--- OA_place: publisher _id: '20556' abstract: - lang: eng 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." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Charlotte full_name: Hoffmann, Charlotte id: 0f78d746-dc7d-11ea-9b2f-83f92091afe7 last_name: Hoffmann orcid: 0000-0003-2027-5549 citation: ama: Hoffmann C. Theory and applications of verifiable delay functions. 2025. doi: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 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. ieee: C. Hoffmann, “Theory and applications of verifiable delay functions,” Institute of Science and Technology Austria, 2025. 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. corr_author: '1' date_created: 2025-10-27T14:16:56Z date_published: 2025-10-31T00:00:00Z date_updated: 2026-07-06T13:15:27Z day: '31' ddc: - '004' degree_awarded: PhD department: - _id: GradSch - _id: KrPi doi: 10.15479/AT-ISTA-20556 file: - access_level: closed checksum: 1fffa4e2c33dd0b9f883d615504a2858 content_type: application/pdf creator: choffman date_created: 2025-10-28T14:33:03Z date_updated: 2026-01-08T14:11:39Z file_id: '20573' file_name: 2025_Hoffmann_Charlotte_Thesis.pdf file_size: 2259304 relation: main_file - access_level: closed checksum: 076ea98a1f0a86c3bbc990b6b9460dc2 content_type: application/x-zip-compressed creator: choffman date_created: 2025-10-28T14:35:06Z date_updated: 2025-11-11T09:34:54Z file_id: '20574' file_name: 2025_Hoffmann_Charlotte_Source.zip file_size: 9987633 relation: source_file file_date_updated: 2026-01-08T14:11:39Z has_accepted_license: '1' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-sa/4.0/ month: '10' oa_version: Published Version page: '116' publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '13143' relation: part_of_dissertation status: public - id: '12176' relation: part_of_dissertation status: public - id: '20920' relation: later_version status: public - id: '19778' relation: part_of_dissertation status: public - id: '20701' relation: part_of_dissertation status: public status: public supervisor: - first_name: Krzysztof Z full_name: Pietrzak, Krzysztof Z id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87 last_name: Pietrzak orcid: 0000-0002-9139-1654 title: Theory and applications of verifiable delay functions tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2025' ... --- OA_place: repository OA_type: green _id: '10011' abstract: - lang: eng 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. 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. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Sebastian full_name: Hensel, Sebastian id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87 last_name: Hensel orcid: 0000-0001-7252-8072 - first_name: Tim full_name: Laux, Tim last_name: Laux citation: 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' 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' 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. corr_author: '1' das_tickbox: '1' date_created: 2021-09-13T12:17:10Z date_published: 2025-05-01T00:00:00Z date_updated: 2026-07-06T13:37:21Z day: '01' department: - _id: JuFi doi: 10.4310/jdg/1747065796 ec_funded: 1 external_id: arxiv: - '2109.04233' intvolume: ' 130' keyword: - Mean curvature flow - gradient flows - varifolds - weak solutions - weak-strong uniqueness - calibrated geometry - gradient-flow calibrations language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2109.04233 month: '05' oa: 1 oa_version: Preprint page: 209-268 project: - _id: 0aa76401-070f-11eb-9043-b5bb049fa26d call_identifier: H2020 grant_number: '948819' name: Bridging Scales in Random Materials publication: Journal of Differential Geometry publication_identifier: eissn: - 1945-743X issn: - 0022-040X publication_status: published publisher: International Press of Boston quality_controlled: '1' scopus_import: '1' status: public title: 'A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 130 year: '2025' ... --- OA_place: publisher OA_type: gold _id: '20004' abstract: - lang: eng 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." alternative_title: - LIPIcs article_number: '75' article_processing_charge: Yes arxiv: 1 author: - first_name: Elizaveta full_name: Streltsova, Elizaveta id: 57a170da-dc96-11ea-b7c8-ab3565071bf7 last_name: Streltsova - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: 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' 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' 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.' 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.' 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.' short: E. Streltsova, U. Wagner, in:, 41st International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. conference: end_date: 2025-06-27 location: Kanazawa, Japan name: 'SoCG: Symposium on Computational Geometry' start_date: 2025-06-23 corr_author: '1' das_tickbox: '1' date_created: 2025-07-13T22:01:22Z date_published: 2025-06-20T00:00:00Z date_updated: 2026-07-07T13:03:16Z day: '20' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2025.75 external_id: arxiv: - '2504.07752' - '2504.07770' file: - access_level: open_access checksum: a8f7feb1aa3b896e31195841a989d622 content_type: application/pdf creator: dernst date_created: 2025-07-14T07:11:04Z date_updated: 2025-07-14T07:11:04Z file_id: '20015' file_name: 2025_LIPIcs.SoCG_Streltsova.pdf file_size: 952807 relation: main_file success: 1 file_date_updated: 2025-07-14T07:11:04Z has_accepted_license: '1' intvolume: ' 332' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: 41st International Symposium on Computational Geometry publication_identifier: eissn: - 1868-8969 isbn: - '9783959773706' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: 'Levels in arrangements: Linear relations, the g-matrix, and applications to crossing numbers' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 332 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '19733' abstract: - lang: eng 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. 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). article_number: L050402 article_processing_charge: No article_type: letter_note arxiv: 1 author: - first_name: Daniel full_name: Kun, Daniel last_name: Kun - first_name: Karl T full_name: Strömberg, Karl T id: 68011cd2-da32-11ee-a930-b2774c7aba5f last_name: Strömberg - first_name: Michele full_name: Spagnolo, Michele last_name: Spagnolo - first_name: Borivoje full_name: Dakić, Borivoje last_name: Dakić - first_name: Lee A. full_name: Rozema, Lee A. last_name: Rozema - first_name: Philip full_name: Walther, Philip last_name: Walther citation: 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 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 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. 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. 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). das_tickbox: '1' dataavailabilitystatement: Data that support the findings of this study are openly available at Zenodo. date_created: 2025-05-25T22:16:54Z date_published: 2025-05-16T00:00:00Z date_updated: 2026-07-07T14:05:51Z day: '16' ddc: - '530' department: - _id: OnHo doi: 10.1103/PhysRevA.111.L050402 external_id: arxiv: - '2405.08065' isi: - '001501941500006' file: - access_level: open_access checksum: b83295a8f597b7781d8e7bfa3b393b42 content_type: application/pdf creator: dernst date_created: 2025-05-28T09:16:03Z date_updated: 2025-05-28T09:16:03Z file_id: '19755' file_name: 2025_PhysReviewA_Kun.pdf file_size: 571784 relation: main_file success: 1 file_date_updated: 2025-05-28T09:16:03Z has_accepted_license: '1' intvolume: ' 111' isi: 1 issue: '5' language: - iso: eng month: '05' oa: 1 oa_version: Published Version publication: Physical Review A publication_identifier: eissn: - 2469-9934 issn: - 2469-9926 publication_status: published publisher: American Physical Society quality_controlled: '1' related_material: record: - id: '22142' relation: research_data status: public researchdata_availability: yes scopus_import: '1' status: public supplementarymaterial: yes title: Direct and efficient detection of quantum superposition tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 68b8ca59-c5b3-11ee-8790-cd641c68093d volume: 111 year: '2025' ... --- OA_place: repository OA_type: green _id: '22142' abstract: - lang: eng 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." article_processing_charge: No author: - first_name: Daniel full_name: Kun, Daniel last_name: Kun citation: ama: Kun D. Direct And Efficient Detection of Quantum Superposition - Data and Figures. 2025. doi:10.5281/zenodo.13375452 apa: Kun, D. (2025). Direct And Efficient Detection of Quantum Superposition - Data and Figures. Zenodo. https://doi.org/10.5281/zenodo.13375452 chicago: Kun, Daniel. “Direct And Efficient Detection of Quantum Superposition - Data and Figures.” Zenodo, 2025. https://doi.org/10.5281/zenodo.13375452. ieee: D. Kun, “Direct And Efficient Detection of Quantum Superposition - Data and Figures.” Zenodo, 2025. 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). contributor: - contributor_type: researcher first_name: Lee last_name: Rozema - contributor_type: researcher first_name: Teodor last_name: Stroemberg - contributor_type: supervisor first_name: Philip last_name: Walther - contributor_type: supervisor first_name: Borivoje last_name: Dakic date_created: 2026-06-25T11:08:53Z date_published: 2025-04-24T00:00:00Z date_updated: 2026-07-07T14:05:51Z day: '24' ddc: - '530' department: - _id: OnHo doi: 10.5281/zenodo.13375452 main_file_link: - open_access: '1' url: https://doi.org/10.5281/zenodo.13375452 month: '4' oa: 1 oa_version: Published Version publisher: Zenodo related_material: record: - id: '19733' relation: used_in_publication status: public status: public title: Direct And Efficient Detection of Quantum Superposition - Data and Figures type: research_data_reference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2025' ... --- DOAJ_listed: '1' OA_place: publisher OA_type: gold _id: '19636' 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). 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." article_number: '42' article_processing_charge: Yes article_type: review arxiv: 1 author: - first_name: Adam full_name: Abdalla, Adam last_name: Abdalla - first_name: Mahiro full_name: Abe, Mahiro last_name: Abe - first_name: Sven full_name: Abend, Sven last_name: Abend - first_name: Mouine full_name: Abidi, Mouine last_name: Abidi - first_name: Monika full_name: Aidelsburger, Monika last_name: Aidelsburger - first_name: Ashkan full_name: Alibabaei, Ashkan last_name: Alibabaei - first_name: Baptiste full_name: Allard, Baptiste last_name: Allard - first_name: John full_name: Antoniadis, John last_name: Antoniadis - first_name: Gianluigi full_name: Arduini, Gianluigi last_name: Arduini - first_name: Nadja full_name: Augst, Nadja last_name: Augst - first_name: Philippos full_name: Balamatsias, Philippos last_name: Balamatsias - first_name: Antun full_name: Balaž, Antun last_name: Balaž - first_name: Hannah full_name: Banks, Hannah last_name: Banks - first_name: Rachel L. full_name: Barcklay, Rachel L. last_name: Barcklay - first_name: Michele full_name: Barone, Michele last_name: Barone - first_name: Michele full_name: Barsanti, Michele last_name: Barsanti - first_name: Mark G. full_name: Bason, Mark G. last_name: Bason - first_name: Angelo full_name: Bassi, Angelo last_name: Bassi - first_name: Jean Baptiste full_name: Bayle, Jean Baptiste last_name: Bayle - first_name: Charles F.A. full_name: Baynham, Charles F.A. last_name: Baynham - first_name: Quentin full_name: Beaufils, Quentin last_name: Beaufils - first_name: Sélyan full_name: Beldjoudi, Sélyan last_name: Beldjoudi - first_name: Aleksandar full_name: Belić, Aleksandar last_name: Belić - first_name: Shayne full_name: Bennetts, Shayne last_name: Bennetts - first_name: Jose full_name: Bernabeu, Jose last_name: Bernabeu - first_name: Andrea full_name: Bertoldi, Andrea last_name: Bertoldi - first_name: Clara full_name: Bigard, Clara last_name: Bigard - first_name: N. 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first_name: Ingmari C. full_name: Tietje, Ingmari C. last_name: Tietje - first_name: Guglielmo M. full_name: Tino, Guglielmo M. last_name: Tino - first_name: Jonathan N. full_name: Tinsley, Jonathan N. last_name: Tinsley - first_name: Ovidiu full_name: Tintareanu Mircea, Ovidiu last_name: Tintareanu Mircea - first_name: Kimberly full_name: Tkalčec, Kimberly last_name: Tkalčec - first_name: Andrew J. full_name: Tolley, Andrew J. last_name: Tolley - first_name: Vincenza full_name: Tornatore, Vincenza last_name: Tornatore - first_name: Alejandro full_name: Torres-Orjuela, Alejandro last_name: Torres-Orjuela - first_name: Philipp full_name: Treutlein, Philipp last_name: Treutlein - first_name: Andrea full_name: Trombettoni, Andrea last_name: Trombettoni - first_name: Christian full_name: Ufrecht, Christian last_name: Ufrecht - first_name: Juan full_name: Urrutia, Juan last_name: Urrutia - first_name: Tristan full_name: Valenzuela, Tristan last_name: Valenzuela - first_name: Linda R. full_name: Valerio, Linda R. last_name: Valerio - first_name: Maurits full_name: Van Der Grinten, Maurits last_name: Van Der Grinten - first_name: Ville full_name: Vaskonen, Ville last_name: Vaskonen - first_name: Verónica full_name: Vázquez-Aceves, Verónica last_name: Vázquez-Aceves - first_name: Hardi full_name: Veermäe, Hardi last_name: Veermäe - first_name: Flavio full_name: Vetrano, Flavio last_name: Vetrano - first_name: Nikolay V. full_name: Vitanov, Nikolay V. last_name: Vitanov - first_name: Wolf full_name: Von Klitzing, Wolf last_name: Von Klitzing - first_name: Sebastian full_name: Wald, Sebastian id: 133F200A-B015-11E9-AD41-0EDAE5697425 last_name: Wald orcid: 0000-0002-5869-1604 - first_name: Thomas full_name: Walker, Thomas last_name: Walker - first_name: Reinhold full_name: Walser, Reinhold last_name: Walser - first_name: Jin full_name: Wang, Jin last_name: Wang - first_name: Yan full_name: Wang, Yan last_name: Wang - first_name: C. A. full_name: Weidner, C. A. last_name: Weidner - first_name: André full_name: Wenzlawski, André last_name: Wenzlawski - first_name: Michael full_name: Werner, Michael last_name: Werner - first_name: Lisa full_name: Wörner, Lisa last_name: Wörner - first_name: Mohamed E. full_name: Yahia, Mohamed E. last_name: Yahia - first_name: Efe full_name: Yazgan, Efe last_name: Yazgan - first_name: Emmanuel full_name: Zambrini Cruzeiro, Emmanuel last_name: Zambrini Cruzeiro - first_name: M. full_name: Zarei, M. last_name: Zarei - first_name: Mingsheng full_name: Zhan, Mingsheng last_name: Zhan - first_name: Shengnan full_name: Zhang, Shengnan last_name: Zhang - first_name: Lin full_name: Zhou, Lin last_name: Zhou - first_name: Erik full_name: Zupanič, Erik last_name: Zupanič citation: ama: 'Abdalla A, Abe M, Abend S, et al. Terrestrial Very-Long-Baseline Atom Interferometry: Summary of the second workshop. EPJ Quantum Technology. 2025;12. doi:10.1140/epjqt/s40507-025-00344-3' apa: 'Abdalla, A., Abe, M., Abend, S., Abidi, M., Aidelsburger, M., Alibabaei, A., … Zupanič, E. (2025). Terrestrial Very-Long-Baseline Atom Interferometry: Summary of the second workshop. EPJ Quantum Technology. Springer Nature. https://doi.org/10.1140/epjqt/s40507-025-00344-3' chicago: 'Abdalla, Adam, Mahiro Abe, Sven Abend, Mouine Abidi, Monika Aidelsburger, Ashkan Alibabaei, Baptiste Allard, et al. “Terrestrial Very-Long-Baseline Atom Interferometry: Summary of the Second Workshop.” EPJ Quantum Technology. Springer Nature, 2025. https://doi.org/10.1140/epjqt/s40507-025-00344-3.' ieee: 'A. Abdalla et al., “Terrestrial Very-Long-Baseline Atom Interferometry: Summary of the second workshop,” EPJ Quantum Technology, vol. 12. Springer Nature, 2025.' ista: 'Abdalla A et al. 2025. Terrestrial Very-Long-Baseline Atom Interferometry: Summary of the second workshop. EPJ Quantum Technology. 12, 42.' mla: 'Abdalla, Adam, et al. “Terrestrial Very-Long-Baseline Atom Interferometry: Summary of the Second Workshop.” EPJ Quantum Technology, vol. 12, 42, Springer Nature, 2025, doi:10.1140/epjqt/s40507-025-00344-3.' short: A. Abdalla, M. Abe, S. Abend, M. Abidi, M. Aidelsburger, A. Alibabaei, B. Allard, J. Antoniadis, G. Arduini, N. Augst, P. Balamatsias, A. Balaž, H. Banks, R.L. Barcklay, M. Barone, M. Barsanti, M.G. Bason, A. Bassi, J.B. Bayle, C.F.A. Baynham, Q. Beaufils, S. Beldjoudi, A. Belić, S. Bennetts, J. Bernabeu, A. Bertoldi, C. Bigard, N.P. Bigelow, R. Bingham, D. Blas, A. Bobrick, S. Boehringer, A. Bogojević, K. Bongs, D. Bortoletto, P. Bouyer, C. Brand, O. Buchmueller, G. Buica, S. Calatroni, L. Calmels, P. Canizares, B. Canuel, A. Caramete, L.I. Caramete, M. Carlesso, J. Carlton, S.P. Carman, A. Carroll, M. Casariego, M. Chairetis, V. Charmandaris, U. Chauhan, J. Chen, M.L.M.L.M. Chiofalo, D. Ciampini, A. Cimbri, P. Cladé, J. Coleman, F.L. Constantin, C.R. Contaldi, R. Corgier, B. Dash, G.J. Davies, C. De Rham, A. De Roeck, D. Derr, S. Dey, F. Di Pumpo, G.S. Djordjevic, B. Döbrich, P. Dornan, M. Doser, G. Drougakis, J. Dunningham, A. Duspayev, S. Easo, J. Eby, M. Efremov, G. Elertas, J. Ellis, N. Entin, S. Fairhurst, M. Fanì, F. Fassi, P. Fayet, D. Felea, J. Feng, R. Flack, C. Foot, T. Freegarde, E. Fuchs, N. Gaaloul, D. Gao, S. Gardner, B.M. Garraway, C.L. Garrido Alzar, A. Gauguet, E. Giese, P. Gill, G.F. Giudice, E.P. Glasbrenner, J. Glick, P.W. Graham, E. Granados, P.F. Griffin, J. Gué, S. Guellati-Khelifa, S. Gupta, V. Gupta, L. Hackermueller, M. Haehnelt, T. Hakulinen, K. Hammerer, E.T. Hanımeli, T. Harte, S. Hartmann, L. Hawkins, A. Hees, A. Herbst, T.M. Hird, R. Hobson, J. Hogan, B. Holst, M. Holynski, O. Hosten, C.C. Hsu, W.C.W. Huang, K.M. Hughes, K. Hussain, G. Hütsi, A. Iovino, M.C. Isfan, G. Janson, P. Jeglič, P. Jetzer, Y. Jiang, G. Juzeliūnas, W. Kaenders, M. Kalliokoski, A. Kehagias, E. Kilian, C. Klempt, P. Knight, S. Koley, B. Konrad, T. Kovachy, M. Krutzik, M. Kumar, P. Kumar, H. Labiad, S.Y. Lan, A. Landragin, G. Landsberg, M. Langlois, B. Lanigan, B. Leone, C. Le Poncin-Lafitte, S. Lellouch, M. Lewicki, Y.H. Lien, L. Lombriser, E.L. Asamar, J.L. Lopez-Gonzalez, C. Lu, G.G. Luciano, N. Lundblad, C. De J. López Monjaraz, A. Lowe, M. Mackoit-Sinkevičienė, M. Maggiore, A. Majumdar, K. Makris, A. Maleknejad, A.L. Marchant, A. Mariotti, C. Markou, B. Matthews, A. Mazumdar, C. Mccabe, M. Meister, G. Mentasti, J. Menu, G. Messineo, B. Meyer-Hoppe, S. Micalizio, F. Migliaccio, P. Millington, M. Milosevic, A. Mishra, J. Mitchell, G.W. Morley, N. Mouelle, J. Müller, D. Newbold, W.T. Ni, C. Niehof, J. Noller, S. Odžak, D.K.L. Oi, A. Oikonomou, Y. Omar, C. Overstreet, V. Puthiya Veettil, J. Pahl, S. Paling, Z. Pan, G. Pappas, V. Pareek, E. Pasatembou, M. Paternostro, V.K. Pathak, E. Pelucchi, F. Pereira Dos Santos, A. Peters, A. Pichery, I. Pikovski, A. Pilaftsis, F.C. Pislan, R. Plunkett, R. Poggiani, M. Prevedelli, J. Rafelski, J. Raidal, M. Raidal, E.M. Rasel, S. Renaux-Petel, A. Richaud, P. Rivero-Antunez, T. Rodzinka, A. Roura, J. Rudolph, D. Sabulsky, M.S. Safronova, M. Sakellariadou, L. Salvi, M. Sameed, S. Sarkar, P. Schach, S.A. Schäffer, J. Schelfhout, M. Schilling, V. Schkolnik, W.P. Schleich, D. Schlippert, U. Schneider, F. Schreck, A. Schwartzman, N. Schwersenz, O. Sergijenko, H.R. Sfar, L. Shao, I. Shipsey, J. Shu, Y. Singh, C.F. Sopuerta, M. Sorba, F. Sorrentino, A.D.A.M. Spallicci, P. Stefanescu, N. Stergioulas, D. Stoerk, H. Thaivalappil Sunilkumar, J. Ströhle, Z. Tam, D. Tandon, Y. Tang, D. Tell, J. Tempere, D.J. Temples, R.P. Thampy, I.C. Tietje, G.M. Tino, J.N. Tinsley, O. Tintareanu Mircea, K. Tkalčec, A.J. Tolley, V. Tornatore, A. Torres-Orjuela, P. Treutlein, A. Trombettoni, C. Ufrecht, J. Urrutia, T. Valenzuela, L.R. Valerio, M. Van Der Grinten, V. Vaskonen, V. Vázquez-Aceves, H. Veermäe, F. Vetrano, N.V. Vitanov, W. Von Klitzing, S. Wald, T. Walker, R. Walser, J. Wang, Y. Wang, C.A. Weidner, A. Wenzlawski, M. Werner, L. Wörner, M.E. Yahia, E. Yazgan, E. Zambrini Cruzeiro, M. Zarei, M. Zhan, S. Zhang, L. Zhou, E. Zupanič, EPJ Quantum Technology 12 (2025). das_tickbox: '1' dataavailabilitystatement: No datasets were generated or analysed during the current study. date_created: 2025-05-04T22:02:30Z date_published: 2025-04-03T00:00:00Z date_updated: 2026-07-08T09:29:52Z day: '03' ddc: - '530' department: - _id: OnHo doi: 10.1140/epjqt/s40507-025-00344-3 external_id: arxiv: - '2412.14960' isi: - '001489653300001' file: - access_level: open_access checksum: 00c7a97d87f7a6314df5b0c2213fbb02 content_type: application/pdf creator: dernst date_created: 2025-05-05T10:52:52Z date_updated: 2025-05-05T10:52:52Z file_id: '19653' file_name: 2025_EPJQuantumTech_Abdalla.pdf file_size: 14352192 relation: main_file success: 1 file_date_updated: 2025-05-05T10:52:52Z has_accepted_license: '1' intvolume: ' 12' isi: 1 language: - iso: eng month: '04' oa: 1 oa_version: Published Version publication: EPJ Quantum Technology publication_identifier: eissn: - 2196-0763 publication_status: published publisher: Springer Nature quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: 'Terrestrial Very-Long-Baseline Atom Interferometry: Summary of the second workshop' tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 68b8ca59-c5b3-11ee-8790-cd641c68093d volume: 12 year: '2025' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '12311' 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. article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Bartosz full_name: Naskręcki, Bartosz last_name: Naskręcki - first_name: Matteo full_name: Verzobio, Matteo id: 7aa8f170-131e-11ed-88e1-a9efd01027cb last_name: Verzobio orcid: 0000-0002-0854-0306 citation: ama: 'Naskręcki B, Verzobio M. Common valuations of division polynomials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2025;155(5):1646-1660. doi:10.1017/prm.2024.7' apa: 'Naskręcki, B., & Verzobio, M. (2025). Common valuations of division polynomials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. Cambridge University Press. https://doi.org/10.1017/prm.2024.7' chicago: 'Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” Proceedings of the Royal Society of Edinburgh Section A: Mathematics. Cambridge University Press, 2025. https://doi.org/10.1017/prm.2024.7.' ieee: 'B. Naskręcki and M. Verzobio, “Common valuations of division polynomials,” Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol. 155, no. 5. Cambridge University Press, pp. 1646–1660, 2025.' 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.' mla: 'Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol. 155, no. 5, Cambridge University Press, 2025, pp. 1646–60, doi:10.1017/prm.2024.7.' short: 'B. Naskręcki, M. Verzobio, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 155 (2025) 1646–1660.' corr_author: '1' das_tickbox: '0' date_created: 2023-01-16T11:45:22Z date_published: 2025-10-01T00:00:00Z date_updated: 2026-07-16T08:43:40Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1017/prm.2024.7 ec_funded: 1 external_id: arxiv: - '2203.02015' isi: - '001174907100001' file: - access_level: open_access checksum: c5ec6e29aca2fb4533cb95fac409a0b2 content_type: application/pdf creator: dernst date_created: 2025-12-30T06:45:47Z date_updated: 2025-12-30T06:45:47Z file_id: '20878' file_name: 2025_ProceedingsRoyalSocEdinburghA_Naskrecki.pdf file_size: 477624 relation: main_file success: 1 file_date_updated: 2025-12-30T06:45:47Z has_accepted_license: '1' intvolume: ' 155' isi: 1 issue: '5' keyword: - Elliptic curves - Néron models - division polynomials - height functions - discrete valuation rings language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 1646-1660 project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: 'Proceedings of the Royal Society of Edinburgh Section A: Mathematics' publication_identifier: eissn: - 1473-7124 issn: - 0308-2105 publication_status: published publisher: Cambridge University Press quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Common valuations of division polynomials tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 155 year: '2025' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '20797' 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. 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). article_number: '024072' article_processing_charge: Yes (in subscription journal) article_type: original arxiv: 1 author: - first_name: Hannah full_name: Seabrook, Hannah last_name: Seabrook - first_name: Emilien full_name: Lavie, Emilien last_name: Lavie - first_name: Karl T full_name: Strömberg, Karl T id: 68011cd2-da32-11ee-a930-b2774c7aba5f last_name: Strömberg - first_name: Matthew P. full_name: Stafford, Matthew P. last_name: Stafford - first_name: Giulia full_name: Rubino, Giulia last_name: Rubino citation: 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 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. 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. ista: Seabrook H, Lavie E, Strömberg KT, Stafford MP, Rubino G. 2025. Surpassing the loss-noise robustness trade-off in quantum key distribution. Physical Review Applied. 24(2), 024072. mla: Seabrook, Hannah, et al. “Surpassing the Loss-Noise Robustness Trade-off in Quantum Key Distribution.” Physical Review Applied, vol. 24, no. 2, 024072, American Physical Society, 2025, doi:10.1103/xq2l-r4r7. short: H. Seabrook, E. Lavie, K.T. Strömberg, M.P. Stafford, G. Rubino, Physical Review Applied 24 (2025). das_tickbox: '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 ' date_created: 2025-12-11T10:46:28Z date_published: 2025-08-29T00:00:00Z date_updated: 2026-07-16T08:27:32Z day: '29' ddc: - '530' department: - _id: OnHo doi: 10.1103/xq2l-r4r7 external_id: arxiv: - '2412.08694' file: - access_level: open_access checksum: 12ddb0414780f65b8e690fe0e6cfb95e content_type: application/pdf creator: dernst date_created: 2025-12-15T09:39:12Z date_updated: 2025-12-15T09:39:12Z file_id: '20824' file_name: 2025_PhysReviewApplied_Seabrook.pdf file_size: 3028735 relation: main_file success: 1 file_date_updated: 2025-12-15T09:39:12Z has_accepted_license: '1' intvolume: ' 24' issue: '2' language: - iso: eng month: '08' oa: 1 oa_version: Published Version publication: Physical Review Applied publication_identifier: eissn: - 2331-7019 publication_status: published publisher: American Physical Society quality_controlled: '1' researchdata_availability: yes scopus_import: '1' status: public supplementarymaterial: no title: Surpassing the loss-noise robustness trade-off in quantum key distribution tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 24 year: '2025' ... --- OA_place: publisher OA_type: diamond PlanS_conform: '1' _id: '21244' abstract: - lang: eng 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. ' 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. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Julian full_name: Lyczak, Julian last_name: Lyczak - first_name: Arne full_name: Smeets, Arne last_name: Smeets citation: 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 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. ista: Browning TD, Lyczak J, Smeets A. 2025. Paucity of rational points on fibrations with multiple fibres. Algebra & Number Theory. 19(10), 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. short: T.D. Browning, J. Lyczak, A. Smeets, Algebra & Number Theory 19 (2025) 2049–2090. corr_author: '1' das_tickbox: '0' date_created: 2026-02-16T15:22:19Z date_published: 2025-09-05T00:00:00Z date_updated: 2026-07-16T08:52:36Z day: '05' ddc: - '510' department: - _id: TiBr doi: 10.2140/ant.2025.19.2049 external_id: arxiv: - '2310.01135' file: - access_level: open_access checksum: e50a60a4303b81563f7adbcadbe2e986 content_type: application/pdf creator: dernst date_created: 2026-02-17T11:56:20Z date_updated: 2026-02-17T11:56:20Z file_id: '21300' file_name: 2025_AlgebraNumberTheory_Browning.pdf file_size: 1505580 relation: main_file success: 1 file_date_updated: 2026-02-17T11:56:20Z has_accepted_license: '1' intvolume: ' 19' issue: '10' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 2049-2090 project: - _id: 26AEDAB2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P32428 name: New frontiers of the Manin conjecture publication: Algebra & Number Theory publication_identifier: eissn: - 1944-7833 issn: - 1937-0652 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' researchdata_availability: no status: public supplementarymaterial: no title: Paucity of rational points on fibrations with multiple fibres tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 19 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '20850' abstract: - lang: eng 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: 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." 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. article_processing_charge: Yes (in subscription journal) article_type: original arxiv: 1 author: - first_name: Yijie full_name: Diao, Yijie id: 7b7eb4ca-eb2c-11ec-b98b-accec0b20c3b last_name: Diao orcid: 0000-0002-4989-5330 citation: 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 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 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. 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. 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. corr_author: '1' das_tickbox: '0' date_created: 2025-12-21T23:01:35Z date_published: 2025-11-27T00:00:00Z date_updated: 2026-07-16T08:45:12Z day: '27' ddc: - '510' department: - _id: TiBr doi: 10.5802/jtnb.1348 external_id: arxiv: - '2408.03774' file: - access_level: open_access checksum: 67aa0afbc0b5bcbff5341f4d25e6ba20 content_type: application/pdf creator: dernst date_created: 2025-12-29T10:05:22Z date_updated: 2025-12-29T10:05:22Z file_id: '20861' file_name: 2025_JTNB_Diao.pdf file_size: 766196 relation: main_file success: 1 file_date_updated: 2025-12-29T10:05:22Z has_accepted_license: '1' intvolume: ' 37' issue: '3' language: - iso: eng license: https://creativecommons.org/licenses/by-nd/4.0/ month: '11' oa: 1 oa_version: Published Version page: 973-988 publication: Journal de theorie des nombres de Bordeaux publication_identifier: eissn: - 2118-8572 issn: - 1246-7405 publication_status: published publisher: Université de Bordeaux quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Class numbers and integer points on some Pellian surfaces tmp: image: /image/cc_by_nd.png legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0) short: CC BY-ND (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 37 year: '2025' ... --- OA_place: publisher OA_type: diamond _id: '21003' 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. 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." article_number: '12' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Matteo full_name: Verzobio, Matteo id: 7aa8f170-131e-11ed-88e1-a9efd01027cb last_name: Verzobio orcid: 0000-0002-0854-0306 citation: ama: Browning TD, Verzobio M. Counting integer points on affine surfaces with a side condition. Discrete Analysis. 2025;2025. doi:10.19086/da.143787 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.' 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.' ista: Browning TD, Verzobio M. 2025. Counting integer points on affine surfaces with a side condition. Discrete Analysis. 2025, 12. 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.' short: T.D. Browning, M. Verzobio, Discrete Analysis 2025 (2025). corr_author: '1' das_tickbox: '0' date_created: 2026-01-18T23:02:44Z date_published: 2025-09-01T00:00:00Z date_updated: 2026-07-16T08:48:35Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.19086/da.143787 ec_funded: 1 external_id: arxiv: - '2408.11453' file: - access_level: open_access checksum: 3d38e850b40f3e1abbfd30073bd4388a content_type: application/pdf creator: dernst date_created: 2026-02-12T07:50:47Z date_updated: 2026-02-12T07:50:47Z file_id: '21214' file_name: 2025_DiscreteAnalysis_Browning.pdf file_size: 393625 relation: main_file success: 1 file_date_updated: 2026-02-12T07:50:47Z has_accepted_license: '1' intvolume: ' 2025' language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Discrete Analysis publication_identifier: eissn: - 2397-3129 publication_status: published publisher: 'Cambridge: Alliance of Diamond Open Access Journals' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Counting integer points on affine surfaces with a side condition tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 2025 year: '2025' ... --- OA_place: publisher OA_type: diamond _id: '21260' abstract: - lang: eng text: We prove that there does not exist F∈Q[x,y] of degree 4 such that F(Z^2 )=Z ≥0. In particular, this answers a question by John S. Lew and Bjorn Poonen for quartic polynomials. 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." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Stanley full_name: Yao Xiao, Stanley last_name: Yao Xiao - first_name: Shuntaro full_name: Yamagishi, Shuntaro id: 0c3fbc5c-f7a6-11ec-8d70-9485e75b416b last_name: Yamagishi citation: 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 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. 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). corr_author: '1' das_tickbox: '0' date_created: 2026-02-16T16:00:02Z date_published: 2025-08-06T00:00:00Z date_updated: 2026-07-16T08:54:37Z day: '06' ddc: - '500' department: - _id: TiBr doi: 10.4171/jems/1697 external_id: arxiv: - '2307.05712' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.4171/JEMS/1697 month: '08' oa: 1 oa_version: Published Version project: - _id: 26AEDAB2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P32428 name: New frontiers of the Manin conjecture publication: Journal of the European Mathematical Society publication_identifier: eissn: - 1435-9863 issn: - 1435-9855 publication_status: epub_ahead publisher: EMS Press quality_controlled: '1' researchdata_availability: no status: public supplementarymaterial: no title: Quartic polynomials in two variables do not represent all non-negative integers type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '18822' 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. 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. article_number: e70008 article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Victor full_name: Wang, Victor id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9 last_name: Wang orcid: 0000-0002-0704-7026 citation: ama: Wang V. Diagonal cubic forms and the large sieve. Mathematika. 2025;71(1). doi:10.1112/mtk.70008 apa: Wang, V. (2025). Diagonal cubic forms and the large sieve. Mathematika. London Mathematical Society. https://doi.org/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. ieee: V. Wang, “Diagonal cubic forms and the large sieve,” Mathematika, vol. 71, no. 1. London Mathematical Society, 2025. 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). corr_author: '1' das_tickbox: '0' date_created: 2025-01-12T23:04:01Z date_published: 2025-01-02T00:00:00Z date_updated: 2026-07-16T09:14:24Z day: '02' ddc: - '510' department: - _id: TiBr doi: 10.1112/mtk.70008 ec_funded: 1 external_id: isi: - '001388255500001' file: - access_level: open_access checksum: 700a8596b4bffce2320d074120962c22 content_type: application/pdf creator: dernst date_created: 2025-01-14T06:52:09Z date_updated: 2025-01-14T06:52:09Z file_id: '18845' file_name: 2025_Mathematika_Wang.pdf file_size: 309893 relation: main_file success: 1 file_date_updated: 2025-01-14T06:52:09Z has_accepted_license: '1' intvolume: ' 71' isi: 1 issue: '1' language: - iso: eng month: '01' oa: 1 oa_version: Published Version project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Mathematika publication_identifier: eissn: - 2041-7942 issn: - 0025-5793 publication_status: published publisher: London Mathematical Society quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Diagonal cubic forms and the large sieve tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 71 year: '2025' ... --- OA_place: repository OA_type: green _id: '21768' 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 HFActa Arithmetica. 2025;221(2):141-151. doi: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 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. 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. ista: Yamagishi S. 2025. Birch’s theorem on forms in many variables with a Hessian condition. Acta Arithmetica. 221(2), 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. short: S. Yamagishi, Acta Arithmetica 221 (2025) 141–151. corr_author: '1' das_tickbox: '0' date_created: 2026-04-26T22:01:48Z date_published: 2025-10-28T00:00:00Z date_updated: 2026-07-16T09:04:43Z day: '28' department: - _id: TiBr doi: 10.4064/aa241029-19-8 external_id: arxiv: - '2304.02620' intvolume: ' 221' issue: '2' keyword: - Diophantine equations - homogeneous forms language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2304.02620 month: '10' oa: 1 oa_version: Preprint page: 141-151 project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication: Acta Arithmetica publication_identifier: eissn: - 1730-6264 issn: - 0065-1036 publication_status: published publisher: Instytut Matematyczny quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Birch’s theorem on forms in many variables with a Hessian condition type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 221 year: '2025' ... --- DOAJ_listed: '1' OA_place: publisher OA_type: diamond _id: '21266' 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." 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). article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Yik Tung full_name: Chan, Yik Tung id: c4c0afc8-9262-11ed-9231-d8b0bc743af1 last_name: Chan orcid: 0000-0001-8467-4106 citation: ama: Browning TD, Chan S. Almost all quadratic twists of an elliptic curve have no integral points. Journal of the European Mathematical Society. 2025. doi:10.4171/jems/1704 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 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. ista: Browning TD, Chan S. 2025. Almost all quadratic twists of an elliptic curve have no integral points. Journal of the European Mathematical Society. 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. short: T.D. Browning, S. Chan, Journal of the European Mathematical Society (2025). corr_author: '1' das_tickbox: '0' date_created: 2026-02-17T07:46:26Z date_published: 2025-09-17T00:00:00Z date_updated: 2026-07-16T09:00:02Z day: '17' ddc: - '510' department: - _id: TiBr doi: 10.4171/jems/1704 external_id: arxiv: - '2401.04375' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.4171/JEMS/1704 month: '09' oa: 1 oa_version: Published Version project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication: Journal of the European Mathematical Society publication_identifier: eissn: - 1435-9863 issn: - 1435-9855 publication_status: epub_ahead publisher: EMS Press quality_controlled: '1' researchdata_availability: no status: public supplementarymaterial: no title: Almost all quadratic twists of an elliptic curve have no integral points type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2025' ... --- OA_place: repository OA_type: green _id: '21265' 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. 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. article_number: rnaf279 article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Victor full_name: Wang, Victor id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9 last_name: Wang orcid: 0000-0002-0704-7026 - first_name: Max Wenqiang full_name: Xu, Max Wenqiang last_name: Xu citation: 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 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. 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). das_tickbox: '0' date_created: 2026-02-17T07:45:45Z date_published: 2025-09-01T00:00:00Z date_updated: 2026-07-16T08:57:40Z day: '01' department: - _id: TiBr doi: 10.1093/imrn/rnaf279 ec_funded: 1 external_id: arxiv: - '2405.04094' intvolume: ' 2025' issue: '18' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2405.04094 month: '09' oa: 1 oa_version: Preprint project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: International Mathematics Research Notices publication_identifier: eissn: - 1687-0247 issn: - 1073-7928 publication_status: published publisher: Oxford University Press quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Harper’s beyond square-root conjecture type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 2025 year: '2025' ... --- OA_place: publisher OA_type: diamond PlanS_conform: '1' _id: '19054' abstract: - lang: eng 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." 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. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Loïs full_name: Faisant, Loïs id: 26ca6926-5797-11ee-9232-f8b51bd19631 last_name: Faisant 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 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 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. 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. corr_author: '1' das_tickbox: '0' date_created: 2025-02-18T13:33:14Z date_published: 2025-04-22T00:00:00Z date_updated: 2026-07-16T09:23:01Z day: '22' ddc: - '510' department: - _id: TiBr doi: 10.2140/ant.2025.19.883 ec_funded: 1 external_id: arxiv: - '2302.07339' file: - access_level: open_access checksum: 56299f55682528a7cd0136497ce8b383 content_type: application/pdf creator: dernst date_created: 2026-02-17T13:17:00Z date_updated: 2026-02-17T13:17:00Z file_id: '21307' file_name: 2025_AlgebraNumberTheory_Faisant.pdf file_size: 2034433 relation: main_file success: 1 file_date_updated: 2026-02-17T13:17:00Z has_accepted_license: '1' intvolume: ' 19' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 883-965 project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Algebra & Number Theory publication_identifier: eissn: - 1944-7833 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' researchdata_availability: no status: public supplementarymaterial: no title: Motivic distribution of rational curves and twisted products of toric varieties tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 19 year: '2025' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '19363' 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. article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Yik Tung full_name: Chan, Yik Tung id: c4c0afc8-9262-11ed-9231-d8b0bc743af1 last_name: Chan orcid: 0000-0001-8467-4106 - first_name: Peter full_name: Koymans, Peter last_name: Koymans - first_name: Carlo full_name: Pagano, Carlo last_name: Pagano - first_name: Efthymios full_name: Sofos, Efthymios last_name: Sofos citation: 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 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 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. 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. ista: Chan S, Koymans P, Pagano C, Sofos E. 2025. Averages of multiplicative functions along equidistributed sequences. Journal of Number Theory. 273, 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. short: S. Chan, P. Koymans, C. Pagano, E. Sofos, Journal of Number Theory 273 (2025) 1–36. corr_author: '1' das_tickbox: '1' dataavailabilitystatement: No data was used for the research described in the article. date_created: 2025-03-09T23:01:26Z date_published: 2025-08-01T00:00:00Z date_updated: 2026-07-16T09:26:47Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1016/j.jnt.2025.01.005 external_id: isi: - '001444208500001' file: - access_level: open_access checksum: 752c407eb186d391380b10a7505f66cf content_type: application/pdf creator: dernst date_created: 2025-12-30T08:05:42Z date_updated: 2025-12-30T08:05:42Z file_id: '20889' file_name: 2025_JourNumberTheory_Chan.pdf file_size: 685204 relation: main_file success: 1 file_date_updated: 2025-12-30T08:05:42Z has_accepted_license: '1' intvolume: ' 273' isi: 1 language: - iso: eng month: '08' oa: 1 oa_version: Published Version page: 1-36 publication: Journal of Number Theory publication_identifier: issn: - 0022-314X publication_status: published publisher: Elsevier quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Averages of multiplicative functions along equidistributed sequences tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 273 year: '2025' ... --- OA_place: repository OA_type: green _id: '19055' abstract: - lang: eng 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." 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" article_number: '2502.11704' article_processing_charge: No arxiv: 1 author: - first_name: Loïs full_name: Faisant, Loïs id: 26ca6926-5797-11ee-9232-f8b51bd19631 last_name: Faisant citation: ama: Faisant L. Motivic counting of rational curves with tangency conditions via universal torsors. arXiv. doi:10.48550/ARXIV.2502.11704 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. 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.). corr_author: '1' das_tickbox: '0' date_created: 2025-02-18T13:34:07Z date_published: 2025-02-17T00:00:00Z date_updated: 2026-07-16T09:24:48Z day: '17' department: - _id: TiBr doi: 10.48550/ARXIV.2502.11704 ec_funded: 1 external_id: arxiv: - '2502.11704' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2502.11704 month: '02' oa: 1 oa_version: Preprint project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: arXiv publication_status: submitted researchdata_availability: no status: public supplementarymaterial: no title: Motivic counting of rational curves with tangency conditions via universal torsors type: preprint user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '19776' 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. 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). article_number: '65' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Jakob full_name: Glas, Jakob id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb last_name: Glas - first_name: Victor full_name: Wang, Victor id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9 last_name: Wang orcid: 0000-0002-0704-7026 citation: 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 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. ista: Browning TD, Glas J, Wang V. 2025. Optimal sums of three cubes in Fq[t]. Mathematische Zeitschrift. 310(4), 65. 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. short: T.D. Browning, J. Glas, V. Wang, Mathematische Zeitschrift 310 (2025). corr_author: '1' das_tickbox: '0' date_created: 2025-06-03T07:30:21Z date_published: 2025-05-23T00:00:00Z date_updated: 2026-07-16T10:50:51Z day: '23' ddc: - '510' department: - _id: TiBr doi: 10.1007/s00209-025-03765-z ec_funded: 1 external_id: arxiv: - '2408.03668 ' isi: - '001494367000001' file: - access_level: open_access checksum: 6f71e25740c28257bf89b8bf116c2b4d content_type: application/pdf creator: dernst date_created: 2025-06-03T08:28:14Z date_updated: 2025-06-03T08:28:14Z file_id: '19782' file_name: 2025_MathZeitschrift_Browning.pdf file_size: 461622 relation: main_file success: 1 file_date_updated: 2025-06-03T08:28:14Z has_accepted_license: '1' intvolume: ' 310' isi: 1 issue: '4' language: - iso: eng month: '05' oa: 1 oa_version: Published Version project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Mathematische Zeitschrift publication_identifier: eissn: - 1432-1823 issn: - 0025-5874 publication_status: published publisher: Springer Nature quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Optimal sums of three cubes in Fq[t] tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 310 year: '2025' ...