilsch about integer points on log K3 surfaces. We also obtain an upper bound on the average of class number in this class, assuming the same conjecture.","lang":"eng"},{"lang":"fre","text":"Nous donnons une estimation du nombre de points entiers non triviaux sur la surface pellienne \r\nt^2 - du^2 = 1 dans une région bornée. Nous établissons une borne inférieure pour la taille des solutions fondamentales pour presque tout d appartenant à une certaine classe, en nous fondant sur une conjecture récente de Browning et Wilsch concernant les points entiers sur les surfaces log K3. Nous obtenons également une borne supérieure pour la moyenne du nombre de classes dans cette classe, sous la même hypothèse conjecturale."}],"doi":"10.5802/jtnb.1348","publication_identifier":{"issn":["1246-7405"],"eissn":["2118-8572"]},"date_updated":"2026-07-16T08:45:12Z","year":"2025","OA_type":"hybrid","file_date_updated":"2025-12-29T10:05:22Z","oa_version":"Published Version","quality_controlled":"1","author":[{"full_name":"Diao, Yijie","id":"7b7eb4ca-eb2c-11ec-b98b-accec0b20c3b","last_name":"Diao","first_name":"Yijie","orcid":"0000-0002-4989-5330"}],"citation":{"apa":"Diao, Y. (2025). Class numbers and integer points on some Pellian surfaces. Journal de Theorie Des Nombres de Bordeaux. Université de Bordeaux. https://doi.org/10.5802/jtnb.1348","ama":"Diao Y. Class numbers and integer points on some Pellian surfaces. Journal de theorie des nombres de Bordeaux. 2025;37(3):973-988. doi:10.5802/jtnb.1348","ieee":"Y. Diao, “Class numbers and integer points on some Pellian surfaces,” Journal de theorie des nombres de Bordeaux, vol. 37, no. 3. Université de Bordeaux, pp. 973–988, 2025.","chicago":"Diao, Yijie. “Class Numbers and Integer Points on Some Pellian Surfaces.” Journal de Theorie Des Nombres de Bordeaux. Université de Bordeaux, 2025. https://doi.org/10.5802/jtnb.1348.","ista":"Diao Y. 2025. Class numbers and integer points on some Pellian surfaces. Journal de theorie des nombres de Bordeaux. 37(3), 973–988.","mla":"Diao, Yijie. “Class Numbers and Integer Points on Some Pellian Surfaces.” Journal de Theorie Des Nombres de Bordeaux, vol. 37, no. 3, Université de Bordeaux, 2025, pp. 973–88, doi:10.5802/jtnb.1348.","short":"Y. Diao, Journal de Theorie Des Nombres de Bordeaux 37 (2025) 973–988."},"department":[{"_id":"TiBr"}],"month":"11","external_id":{"arxiv":["2408.03774"]},"volume":37,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_type":"original","day":"27","tmp":{"image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","short":"CC BY-ND (4.0)"},"file":[{"relation":"main_file","success":1,"file_id":"20861","checksum":"67aa0afbc0b5bcbff5341f4d25e6ba20","file_size":766196,"access_level":"open_access","creator":"dernst","file_name":"2025_JTNB_Diao.pdf","date_updated":"2025-12-29T10:05:22Z","content_type":"application/pdf","date_created":"2025-12-29T10:05:22Z"}],"scopus_import":"1","status":"public","publisher":"Université de Bordeaux","has_accepted_license":"1"},{"acknowledgement":"Supported by FWF grant (DOI 10.55776/P36278), Supported by European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant\r\nAgreement No. 101034413.","OA_place":"publisher","language":[{"iso":"eng"}],"oa":1,"publication_status":"published","publication":"Discrete Analysis","date_updated":"2026-07-16T08:48:35Z","publication_identifier":{"eissn":["2397-3129"]},"doi":"10.19086/da.143787","abstract":[{"lang":"eng","text":"We extend work of Heath-Brown and Salberger, based on the determinant method, to provide a uniform upper bound for the number of integral points of bounded height on an affine surface, which are subject to a polynomial congruence condition. This is applied to get a new uniform bound for points on diagonal quadric surfaces, and to a problem about the representation of integers as a sum of four unlike powers."}],"title":"Counting integer points on affine surfaces with a side condition","date_published":"2025-09-01T00:00:00Z","intvolume":" 2025","corr_author":"1","researchdata_availability":"no","supplementarymaterial":"no","type":"journal_article","date_created":"2026-01-18T23:02:44Z","_id":"21003","ddc":["510"],"das_tickbox":"0","article_processing_charge":"No","arxiv":1,"volume":2025,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","external_id":{"arxiv":["2408.11453"]},"month":"09","department":[{"_id":"TiBr"}],"citation":{"short":"T.D. Browning, M. Verzobio, Discrete Analysis 2025 (2025).","mla":"Browning, Timothy D., and Matteo Verzobio. “Counting Integer Points on Affine Surfaces with a Side Condition.” Discrete Analysis, vol. 2025, 12, Cambridge: Alliance of Diamond Open Access Journals, 2025, doi:10.19086/da.143787.","ista":"Browning TD, Verzobio M. 2025. Counting integer points on affine surfaces with a side condition. Discrete Analysis. 2025, 12.","apa":"Browning, T. D., & Verzobio, M. (2025). Counting integer points on affine surfaces with a side condition. Discrete Analysis. Cambridge: Alliance of Diamond Open Access Journals. https://doi.org/10.19086/da.143787","chicago":"Browning, Timothy D, and Matteo Verzobio. “Counting Integer Points on Affine Surfaces with a Side Condition.” Discrete Analysis. Cambridge: Alliance of Diamond Open Access Journals, 2025. https://doi.org/10.19086/da.143787.","ama":"Browning TD, Verzobio M. Counting integer points on affine surfaces with a side condition. Discrete Analysis. 2025;2025. doi:10.19086/da.143787","ieee":"T. D. Browning and M. Verzobio, “Counting integer points on affine surfaces with a side condition,” Discrete Analysis, vol. 2025. Cambridge: Alliance of Diamond Open Access Journals, 2025."},"has_accepted_license":"1","ec_funded":1,"file":[{"creator":"dernst","file_name":"2025_DiscreteAnalysis_Browning.pdf","access_level":"open_access","file_size":393625,"checksum":"3d38e850b40f3e1abbfd30073bd4388a","file_id":"21214","date_created":"2026-02-12T07:50:47Z","content_type":"application/pdf","date_updated":"2026-02-12T07:50:47Z","success":1,"relation":"main_file"}],"publisher":"Cambridge: Alliance of Diamond Open Access Journals","status":"public","scopus_import":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"article_type":"original","day":"01","article_number":"12","oa_version":"Published Version","file_date_updated":"2026-02-12T07:50:47Z","OA_type":"diamond","year":"2025","project":[{"_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","name":"Rational curves via function field analytic number theory","grant_number":"P36278"},{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","first_name":"Timothy D","last_name":"Browning"},{"last_name":"Verzobio","orcid":"0000-0002-0854-0306","first_name":"Matteo","full_name":"Verzobio, Matteo","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb"}]},{"citation":{"apa":"Yao Xiao, S., & Yamagishi, S. (2025). Quartic polynomials in two variables do not represent all non-negative integers. Journal of the European Mathematical Society. EMS Press. https://doi.org/10.4171/jems/1697","chicago":"Yao Xiao, Stanley, and Shuntaro Yamagishi. “Quartic Polynomials in Two Variables Do Not Represent All Non-Negative Integers.” Journal of the European Mathematical Society. EMS Press, 2025. https://doi.org/10.4171/jems/1697.","ama":"Yao Xiao S, Yamagishi S. Quartic polynomials in two variables do not represent all non-negative integers. Journal of the European Mathematical Society. 2025. doi:10.4171/jems/1697","ieee":"S. Yao Xiao and S. Yamagishi, “Quartic polynomials in two variables do not represent all non-negative integers,” Journal of the European Mathematical Society. EMS Press, 2025.","ista":"Yao Xiao S, Yamagishi S. 2025. Quartic polynomials in two variables do not represent all non-negative integers. Journal of the European Mathematical Society.","mla":"Yao Xiao, Stanley, and Shuntaro Yamagishi. “Quartic Polynomials in Two Variables Do Not Represent All Non-Negative Integers.” Journal of the European Mathematical Society, EMS Press, 2025, doi:10.4171/jems/1697.","short":"S. Yao Xiao, S. Yamagishi, Journal of the European Mathematical Society (2025)."},"department":[{"_id":"TiBr"}],"month":"08","external_id":{"arxiv":["2307.05712"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_type":"original","day":"06","publisher":"EMS Press","status":"public","year":"2025","OA_type":"diamond","oa_version":"Published Version","quality_controlled":"1","author":[{"full_name":"Yao Xiao, Stanley","last_name":"Yao Xiao","first_name":"Stanley"},{"full_name":"Yamagishi, Shuntaro","id":"0c3fbc5c-f7a6-11ec-8d70-9485e75b416b","last_name":"Yamagishi","first_name":"Shuntaro"}],"project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","name":"New frontiers of the Manin conjecture","call_identifier":"FWF"}],"publication_status":"epub_ahead","publication":"Journal of the European Mathematical Society","oa":1,"language":[{"iso":"eng"}],"OA_place":"publisher","acknowledgement":"The first author would like to thank Samir Siksek for introducing the problem\r\nto him. The material in Section 6 is a result of discussing with many people, and the second author is very grateful to Tim Browning, Stephanie Chan, Jakob Glas, Jakub Löwit, Mirko Mauri, Marta Pieropan, Mike Roth, Matteo Verzobio and Victor Wang for taking the time to answer his questions and for their valuable suggestions. We thank Tim Browning, Yijie Diao, Ana Marija Vego and the anonymous referee for their helpful comments.\r\nThe first author was supported by NSERC Discovery Grant RGPIN-2024-06810. The\r\nsecond author was supported by the NWO Veni Grant 016.Veni.192.047 during his time at\r\nUtrecht University and by a FWF grant (DOI 10.55776/P32428) at the Institute of Science and\r\nTechnology Austria while working on this paper.","main_file_link":[{"open_access":"1","url":"https://doi.org/10.4171/JEMS/1697"}],"date_published":"2025-08-06T00:00:00Z","title":"Quartic polynomials in two variables do not represent all non-negative integers","abstract":[{"lang":"eng","text":"We prove that there does not exist F∈Q[x,y] of degree 4 such that F(Z^2 )=Z ≥0. In particular, this answers a question by John S. Lew and Bjorn Poonen for quartic polynomials."}],"doi":"10.4171/jems/1697","publication_identifier":{"eissn":["1435-9863"],"issn":["1435-9855"]},"date_updated":"2026-07-16T08:54:37Z","researchdata_availability":"no","corr_author":"1","arxiv":1,"article_processing_charge":"No","_id":"21260","ddc":["500"],"das_tickbox":"0","date_created":"2026-02-16T16:00:02Z","supplementarymaterial":"no","type":"journal_article"},{"month":"01","department":[{"_id":"TiBr"}],"external_id":{"isi":["001388255500001"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","volume":71,"citation":{"apa":"Wang, V. (2025). Diagonal cubic forms and the large sieve. Mathematika. London Mathematical Society. https://doi.org/10.1112/mtk.70008","ieee":"V. Wang, “Diagonal cubic forms and the large sieve,” Mathematika, vol. 71, no. 1. London Mathematical Society, 2025.","ama":"Wang V. Diagonal cubic forms and the large sieve. Mathematika. 2025;71(1). doi:10.1112/mtk.70008","chicago":"Wang, Victor. “Diagonal Cubic Forms and the Large Sieve.” Mathematika. London Mathematical Society, 2025. https://doi.org/10.1112/mtk.70008.","ista":"Wang V. 2025. Diagonal cubic forms and the large sieve. Mathematika. 71(1), e70008.","mla":"Wang, Victor. “Diagonal Cubic Forms and the Large Sieve.” Mathematika, vol. 71, no. 1, e70008, London Mathematical Society, 2025, doi:10.1112/mtk.70008.","short":"V. Wang, Mathematika 71 (2025)."},"scopus_import":"1","file":[{"file_id":"18845","checksum":"700a8596b4bffce2320d074120962c22","file_size":309893,"access_level":"open_access","file_name":"2025_Mathematika_Wang.pdf","creator":"dernst","date_updated":"2025-01-14T06:52:09Z","content_type":"application/pdf","date_created":"2025-01-14T06:52:09Z","relation":"main_file","success":1}],"ec_funded":1,"publisher":"London Mathematical Society","status":"public","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"has_accepted_license":"1","article_type":"original","day":"02","quality_controlled":"1","OA_type":"hybrid","year":"2025","oa_version":"Published Version","article_number":"e70008","file_date_updated":"2025-01-14T06:52:09Z","isi":1,"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"}],"author":[{"full_name":"Wang, Victor","id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","last_name":"Wang","first_name":"Victor","orcid":"0000-0002-0704-7026"}],"acknowledgement":"I thank Peter Sarnak for suggesting projects that ultimately led to the present paper. I also thank him for many encouraging discussions, helpful comments, and references. Thanks also to Tim Browning, Trevor Wooley, and Nina Zubrilina for helpful comments, and to Levent Alpöge and Will Sawin for some interesting old discussions. I thank Yang Liu, Evan O'Dorney, Ashwin Sah, and Mark Sellke for conversations illuminating the combinatorics of an older, counting version of the present Lemma 4.9. Finally, special thanks are due to the editors and referees for their patience and help with the exposition. 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 Agreement No. 101034413.","oa":1,"publication":"Mathematika","publication_status":"published","OA_place":"publisher","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2041-7942"],"issn":["0025-5793"]},"doi":"10.1112/mtk.70008","date_updated":"2026-07-16T09:14:24Z","title":"Diagonal cubic forms and the large sieve","date_published":"2025-01-02T00:00:00Z","abstract":[{"lang":"eng","text":"Let N(X) be the number of integral zeros (mathematical equation). Works of Hooley and Heath-Brown imply (mathematical equation), if one assumes automorphy and grand Riemann hypothesis for certain Hasse–Weil L-functions. Assuming instead a natural large sieve inequality, we recover the same bound on N(X). This is part of a more general statement, for diagonal cubic forms in (mathematical equation) variables, where we allow approximations to Hasse–Weil L-functions."}],"corr_author":"1","intvolume":" 71","researchdata_availability":"no","issue":"1","date_created":"2025-01-12T23:04:01Z","type":"journal_article","supplementarymaterial":"no","article_processing_charge":"Yes (via OA deal)","das_tickbox":"0","_id":"18822","ddc":["510"]},{"status":"public","publisher":"Instytut Matematyczny","scopus_import":"1","day":"28","article_type":"original","month":"10","department":[{"_id":"TiBr"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","volume":221,"external_id":{"arxiv":["2304.02620"]},"citation":{"short":"S. Yamagishi, Acta Arithmetica 221 (2025) 141–151.","mla":"Yamagishi, Shuntaro. “Birch’s Theorem on Forms in Many Variables with a Hessian Condition.” Acta Arithmetica, vol. 221, no. 2, Instytut Matematyczny, 2025, pp. 141–51, doi:10.4064/aa241029-19-8.","ista":"Yamagishi S. 2025. Birch’s theorem on forms in many variables with a Hessian condition. Acta Arithmetica. 221(2), 141–151.","ieee":"S. Yamagishi, “Birch’s theorem on forms in many variables with a Hessian condition,” Acta Arithmetica, vol. 221, no. 2. Instytut Matematyczny, pp. 141–151, 2025.","ama":"Yamagishi S. Birch’s theorem on forms in many variables with a Hessian condition. Acta Arithmetica. 2025;221(2):141-151. doi:10.4064/aa241029-19-8","chicago":"Yamagishi, Shuntaro. “Birch’s Theorem on Forms in Many Variables with a Hessian Condition.” Acta Arithmetica. Instytut Matematyczny, 2025. https://doi.org/10.4064/aa241029-19-8.","apa":"Yamagishi, S. (2025). Birch’s theorem on forms in many variables with a Hessian condition. Acta Arithmetica. Instytut Matematyczny. https://doi.org/10.4064/aa241029-19-8"},"author":[{"full_name":"Yamagishi, Shuntaro","id":"0c3fbc5c-f7a6-11ec-8d70-9485e75b416b","last_name":"Yamagishi","first_name":"Shuntaro"}],"project":[{"_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","name":"Rational curves via function field analytic number theory","grant_number":"P36278"}],"quality_controlled":"1","OA_type":"green","year":"2025","oa_version":"Preprint","publication_identifier":{"eissn":["1730-6264"],"issn":["0065-1036"]},"doi":"10.4064/aa241029-19-8","date_updated":"2026-07-16T09:04:43Z","title":"Birch’s theorem on forms in many variables with a Hessian condition","date_published":"2025-10-28T00:00:00Z","abstract":[{"lang":"eng","text":"Let F∈Z[x1,…,xn] be a homogeneous form of degree d≥2, and V∗F the singular locus of the hypersurface {x∈AnC:F(x)=0}. A longstanding result of Birch states that there is a non-trivial integral solution to the equation F(x1,…,xn)=0 provided n>dimV∗F+(d−1)2d, and there is a non-singular solution in R and Qp for all primes p. We give a different formulation of this result. More precisely, we replace dimV∗F with a quantity HF defined in terms of the Hessian matrix of F. This quantity satisfies 0≤HF≤dimV∗F; therefore, we improve on the aforementioned result of Birch if HFJournal of the European Mathematical Society. 2025. doi:10.4171/jems/1704","chicago":"Browning, Timothy D, and Stephanie Chan. “Almost All Quadratic Twists of an Elliptic Curve Have No Integral Points.” Journal of the European Mathematical Society. EMS Press, 2025. https://doi.org/10.4171/jems/1704.","ieee":"T. D. Browning and S. Chan, “Almost all quadratic twists of an elliptic curve have no integral points,” Journal of the European Mathematical Society. EMS Press, 2025.","apa":"Browning, T. D., & Chan, S. (2025). Almost all quadratic twists of an elliptic curve have no integral points. Journal of the European Mathematical Society. EMS Press. https://doi.org/10.4171/jems/1704","short":"T.D. Browning, S. Chan, Journal of the European Mathematical Society (2025).","mla":"Browning, Timothy D., and Stephanie Chan. “Almost All Quadratic Twists of an Elliptic Curve Have No Integral Points.” Journal of the European Mathematical Society, EMS Press, 2025, doi:10.4171/jems/1704."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","external_id":{"arxiv":["2401.04375"]},"department":[{"_id":"TiBr"}],"month":"09","_id":"21266","ddc":["510"],"das_tickbox":"0","arxiv":1,"article_processing_charge":"No","type":"journal_article","supplementarymaterial":"no","date_created":"2026-02-17T07:46:26Z","researchdata_availability":"no","corr_author":"1","abstract":[{"lang":"eng","text":"For a given elliptic curve E in short Weierstrass form, we show that almost all quadratic twists E \r\nD have no integral points, as D ranges over square-free integers ordered by size. Our result is conditional on a weak form of the Hall–Lang conjecture in the case that E has partial 2-torsion. The proof uses a correspondence of Mordell and the reduction theory of binary quartic forms in order to transfer the problem to counting rational points of bounded height on a certain singular cubic surface, together with extensive use of cancellation in character sum estimates, drawn from Heath-Brown’s analysis of Selmer group statistics for the congruent number curve."}],"date_published":"2025-09-17T00:00:00Z","title":"Almost all quadratic twists of an elliptic curve have no integral points","date_updated":"2026-07-16T09:00:02Z","doi":"10.4171/jems/1704","publication_identifier":{"eissn":["1435-9863"],"issn":["1435-9855"]},"language":[{"iso":"eng"}],"OA_place":"publisher","DOAJ_listed":"1","publication_status":"epub_ahead","publication":"Journal of the European Mathematical Society","oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.4171/JEMS/1704"}],"acknowledgement":"The authors are grateful to Roger Heath-Brown and to the anonymous referees for useful comments. The first author was supported by an FWF grant (DOI 10.55776/P36278)."},{"abstract":[{"lang":"eng","text":"We explain how the (shifted) Ratios Conjecture for $L(s,\\chi )$ would extend a randomization argument of Harper from a conductor-limited range to an unlimited range of “beyond square-root cancellation” for character twists of the Liouville function. As a corollary, the Liouville function would have nontrivial cancellation in arithmetic progressions of modulus just exceeding the well-known square-root barrier. Morally, the paper passes from random matrices to random multiplicative functions."}],"title":"Harper’s beyond square-root conjecture","date_published":"2025-09-01T00:00:00Z","date_updated":"2026-07-16T08:57:40Z","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"doi":"10.1093/imrn/rnaf279","OA_place":"repository","language":[{"iso":"eng"}],"oa":1,"publication_status":"published","publication":"International Mathematics Research Notices","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2405.04094","open_access":"1"}],"acknowledgement":"The first author is supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101034413. The second author is supported by a Simons Junior Fellowship from Simons Foundation. We thank Paul Bourgade and Kannan Soundararajan for discussions on random matrices and probability, Alexandra Florea for helpful comments on the Ratios Conjecture, and Joni Teräväinen for providing several references. We are also grateful to Alexandra Florea, Adam Harper, Joni Teräväinen, and the referee for helpful comments on earlier drafts.","_id":"21265","das_tickbox":"0","article_processing_charge":"No","arxiv":1,"supplementarymaterial":"no","type":"journal_article","date_created":"2026-02-17T07:45:45Z","issue":"18","researchdata_availability":"no","intvolume":" 2025","day":"01","article_type":"original","scopus_import":"1","publisher":"Oxford University Press","status":"public","ec_funded":1,"citation":{"chicago":"Wang, Victor, and Max Wenqiang Xu. “Harper’s beyond Square-Root Conjecture.” International Mathematics Research Notices. Oxford University Press, 2025. https://doi.org/10.1093/imrn/rnaf279.","ieee":"V. Wang and M. W. Xu, “Harper’s beyond square-root conjecture,” International Mathematics Research Notices, vol. 2025, no. 18. Oxford University Press, 2025.","ama":"Wang V, Xu MW. Harper’s beyond square-root conjecture. International Mathematics Research Notices. 2025;2025(18). doi:10.1093/imrn/rnaf279","apa":"Wang, V., & Xu, M. W. (2025). Harper’s beyond square-root conjecture. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnaf279","ista":"Wang V, Xu MW. 2025. Harper’s beyond square-root conjecture. International Mathematics Research Notices. 2025(18), rnaf279.","mla":"Wang, Victor, and Max Wenqiang Xu. “Harper’s beyond Square-Root Conjecture.” International Mathematics Research Notices, vol. 2025, no. 18, rnaf279, Oxford University Press, 2025, doi:10.1093/imrn/rnaf279.","short":"V. Wang, M.W. Xu, International Mathematics Research Notices 2025 (2025)."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","external_id":{"arxiv":["2405.04094"]},"volume":2025,"month":"09","department":[{"_id":"TiBr"}],"project":[{"name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020"}],"author":[{"last_name":"Wang","orcid":"0000-0002-0704-7026","first_name":"Victor","full_name":"Wang, Victor","id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9"},{"full_name":"Xu, Max Wenqiang","last_name":"Xu","first_name":"Max Wenqiang"}],"article_number":"rnaf279","oa_version":"Preprint","OA_type":"green","year":"2025","quality_controlled":"1"},{"has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"publisher":"Mathematical Sciences Publishers","ec_funded":1,"file":[{"file_name":"2025_AlgebraNumberTheory_Faisant.pdf","creator":"dernst","file_size":2034433,"access_level":"open_access","checksum":"56299f55682528a7cd0136497ce8b383","file_id":"21307","date_created":"2026-02-17T13:17:00Z","content_type":"application/pdf","date_updated":"2026-02-17T13:17:00Z","success":1,"relation":"main_file"}],"status":"public","article_type":"original","day":"22","external_id":{"arxiv":["2302.07339"]},"volume":19,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","department":[{"_id":"TiBr"}],"month":"04","citation":{"ama":"Faisant L. Motivic distribution of rational curves and twisted products of toric varieties. Algebra & Number Theory. 2025;19:883-965. doi:10.2140/ant.2025.19.883","chicago":"Faisant, Loïs. “Motivic Distribution of Rational Curves and Twisted Products of Toric Varieties.” Algebra & Number Theory. Mathematical Sciences Publishers, 2025. https://doi.org/10.2140/ant.2025.19.883.","ieee":"L. Faisant, “Motivic distribution of rational curves and twisted products of toric varieties,” Algebra & Number Theory, vol. 19. Mathematical Sciences Publishers, pp. 883–965, 2025.","apa":"Faisant, L. (2025). Motivic distribution of rational curves and twisted products of toric varieties. Algebra & Number Theory. Mathematical Sciences Publishers. https://doi.org/10.2140/ant.2025.19.883","ista":"Faisant L. 2025. Motivic distribution of rational curves and twisted products of toric varieties. Algebra & Number Theory. 19, 883–965.","mla":"Faisant, Loïs. “Motivic Distribution of Rational Curves and Twisted Products of Toric Varieties.” Algebra & Number Theory, vol. 19, Mathematical Sciences Publishers, 2025, pp. 883–965, doi:10.2140/ant.2025.19.883.","short":"L. Faisant, Algebra & Number Theory 19 (2025) 883–965."},"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"}],"author":[{"id":"26ca6926-5797-11ee-9232-f8b51bd19631","full_name":"Faisant, Loïs","first_name":"Loïs","last_name":"Faisant"}],"quality_controlled":"1","file_date_updated":"2026-02-17T13:17:00Z","oa_version":"Published Version","year":"2025","OA_type":"diamond","date_updated":"2026-07-16T09:23:01Z","doi":"10.2140/ant.2025.19.883","publication_identifier":{"eissn":["1944-7833"]},"abstract":[{"text":"This work concerns asymptotical stabilisation phenomena occurring in the moduli space of sections of certain algebraic families over a smooth projective curve, whenever the generic fibre of the family is a smooth projective Fano variety, or not far from being Fano.\r\n We describe the expected behaviour of the class, in a ring of motivic integration, of the moduli space of sections of given numerical class. Up to an adequate normalisation, it should converge, when the class of the sections goes arbitrarily far from the boundary of the dual of the effective cone, to an effective element given by a motivic Euler product. Such a principle can be seen as an analogue for rational curves of the Batyrev-Manin-Peyre principle for rational points.\r\n The central tool of this article is the property of equidistribution of curves. We show that this notion does not depend on the choice of a model of the generic fibre, and that equidistribution of curves holds for smooth projective split toric varieties. As an application, we study the Batyrev-Manin-Peyre principle for curves on a certain kind of twisted products.","lang":"eng"}],"date_published":"2025-04-22T00:00:00Z","title":"Motivic distribution of rational curves and twisted products of toric varieties","acknowledgement":"I am very grateful to my Ph.D. advisor Emmanuel Peyre for all the remarks and suggestions he made during the writing of this article. I warmly thank Margaret Bilu and Tim Browning for some valuable comments they made on a preliminary version of this work. I would like to thank David Bourqui as well for several helpful conversations. Finally, I thank the anonymous referee for their very careful reading and their numerous comments and suggestions which helped me a lot in improving the exposition, besides fixing several typos, and Elizabeth Weaver for the final editing work. During the revision process of this work, the author received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.","language":[{"iso":"eng"}],"OA_place":"publisher","publication":"Algebra & Number Theory","publication_status":"published","oa":1,"type":"journal_article","supplementarymaterial":"no","date_created":"2025-02-18T13:33:14Z","page":"883-965","ddc":["510"],"_id":"19054","das_tickbox":"0","arxiv":1,"article_processing_charge":"No","intvolume":" 19","corr_author":"1","PlanS_conform":"1","researchdata_availability":"no"},{"citation":{"ista":"Chan S, Koymans P, Pagano C, Sofos E. 2025. Averages of multiplicative functions along equidistributed sequences. Journal of Number Theory. 273, 1–36.","apa":"Chan, S., Koymans, P., Pagano, C., & Sofos, E. (2025). Averages of multiplicative functions along equidistributed sequences. Journal of Number Theory. Elsevier. https://doi.org/10.1016/j.jnt.2025.01.005","ama":"Chan S, Koymans P, Pagano C, Sofos E. Averages of multiplicative functions along equidistributed sequences. Journal of Number Theory. 2025;273:1-36. doi:10.1016/j.jnt.2025.01.005","ieee":"S. Chan, P. Koymans, C. Pagano, and E. Sofos, “Averages of multiplicative functions along equidistributed sequences,” Journal of Number Theory, vol. 273. Elsevier, pp. 1–36, 2025.","chicago":"Chan, Stephanie, Peter Koymans, Carlo Pagano, and Efthymios Sofos. “Averages of Multiplicative Functions along Equidistributed Sequences.” Journal of Number Theory. Elsevier, 2025. https://doi.org/10.1016/j.jnt.2025.01.005.","short":"S. Chan, P. Koymans, C. Pagano, E. Sofos, Journal of Number Theory 273 (2025) 1–36.","mla":"Chan, Stephanie, et al. “Averages of Multiplicative Functions along Equidistributed Sequences.” Journal of Number Theory, vol. 273, Elsevier, 2025, pp. 1–36, doi:10.1016/j.jnt.2025.01.005."},"department":[{"_id":"TiBr"}],"month":"08","volume":273,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","external_id":{"isi":["001444208500001"]},"article_type":"original","day":"01","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"publisher":"Elsevier","scopus_import":"1","status":"public","file":[{"date_updated":"2025-12-30T08:05:42Z","content_type":"application/pdf","date_created":"2025-12-30T08:05:42Z","file_id":"20889","checksum":"752c407eb186d391380b10a7505f66cf","file_size":685204,"access_level":"open_access","creator":"dernst","file_name":"2025_JourNumberTheory_Chan.pdf","relation":"main_file","success":1}],"has_accepted_license":"1","year":"2025","OA_type":"hybrid","file_date_updated":"2025-12-30T08:05:42Z","oa_version":"Published Version","quality_controlled":"1","author":[{"full_name":"Chan, Yik Tung","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","last_name":"Chan","orcid":"0000-0001-8467-4106","first_name":"Yik Tung"},{"last_name":"Koymans","first_name":"Peter","full_name":"Koymans, Peter"},{"full_name":"Pagano, Carlo","last_name":"Pagano","first_name":"Carlo"},{"last_name":"Sofos","first_name":"Efthymios","full_name":"Sofos, Efthymios"}],"isi":1,"publication_status":"published","publication":"Journal of Number Theory","oa":1,"dataavailabilitystatement":"No data was used for the research described in the article.","language":[{"iso":"eng"}],"OA_place":"publisher","date_published":"2025-08-01T00:00:00Z","title":"Averages of multiplicative functions along equidistributed sequences","abstract":[{"lang":"eng","text":"For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence."}],"doi":"10.1016/j.jnt.2025.01.005","publication_identifier":{"issn":["0022-314X"]},"date_updated":"2026-07-16T09:26:47Z","researchdata_availability":"no","corr_author":"1","PlanS_conform":"1","intvolume":" 273","article_processing_charge":"Yes (in subscription journal)","ddc":["510"],"_id":"19363","das_tickbox":"1","date_created":"2025-03-09T23:01:26Z","page":"1-36","supplementarymaterial":"no","type":"journal_article"},{"doi":"10.48550/ARXIV.2502.11704","date_updated":"2026-07-16T09:24:48Z","date_published":"2025-02-17T00:00:00Z","title":"Motivic counting of rational curves with tangency conditions via universal torsors","abstract":[{"text":"Using the formalism of Cox rings and universal torsors, we prove a decomposition of the Grothendieck motive of the moduli space of morphisms from an arbitrary smooth projective curve to a Mori Dream Space (MDS).\r\n For the simplest cases of MDS, that of toric varieties, we use this decomposition to prove an instance of the motivic Batyrev--Manin--Peyre principle for curves satisfying tangency conditions with respect to the boundary divisors, often called Campana curves.","lang":"eng"}],"acknowledgement":"The author acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413.\r\n","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2502.11704"}],"publication":"arXiv","publication_status":"submitted","oa":1,"language":[{"iso":"eng"}],"OA_place":"repository","date_created":"2025-02-18T13:34:07Z","supplementarymaterial":"no","type":"preprint","arxiv":1,"article_processing_charge":"No","das_tickbox":"0","_id":"19055","corr_author":"1","researchdata_availability":"no","status":"public","ec_funded":1,"day":"17","department":[{"_id":"TiBr"}],"month":"02","external_id":{"arxiv":["2502.11704"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"apa":"Faisant, L. (n.d.). Motivic counting of rational curves with tangency conditions via universal torsors. arXiv. https://doi.org/10.48550/ARXIV.2502.11704","chicago":"Faisant, Loïs. “Motivic Counting of Rational Curves with Tangency Conditions via Universal Torsors.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2502.11704.","ama":"Faisant L. Motivic counting of rational curves with tangency conditions via universal torsors. arXiv. doi:10.48550/ARXIV.2502.11704","ieee":"L. Faisant, “Motivic counting of rational curves with tangency conditions via universal torsors,” arXiv. .","ista":"Faisant L. Motivic counting of rational curves with tangency conditions via universal torsors. arXiv, 2502.11704.","mla":"Faisant, Loïs. “Motivic Counting of Rational Curves with Tangency Conditions via Universal Torsors.” ArXiv, 2502.11704, doi:10.48550/ARXIV.2502.11704.","short":"L. Faisant, ArXiv (n.d.)."},"author":[{"last_name":"Faisant","first_name":"Loïs","full_name":"Faisant, Loïs","id":"26ca6926-5797-11ee-9232-f8b51bd19631"}],"project":[{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"year":"2025","OA_type":"green","oa_version":"Preprint","article_number":"2502.11704"},{"article_processing_charge":"Yes (via OA deal)","arxiv":1,"ddc":["510"],"_id":"19776","das_tickbox":"0","date_created":"2025-06-03T07:30:21Z","supplementarymaterial":"no","type":"journal_article","researchdata_availability":"no","issue":"4","corr_author":"1","intvolume":" 310","title":"Optimal sums of three cubes in Fq[t]","date_published":"2025-05-23T00:00:00Z","abstract":[{"lang":"eng","text":"We use the circle method to prove that a density 1 of elements in Fq[t] are representable as a sum of three cubes of essentially minimal degree from Fq[t], assuming the Ratios Conjecture and that char(Fq)>3. Roughly speaking, to do so, we upgrade an order of magnitude result to a full asymptotic formula that was conjectured by Hooley in the number field setting."}],"publication_identifier":{"eissn":["1432-1823"],"issn":["0025-5874"]},"doi":"10.1007/s00209-025-03765-z","date_updated":"2026-07-16T10:50:51Z","oa":1,"publication_status":"published","publication":"Mathematische Zeitschrift","OA_place":"publisher","language":[{"iso":"eng"}],"acknowledgement":"We thank Alexandra Florea for discussions on cubic Gauss sums over function fields, in addition to the anonymous referee for helpful comments. While working on this paper the first two authors were supported by a FWF grant (DOI 10.55776/P36278) and the third author was supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413. Open access funding provided by Institute of Science and Technology (IST Austria).","project":[{"_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","name":"Rational curves via function field analytic number theory","grant_number":"P36278"},{"call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"author":[{"last_name":"Browning","orcid":"0000-0002-8314-0177","first_name":"Timothy D","full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"id":"d6423cba-dc74-11ea-a0a7-ee61689ff5fb","full_name":"Glas, Jakob","first_name":"Jakob","last_name":"Glas"},{"id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","full_name":"Wang, Victor","orcid":"0000-0002-0704-7026","first_name":"Victor","last_name":"Wang"}],"isi":1,"OA_type":"hybrid","year":"2025","oa_version":"Published Version","article_number":"65","file_date_updated":"2025-06-03T08:28:14Z","quality_controlled":"1","article_type":"original","day":"23","publisher":"Springer Nature","status":"public","file":[{"access_level":"open_access","file_size":461622,"file_id":"19782","checksum":"6f71e25740c28257bf89b8bf116c2b4d","creator":"dernst","file_name":"2025_MathZeitschrift_Browning.pdf","date_updated":"2025-06-03T08:28:14Z","date_created":"2025-06-03T08:28:14Z","content_type":"application/pdf","success":1,"relation":"main_file"}],"ec_funded":1,"scopus_import":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"has_accepted_license":"1","citation":{"short":"T.D. Browning, J. Glas, V. Wang, Mathematische Zeitschrift 310 (2025).","mla":"Browning, Timothy D., et al. “Optimal Sums of Three Cubes in Fq[T].” Mathematische Zeitschrift, vol. 310, no. 4, 65, Springer Nature, 2025, doi:10.1007/s00209-025-03765-z.","ista":"Browning TD, Glas J, Wang V. 2025. Optimal sums of three cubes in Fq[t]. Mathematische Zeitschrift. 310(4), 65.","chicago":"Browning, Timothy D, Jakob Glas, and Victor Wang. “Optimal Sums of Three Cubes in Fq[T].” Mathematische Zeitschrift. Springer Nature, 2025. https://doi.org/10.1007/s00209-025-03765-z.","ieee":"T. D. Browning, J. Glas, and V. Wang, “Optimal sums of three cubes in Fq[t],” Mathematische Zeitschrift, vol. 310, no. 4. Springer Nature, 2025.","ama":"Browning TD, Glas J, Wang V. Optimal sums of three cubes in Fq[t]. Mathematische Zeitschrift. 2025;310(4). doi:10.1007/s00209-025-03765-z","apa":"Browning, T. D., Glas, J., & Wang, V. (2025). Optimal sums of three cubes in Fq[t]. Mathematische Zeitschrift. Springer Nature. https://doi.org/10.1007/s00209-025-03765-z"},"month":"05","department":[{"_id":"TiBr"}],"volume":310,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","external_id":{"arxiv":["2408.03668 "],"isi":["001494367000001"]}}]