[{"quality_controlled":"1","status":"public","year":"2025","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2404.01057 "}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0012-365X"]},"month":"04","_id":"22163","extern":"1","date_created":"2026-06-29T10:53:05Z","date_published":"2025-04-01T00:00:00Z","title":"Larger nearly orthogonal sets over finite fields","oa_version":"Preprint","external_id":{"arxiv":["2404.01057"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","citation":{"chicago":"Haviv, Ishay, Sam Mattheus, Aleksa Milojević, and Yuval Wigderson. “Larger Nearly Orthogonal Sets over Finite Fields.” <i>Discrete Mathematics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.disc.2024.114373\">https://doi.org/10.1016/j.disc.2024.114373</a>.","short":"I. Haviv, S. Mattheus, A. Milojević, Y. Wigderson, Discrete Mathematics 348 (2025).","ista":"Haviv I, Mattheus S, Milojević A, Wigderson Y. 2025. Larger nearly orthogonal sets over finite fields. Discrete Mathematics. 348(4), 114373.","mla":"Haviv, Ishay, et al. “Larger Nearly Orthogonal Sets over Finite Fields.” <i>Discrete Mathematics</i>, vol. 348, no. 4, 114373, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.disc.2024.114373\">10.1016/j.disc.2024.114373</a>.","ama":"Haviv I, Mattheus S, Milojević A, Wigderson Y. Larger nearly orthogonal sets over finite fields. <i>Discrete Mathematics</i>. 2025;348(4). doi:<a href=\"https://doi.org/10.1016/j.disc.2024.114373\">10.1016/j.disc.2024.114373</a>","ieee":"I. Haviv, S. Mattheus, A. Milojević, and Y. Wigderson, “Larger nearly orthogonal sets over finite fields,” <i>Discrete Mathematics</i>, vol. 348, no. 4. Elsevier, 2025.","apa":"Haviv, I., Mattheus, S., Milojević, A., &#38; Wigderson, Y. (2025). Larger nearly orthogonal sets over finite fields. <i>Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.disc.2024.114373\">https://doi.org/10.1016/j.disc.2024.114373</a>"},"article_number":"114373","type":"journal_article","volume":348,"publication":"Discrete Mathematics","das_tickbox":"1","issue":"4","publisher":"Elsevier","scopus_import":"1","oa":1,"intvolume":"       348","date_updated":"2026-07-14T08:17:17Z","doi":"10.1016/j.disc.2024.114373","article_type":"original","OA_type":"green","author":[{"last_name":"Haviv","first_name":"Ishay","full_name":"Haviv, Ishay"},{"last_name":"Mattheus","first_name":"Sam","full_name":"Mattheus, Sam"},{"last_name":"Milojević","full_name":"Milojević, Aleksa","first_name":"Aleksa"},{"last_name":"Wigderson","full_name":"Wigderson, Yuval","first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5"}],"arxiv":1,"publication_status":"published","keyword":["Nearly orthogonal sets","Ramsey theory","Finite fields"],"day":"01","OA_place":"repository","fulldoi":"https://doi.org/10.1016/j.disc.2024.114373","abstract":[{"lang":"eng","text":"For a field F and integers d and k, a set A ⊆ Fd is called k-nearly orthogonal if its\r\nmembers are non-self-orthogonal and every k + 1 vectors of A include an orthogonal pair.\r\nWe prove that for every prime p there exists some δ = δ(p)> 0, such that for every field\r\nF of characteristic p and for all integers k ≥ 2 and d ≥ k, there exists a k-nearly orthogonal\r\nset of at least dδ·k/ logk vectors of Fd. The size of the set is optimal up to the logk term\r\nin the exponent. We further prove two extensions of this result. In the first, we provide a\r\nlarge set A of non-self-orthogonal vectors of Fd such that for every two subsets of A of\r\nsize k+1 each, some vector of one of the subsets is orthogonal to some vector of the other.\r\nIn the second extension, every k + 1 vectors of the produced set A include ℓ + 1 pairwise\r\northogonal vectors for an arbitrary fixed integer 1 ≤ ℓ ≤ k. The proofs involve probabilistic\r\nand spectral arguments and the hypergraph container method"}]},{"oa_version":"Preprint","title":"On the Kohayakawa–Kreuter conjecture","external_id":{"arxiv":["2307.16611"]},"mathsc":["05C80","05C55","05D10"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","date_created":"2026-06-29T10:55:00Z","date_published":"2025-04-28T00:00:00Z","publication_identifier":{"issn":["0305-0041"],"eissn":["1469-8064"]},"language":[{"iso":"eng"}],"month":"04","extern":"1","_id":"22168","quality_controlled":"1","status":"public","year":"2025","page":"293-320","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2307.16611","open_access":"1"}],"day":"28","arxiv":1,"publication_status":"published","fulldoi":"https://doi.org/10.1017/s0305004125000143","OA_place":"repository","abstract":[{"lang":"eng","text":"Let us say that a graph G is Ramsey for a tuple (H1, ... , Hr) of graphs if every r-colouring\r\nof the edges of G contains a monochromatic copy of Hi in colour i, for some i ∈ [[r]].\r\nA famous conjecture of Kohayakawa and Kreuter, extending seminal work of Rödl and\r\nRucinski, predicts the threshold at which the binomial random graph ´ Gn,p becomes Ramsey\r\nfor (H1, ... , Hr) asymptotically almost surely.\r\nIn this paper, we resolve the Kohayakawa–Kreuter conjecture for almost all tuples of\r\ngraphs. Moreover, we reduce its validity to the truth of a certain deterministic statement,\r\nwhich is a clear necessary condition for the conjecture to hold. All of our results actually hold in greater generality, when one replaces the graphs H1, ... , Hr by finite families\r\nH1, ... , Hr. Additionally, we pose a natural (deterministic) graph-partitioning conjecture,\r\nwhich we believe to be of independent interest, and whose resolution would imply the\r\nKohayakawa–Kreuter conjecture."}],"article_type":"original","OA_type":"green","author":[{"first_name":"EDEN","full_name":"KUPERWASSER, EDEN","last_name":"KUPERWASSER"},{"last_name":"SAMOTIJ","full_name":"SAMOTIJ, WOJCIECH","first_name":"WOJCIECH"},{"id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","first_name":"Yuval","full_name":"Wigderson, Yuval","last_name":"Wigderson"}],"scopus_import":"1","publisher":"Cambridge University Press","oa":1,"date_updated":"2026-07-14T08:38:08Z","intvolume":"       178","doi":"10.1017/s0305004125000143","citation":{"apa":"KUPERWASSER, E., SAMOTIJ, W., &#38; Wigderson, Y. (2025). On the Kohayakawa–Kreuter conjecture. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s0305004125000143\">https://doi.org/10.1017/s0305004125000143</a>","ieee":"E. KUPERWASSER, W. SAMOTIJ, and Y. Wigderson, “On the Kohayakawa–Kreuter conjecture,” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 178, no. 3. Cambridge University Press, pp. 293–320, 2025.","ista":"KUPERWASSER E, SAMOTIJ W, Wigderson Y. 2025. On the Kohayakawa–Kreuter conjecture. Mathematical Proceedings of the Cambridge Philosophical Society. 178(3), 293–320.","short":"E. KUPERWASSER, W. SAMOTIJ, Y. Wigderson, Mathematical Proceedings of the Cambridge Philosophical Society 178 (2025) 293–320.","mla":"KUPERWASSER, EDEN, et al. “On the Kohayakawa–Kreuter Conjecture.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 178, no. 3, Cambridge University Press, 2025, pp. 293–320, doi:<a href=\"https://doi.org/10.1017/s0305004125000143\">10.1017/s0305004125000143</a>.","ama":"KUPERWASSER E, SAMOTIJ W, Wigderson Y. On the Kohayakawa–Kreuter conjecture. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. 2025;178(3):293-320. doi:<a href=\"https://doi.org/10.1017/s0305004125000143\">10.1017/s0305004125000143</a>","chicago":"KUPERWASSER, EDEN, WOJCIECH SAMOTIJ, and Yuval Wigderson. “On the Kohayakawa–Kreuter Conjecture.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/s0305004125000143\">https://doi.org/10.1017/s0305004125000143</a>."},"volume":178,"publication":"Mathematical Proceedings of the Cambridge Philosophical Society","type":"journal_article","issue":"3"},{"_id":"22172","extern":"1","language":[{"iso":"eng"}],"month":"12","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2408.12913"}],"quality_controlled":"1","year":"2025","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","title":"Blowups of triangle-free graphs","oa_version":"Preprint","external_id":{"arxiv":["2408.12913"]},"date_created":"2026-06-29T10:56:44Z","date_published":"2025-12-19T00:00:00Z","date_updated":"2026-07-14T08:50:55Z","intvolume":"        10","doi":"10.19086/aic.2025.10","publisher":"Alliance of Diamond Open Access Journals","scopus_import":"1","oa":1,"type":"journal_article","volume":10,"publication":"Advances in Combinatorics","citation":{"ieee":"A. Girão, Z. Hunter, and Y. Wigderson, “Blowups of triangle-free graphs,” <i>Advances in Combinatorics</i>, vol. 10. Alliance of Diamond Open Access Journals, 2025.","apa":"Girão, A., Hunter, Z., &#38; Wigderson, Y. (2025). Blowups of triangle-free graphs. <i>Advances in Combinatorics</i>. Alliance of Diamond Open Access Journals. <a href=\"https://doi.org/10.19086/aic.2025.10\">https://doi.org/10.19086/aic.2025.10</a>","chicago":"Girão, António, Zach Hunter, and Yuval Wigderson. “Blowups of Triangle-Free Graphs.” <i>Advances in Combinatorics</i>. Alliance of Diamond Open Access Journals, 2025. <a href=\"https://doi.org/10.19086/aic.2025.10\">https://doi.org/10.19086/aic.2025.10</a>.","ista":"Girão A, Hunter Z, Wigderson Y. 2025. Blowups of triangle-free graphs. Advances in Combinatorics. 10.","short":"A. Girão, Z. Hunter, Y. Wigderson, Advances in Combinatorics 10 (2025).","mla":"Girão, António, et al. “Blowups of Triangle-Free Graphs.” <i>Advances in Combinatorics</i>, vol. 10, Alliance of Diamond Open Access Journals, 2025, doi:<a href=\"https://doi.org/10.19086/aic.2025.10\">10.19086/aic.2025.10</a>.","ama":"Girão A, Hunter Z, Wigderson Y. Blowups of triangle-free graphs. <i>Advances in Combinatorics</i>. 2025;10. doi:<a href=\"https://doi.org/10.19086/aic.2025.10\">10.19086/aic.2025.10</a>"},"OA_place":"repository","fulldoi":"https://doi.org/10.19086/aic.2025.10","abstract":[{"text":"A highly influential result of Nikiforov states that if an n-vertex graph G contains\r\nat least γnh copies of a fixed h-vertex graph H, then G contains a blowup of H of order\r\nΩγ,H(logn). While the dependence on n is optimal, the correct dependence on γ is unknown;\r\nall known proofs yield bounds that are polynomial in γ, but the best known upper bound,\r\ncoming from random graphs, is only logarithmic in γ. It is a major open problem to narrow\r\nthis gap.\r\nWe prove that if H is triangle-free, then the logarithmic behavior of the upper bound\r\nis the truth. That is, under the assumptions above, G contains a blowup of H of order\r\nΩH(logn/log(1/γ)). This is the first non-trivial instance where the optimal dependence in\r\nNikiforov’s theorem is known.\r\nAs a consequence, we also prove an upper bound on multicolor Ramsey numbers of\r\nblowups of triangle-free graphs, proving that the dependence on the number of colors is\r\npolynomial once the blowup is sufficiently large. This shows that, from the perspective\r\nof multicolor Ramsey numbers, blowups of fixed triangle-free graphs behave like bipartite\r\ngraphs.","lang":"eng"}],"arxiv":1,"day":"19","publication_status":"published","OA_type":"green","author":[{"first_name":"António","full_name":"Girão, António","last_name":"Girão"},{"first_name":"Zach","full_name":"Hunter, Zach","last_name":"Hunter"},{"last_name":"Wigderson","full_name":"Wigderson, Yuval","first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5"}],"article_type":"original"},{"extern":"1","_id":"22181","month":"08","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0195-6698"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2409.05931 "}],"quality_controlled":"1","status":"public","year":"2025","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2409.05931"]},"oa_version":"Preprint","title":"Infinitely many minimally non-Ramsey size-linear graphs","date_published":"2025-08-01T00:00:00Z","date_created":"2026-06-29T10:59:47Z","doi":"10.1016/j.ejc.2025.104175","date_updated":"2026-07-14T09:13:09Z","intvolume":"       128","oa":1,"scopus_import":"1","publisher":"Elsevier","publication":"European Journal of Combinatorics","volume":128,"type":"journal_article","article_number":"104175","citation":{"ieee":"Y. Wigderson, “Infinitely many minimally non-Ramsey size-linear graphs,” <i>European Journal of Combinatorics</i>, vol. 128. Elsevier, 2025.","apa":"Wigderson, Y. (2025). Infinitely many minimally non-Ramsey size-linear graphs. <i>European Journal of Combinatorics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ejc.2025.104175\">https://doi.org/10.1016/j.ejc.2025.104175</a>","chicago":"Wigderson, Yuval. “Infinitely Many Minimally Non-Ramsey Size-Linear Graphs.” <i>European Journal of Combinatorics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.ejc.2025.104175\">https://doi.org/10.1016/j.ejc.2025.104175</a>.","mla":"Wigderson, Yuval. “Infinitely Many Minimally Non-Ramsey Size-Linear Graphs.” <i>European Journal of Combinatorics</i>, vol. 128, 104175, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104175\">10.1016/j.ejc.2025.104175</a>.","ama":"Wigderson Y. Infinitely many minimally non-Ramsey size-linear graphs. <i>European Journal of Combinatorics</i>. 2025;128. doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104175\">10.1016/j.ejc.2025.104175</a>","short":"Y. Wigderson, European Journal of Combinatorics 128 (2025).","ista":"Wigderson Y. 2025. Infinitely many minimally non-Ramsey size-linear graphs. European Journal of Combinatorics. 128, 104175."},"abstract":[{"lang":"eng","text":"A graph G is said to be Ramsey size-linear if r(G, H) = OG(e(H))\r\nfor every graph H with no isolated vertices. Erdős, Faudree,\r\nRousseau, and Schelp observed that K4 is not Ramsey size-linear,\r\nbut each of its proper subgraphs is, and they asked whether there\r\nexist infinitely many such graphs. In this short note, we answer\r\nthis question in the affirmative"}],"fulldoi":"https://doi.org/10.1016/j.ejc.2025.104175","OA_place":"repository","day":"01","publication_status":"published","arxiv":1,"author":[{"last_name":"Wigderson","first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","full_name":"Wigderson, Yuval"}],"OA_type":"green","article_type":"original"},{"scopus_import":"1","publisher":"Theory of Computing Exchange","oa":1,"intvolume":"        21","date_updated":"2026-07-14T09:47:56Z","doi":"10.4086/toc.2025.v021a001","article_number":"1","citation":{"ieee":"Y. Li, Y. Qiao, A. Wigderson, Y. Wigderson, and C. Zhang, “On linear-algebraic notions of expansion,” <i>Theory of Computing</i>, vol. 21. Theory of Computing Exchange, 2025.","apa":"Li, Y., Qiao, Y., Wigderson, A., Wigderson, Y., &#38; Zhang, C. (2025). On linear-algebraic notions of expansion. <i>Theory of Computing</i>. Theory of Computing Exchange. <a href=\"https://doi.org/10.4086/toc.2025.v021a001\">https://doi.org/10.4086/toc.2025.v021a001</a>","chicago":"Li, Yinan, Youming Qiao, Avi Wigderson, Yuval Wigderson, and Chuanqi Zhang. “On Linear-Algebraic Notions of Expansion.” <i>Theory of Computing</i>. Theory of Computing Exchange, 2025. <a href=\"https://doi.org/10.4086/toc.2025.v021a001\">https://doi.org/10.4086/toc.2025.v021a001</a>.","mla":"Li, Yinan, et al. “On Linear-Algebraic Notions of Expansion.” <i>Theory of Computing</i>, vol. 21, 1, Theory of Computing Exchange, 2025, doi:<a href=\"https://doi.org/10.4086/toc.2025.v021a001\">10.4086/toc.2025.v021a001</a>.","ama":"Li Y, Qiao Y, Wigderson A, Wigderson Y, Zhang C. On linear-algebraic notions of expansion. <i>Theory of Computing</i>. 2025;21. doi:<a href=\"https://doi.org/10.4086/toc.2025.v021a001\">10.4086/toc.2025.v021a001</a>","ista":"Li Y, Qiao Y, Wigderson A, Wigderson Y, Zhang C. 2025. On linear-algebraic notions of expansion. Theory of Computing. 21, 1.","short":"Y. Li, Y. Qiao, A. Wigderson, Y. Wigderson, C. Zhang, Theory of Computing 21 (2025)."},"publication":"Theory of Computing","volume":21,"type":"journal_article","day":"12","arxiv":1,"publication_status":"published","keyword":["linear algebraic expansion","quantum expanders","dimension expanders"],"fulldoi":"https://doi.org/10.4086/toc.2025.v021a001","OA_place":"repository","abstract":[{"text":"A fundamental fact about bounded-degree graph expanders is that three notions of expansion—vertex expansion, edge expansion, and spectral expansion—are all equivalent. In this paper, we study to what extent such a statement is true for linear-algebraic notions of expansion.\r\n\r\nThere are two well-studied notions of linear-algebraic expansion, namely, dimension expansion (defined in analogy to vertex expansion of graphs) and quantum expansion (defined in analogy to spectral expansion of graphs). Lubotzky and Zelmanov proved that the latter implies the former. We prove that the converse is false: There are dimension expanders which are not quantum expanders. This also answers in the negative questions of Lubotzky--Zelmanov and Dvir--Shpilka on the relation between dimension expansion and Kazhdan's property T.\r\n\r\nMoreover, this asymmetry is explained by the fact that there are two distinct linear-algebraic analogues of edge expansion of graphs. The first of these is quantum edge expansion, which was introduced by Hastings, and which he proved to be equivalent to quantum expansion. We introduce a new notion, termed dimension edge expansion, which we prove is equivalent to dimension expansion and which is implied by quantum edge expansion. Thus, the separation above is implied by a finer one: dimension edge expansion is strictly weaker than quantum edge expansion. This new notion also leads to a new, more modular proof of the Lubotzky--Zelmanov result that quantum expanders are dimension expanders.","lang":"eng"}],"article_type":"original","OA_type":"green","author":[{"last_name":"Li","full_name":"Li, Yinan","first_name":"Yinan"},{"last_name":"Qiao","first_name":"Youming","full_name":"Qiao, Youming"},{"last_name":"Wigderson","full_name":"Wigderson, Avi","first_name":"Avi"},{"last_name":"Wigderson","full_name":"Wigderson, Yuval","first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5"},{"last_name":"Zhang","full_name":"Zhang, Chuanqi","first_name":"Chuanqi"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1557-2862"]},"month":"04","extern":"1","_id":"22188","year":"2025","quality_controlled":"1","status":"public","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2212.13154","open_access":"1"}],"oa_version":"Preprint","title":"On linear-algebraic notions of expansion","external_id":{"arxiv":["2212.13154"]},"mathsc":["05C18","68R10"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","date_created":"2026-06-29T12:14:06Z","date_published":"2025-04-12T00:00:00Z"},{"_id":"22191","extern":"1","month":"03","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1937-0652"],"eissn":["1944-7833"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2109.03767"}],"page":"617-666","quality_controlled":"1","status":"public","year":"2025","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"unknown":["2109.03767"]},"mathsc":["11N05","11N13"],"title":"Odd moments in the distribution of primes","oa_version":"Preprint","date_published":"2025-03-24T00:00:00Z","date_created":"2026-06-29T12:56:09Z","doi":"10.2140/ant.2025.19.617","date_updated":"2026-07-14T10:52:02Z","intvolume":"        19","oa":1,"scopus_import":"1","publisher":"Mathematical Sciences Publishers","issue":"4","type":"journal_article","publication":"Algebra & Number Theory","volume":19,"citation":{"ieee":"V. Z. Kuperberg, “Odd moments in the distribution of primes,” <i>Algebra &#38; Number Theory</i>, vol. 19, no. 4. Mathematical Sciences Publishers, pp. 617–666, 2025.","apa":"Kuperberg, V. Z. (2025). Odd moments in the distribution of primes. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2025.19.617\">https://doi.org/10.2140/ant.2025.19.617</a>","chicago":"Kuperberg, Vivian Zieve. “Odd Moments in the Distribution of Primes.” <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2025. <a href=\"https://doi.org/10.2140/ant.2025.19.617\">https://doi.org/10.2140/ant.2025.19.617</a>.","short":"V.Z. Kuperberg, Algebra &#38; Number Theory 19 (2025) 617–666.","ista":"Kuperberg VZ. 2025. Odd moments in the distribution of primes. Algebra &#38; Number Theory. 19(4), 617–666.","ama":"Kuperberg VZ. Odd moments in the distribution of primes. <i>Algebra &#38; Number Theory</i>. 2025;19(4):617-666. doi:<a href=\"https://doi.org/10.2140/ant.2025.19.617\">10.2140/ant.2025.19.617</a>","mla":"Kuperberg, Vivian Zieve. “Odd Moments in the Distribution of Primes.” <i>Algebra &#38; Number Theory</i>, vol. 19, no. 4, Mathematical Sciences Publishers, 2025, pp. 617–66, doi:<a href=\"https://doi.org/10.2140/ant.2025.19.617\">10.2140/ant.2025.19.617</a>."},"abstract":[{"lang":"eng","text":"Montgomery and Soundararajan showed that the distribution of ψ(x+H)−ψ(x), for 0≤ x ≤ N, is approximately normal with mean ∼ H and variance ∼ H log(N/H), when N\r\nδ ≤ H ≤ N\r\n1−δ\r\n. Their work depends\r\non showing that sums Rk (h) of k-term singular series are µk (−h log h + Ah)\r\nk/2 + Ok (h\r\nk/2−1/(7k)+ε\r\n),\r\nwhere A is a constant and µk are the Gaussian moment constants. We study lower-order terms in the size\r\nof these moments. We conjecture that when k is odd, Rk (h) ≍ h\r\n(k−1)/2\r\n(log h)\r\n(k+1)/2\r\n. We prove an upper\r\nbound with the correct power of h when k = 3, and prove analogous upper bounds in the function field\r\nsetting when k = 3 and k = 5. We provide further evidence for this conjecture in the form of numerical\r\ncomputations."}],"OA_place":"repository","fulldoi":"https://doi.org/10.2140/ant.2025.19.617","day":"24","publication_status":"published","author":[{"id":"c3bac823-112d-11f0-a3f5-c264f852e697","full_name":"Kuperberg, Vivian Zieve","first_name":"Vivian Zieve","last_name":"Kuperberg"}],"OA_type":"green","article_type":"original"},{"publisher":"World Scientific Publishing","scopus_import":"1","oa":1,"date_updated":"2026-07-14T11:04:58Z","intvolume":"        21","doi":"10.1142/s1793042125500046","citation":{"ieee":"V. Z. Kuperberg, “Sums of singular series along arithmetic progressions and with smooth weights,” <i>International Journal of Number Theory</i>, vol. 21, no. 01. World Scientific Publishing, pp. 53–74, 2025.","apa":"Kuperberg, V. Z. (2025). Sums of singular series along arithmetic progressions and with smooth weights. <i>International Journal of Number Theory</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s1793042125500046\">https://doi.org/10.1142/s1793042125500046</a>","chicago":"Kuperberg, Vivian Zieve. “Sums of Singular Series along Arithmetic Progressions and with Smooth Weights.” <i>International Journal of Number Theory</i>. World Scientific Publishing, 2025. <a href=\"https://doi.org/10.1142/s1793042125500046\">https://doi.org/10.1142/s1793042125500046</a>.","short":"V.Z. Kuperberg, International Journal of Number Theory 21 (2025) 53–74.","ista":"Kuperberg VZ. 2025. Sums of singular series along arithmetic progressions and with smooth weights. International Journal of Number Theory. 21(01), 53–74.","mla":"Kuperberg, Vivian Zieve. “Sums of Singular Series along Arithmetic Progressions and with Smooth Weights.” <i>International Journal of Number Theory</i>, vol. 21, no. 01, World Scientific Publishing, 2025, pp. 53–74, doi:<a href=\"https://doi.org/10.1142/s1793042125500046\">10.1142/s1793042125500046</a>.","ama":"Kuperberg VZ. Sums of singular series along arithmetic progressions and with smooth weights. <i>International Journal of Number Theory</i>. 2025;21(01):53-74. doi:<a href=\"https://doi.org/10.1142/s1793042125500046\">10.1142/s1793042125500046</a>"},"type":"journal_article","volume":21,"publication":"International Journal of Number Theory","issue":"01","publication_status":"published","day":"01","arxiv":1,"OA_place":"repository","fulldoi":"https://doi.org/10.1142/s1793042125500046","abstract":[{"text":"Sums of the singular series constants that appear in the Hardy–Littlewood k-tuples conjectures have long been studied in connection to the distribution of primes. We study constrained sums of singular series, where the sum is taken over sets whose elements are specified modulo r or weighted by smooth functions. We show that the value of the sum is governed by incidences modulo r of elements of the set in the case of arithmetic progressions and by pairings of the smooth functions in the case of weights. These sums shed light on sums of singular series in other formats. ","lang":"eng"}],"article_type":"original","OA_type":"green","author":[{"last_name":"Kuperberg","full_name":"Kuperberg, Vivian Zieve","first_name":"Vivian Zieve","id":"c3bac823-112d-11f0-a3f5-c264f852e697"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1793-7310"],"issn":["1793-0421"]},"month":"01","_id":"22195","extern":"1","year":"2025","quality_controlled":"1","status":"public","page":"53-74","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2301.06095","open_access":"1"}],"title":"Sums of singular series along arithmetic progressions and with smooth weights","oa_version":"Preprint","external_id":{"arxiv":["2301.06095"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","date_created":"2026-06-29T12:57:46Z","date_published":"2025-01-01T00:00:00Z"},{"status":"public","quality_controlled":"1","year":"2025","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2212.04969"}],"page":"323-370","month":"03","publication_identifier":{"issn":["2330-0000"]},"language":[{"iso":"eng"}],"extern":"1","_id":"22200","date_published":"2025-03-20T00:00:00Z","date_created":"2026-06-29T12:59:46Z","external_id":{"arxiv":["2212.04969"]},"mathsc":["11N60","05A15","11M50","11N56"],"oa_version":"Preprint","title":"Symplectic conjectures for sums of divisor functions and explorations of an orthogonal regime","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Kuperberg, V. Z., &#38; Lalín, M. (2025). Symplectic conjectures for sums of divisor functions and explorations of an orthogonal regime. <i>Transactions of the American Mathematical Society, Series B</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/btran/186\">https://doi.org/10.1090/btran/186</a>","ieee":"V. Z. Kuperberg and M. Lalín, “Symplectic conjectures for sums of divisor functions and explorations of an orthogonal regime,” <i>Transactions of the American Mathematical Society, Series B</i>, vol. 12, no. 10. American Mathematical Society, pp. 323–370, 2025.","ama":"Kuperberg VZ, Lalín M. Symplectic conjectures for sums of divisor functions and explorations of an orthogonal regime. <i>Transactions of the American Mathematical Society, Series B</i>. 2025;12(10):323-370. doi:<a href=\"https://doi.org/10.1090/btran/186\">10.1090/btran/186</a>","mla":"Kuperberg, Vivian Zieve, and Matilde Lalín. “Symplectic Conjectures for Sums of Divisor Functions and Explorations of an Orthogonal Regime.” <i>Transactions of the American Mathematical Society, Series B</i>, vol. 12, no. 10, American Mathematical Society, 2025, pp. 323–70, doi:<a href=\"https://doi.org/10.1090/btran/186\">10.1090/btran/186</a>.","short":"V.Z. Kuperberg, M. Lalín, Transactions of the American Mathematical Society, Series B 12 (2025) 323–370.","ista":"Kuperberg VZ, Lalín M. 2025. Symplectic conjectures for sums of divisor functions and explorations of an orthogonal regime. Transactions of the American Mathematical Society, Series B. 12(10), 323–370.","chicago":"Kuperberg, Vivian Zieve, and Matilde Lalín. “Symplectic Conjectures for Sums of Divisor Functions and Explorations of an Orthogonal Regime.” <i>Transactions of the American Mathematical Society, Series B</i>. American Mathematical Society, 2025. <a href=\"https://doi.org/10.1090/btran/186\">https://doi.org/10.1090/btran/186</a>."},"issue":"10","publication":"Transactions of the American Mathematical Society, Series B","volume":12,"type":"journal_article","oa":1,"publisher":"American Mathematical Society","scopus_import":"1","doi":"10.1090/btran/186","date_updated":"2026-07-14T11:24:55Z","intvolume":"        12","article_type":"original","author":[{"last_name":"Kuperberg","full_name":"Kuperberg, Vivian Zieve","first_name":"Vivian Zieve","id":"c3bac823-112d-11f0-a3f5-c264f852e697"},{"full_name":"Lalín, Matilde","first_name":"Matilde","last_name":"Lalín"}],"OA_type":"green","day":"20","arxiv":1,"publication_status":"published","abstract":[{"text":"In Kuperberg and Lal´ın [Forum Math. 34 (2022), pp. 711–747],\r\nthe authors studied the mean-square of certain sums of the divisor function\r\ndk(f) over the function field Fq[T] in the limit as q →∞ and related these\r\nsums to integrals over the ensemble of symplectic matrices, along similar lines\r\nas previous work of Keating, Rodgers, Roditty-Gershon and Rudnick [Math. Z.\r\n288 (2018), pp. 167–198] for unitary matrices. We present an analogous problem yielding an integral over the ensemble of orthogonal matrices and pursue\r\na more detailed study of both the symplectic and orthogonal matrix integrals,\r\nrelating them to symmetric function theory. The function field results lead to\r\nconjectures concerning analogous questions over number fields.","lang":"eng"}],"fulldoi":"https://doi.org/10.1090/btran/186","OA_place":"repository"},{"month":"05","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0025-5793","2041-7942"]},"extern":"1","_id":"22199","quality_controlled":"1","status":"public","year":"2025","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2410.17939"}],"mathsc":["11N60","05A15","11M50","11N56"],"external_id":{"arxiv":["2410.17939"]},"oa_version":"Preprint","title":"Arithmetic constants for symplectic variances of the divisor function","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2025-05-01T00:00:00Z","date_created":"2026-06-29T12:59:16Z","oa":1,"publisher":"Wiley","scopus_import":"1","doi":"10.1112/mtk.70029","date_updated":"2026-07-14T11:20:10Z","intvolume":"        71","article_number":"e70029","citation":{"chicago":"Kuperberg, Vivian Zieve, and Matilde Lalín. “Arithmetic Constants for Symplectic Variances of the Divisor Function.” <i>Mathematika</i>. Wiley, 2025. <a href=\"https://doi.org/10.1112/mtk.70029\">https://doi.org/10.1112/mtk.70029</a>.","ama":"Kuperberg VZ, Lalín M. Arithmetic constants for symplectic variances of the divisor function. <i>Mathematika</i>. 2025;71(3). doi:<a href=\"https://doi.org/10.1112/mtk.70029\">10.1112/mtk.70029</a>","mla":"Kuperberg, Vivian Zieve, and Matilde Lalín. “Arithmetic Constants for Symplectic Variances of the Divisor Function.” <i>Mathematika</i>, vol. 71, no. 3, e70029, Wiley, 2025, doi:<a href=\"https://doi.org/10.1112/mtk.70029\">10.1112/mtk.70029</a>.","ista":"Kuperberg VZ, Lalín M. 2025. Arithmetic constants for symplectic variances of the divisor function. Mathematika. 71(3), e70029.","short":"V.Z. Kuperberg, M. Lalín, Mathematika 71 (2025).","ieee":"V. Z. Kuperberg and M. Lalín, “Arithmetic constants for symplectic variances of the divisor function,” <i>Mathematika</i>, vol. 71, no. 3. Wiley, 2025.","apa":"Kuperberg, V. Z., &#38; Lalín, M. (2025). Arithmetic constants for symplectic variances of the divisor function. <i>Mathematika</i>. Wiley. <a href=\"https://doi.org/10.1112/mtk.70029\">https://doi.org/10.1112/mtk.70029</a>"},"issue":"3","volume":71,"publication":"Mathematika","type":"journal_article","arxiv":1,"publication_status":"published","day":"01","abstract":[{"lang":"eng","text":"Kuperberg and Lalín stated some conjectures on the variance of certain sums of the divisor function dk(n) over number fields, which were inspired by analogous results over function fields proven by the authors. These problems are related to certain symplectic matrix integrals. While the function field results can be directly related to the random matrix integrals, the connection between the random matrix integrals and the number field results is less direct and involves arithmetic factors. The goal of this article is to give heuristic arguments for the formulas of these arithmetic factors."}],"fulldoi":"https://doi.org/10.1112/mtk.70029","OA_place":"repository","article_type":"original","author":[{"last_name":"Kuperberg","id":"c3bac823-112d-11f0-a3f5-c264f852e697","first_name":"Vivian Zieve","full_name":"Kuperberg, Vivian Zieve"},{"last_name":"Lalín","first_name":"Matilde","full_name":"Lalín, Matilde"}],"OA_type":"green"},{"doi":"10.1007/s11856-024-2711-0","date_updated":"2026-07-14T11:28:49Z","intvolume":"       267","oa":1,"publisher":"Springer Nature","scopus_import":"1","issue":"1","type":"journal_article","publication":"Israel Journal of Mathematics","volume":267,"citation":{"ieee":"R. de la Bretèche and V. Z. Kuperberg, “Lower bounds on weighted moments of primes in short intervals in number fields,” <i>Israel Journal of Mathematics</i>, vol. 267, no. 1. Springer Nature, pp. 437–461, 2025.","apa":"de la Bretèche, R., &#38; Kuperberg, V. Z. (2025). Lower bounds on weighted moments of primes in short intervals in number fields. <i>Israel Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11856-024-2711-0\">https://doi.org/10.1007/s11856-024-2711-0</a>","chicago":"Bretèche, Régis de la, and Vivian Zieve Kuperberg. “Lower Bounds on Weighted Moments of Primes in Short Intervals in Number Fields.” <i>Israel Journal of Mathematics</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s11856-024-2711-0\">https://doi.org/10.1007/s11856-024-2711-0</a>.","short":"R. de la Bretèche, V.Z. Kuperberg, Israel Journal of Mathematics 267 (2025) 437–461.","ista":"de la Bretèche R, Kuperberg VZ. 2025. Lower bounds on weighted moments of primes in short intervals in number fields. Israel Journal of Mathematics. 267(1), 437–461.","mla":"de la Bretèche, Régis, and Vivian Zieve Kuperberg. “Lower Bounds on Weighted Moments of Primes in Short Intervals in Number Fields.” <i>Israel Journal of Mathematics</i>, vol. 267, no. 1, Springer Nature, 2025, pp. 437–61, doi:<a href=\"https://doi.org/10.1007/s11856-024-2711-0\">10.1007/s11856-024-2711-0</a>.","ama":"de la Bretèche R, Kuperberg VZ. Lower bounds on weighted moments of primes in short intervals in number fields. <i>Israel Journal of Mathematics</i>. 2025;267(1):437-461. doi:<a href=\"https://doi.org/10.1007/s11856-024-2711-0\">10.1007/s11856-024-2711-0</a>"},"abstract":[{"text":"We consider an analog of a conjecture of Montgomery and Soundararajan on the moments of primes in short intervals in number fields; this analog was discussed and heuristically derived in a paper of the second author, Rodgers, and Roditty-Gershon. Adapting work of the first author and Fiorilli in the integer case, we establish lower bounds on a weighted version of these moments which agree with the conjectured values.","lang":"eng"}],"OA_place":"repository","fulldoi":"https://doi.org/10.1007/s11856-024-2711-0","day":"01","publication_status":"published","arxiv":1,"author":[{"full_name":"de la Bretèche, Régis","first_name":"Régis","last_name":"de la Bretèche"},{"last_name":"Kuperberg","full_name":"Kuperberg, Vivian Zieve","id":"c3bac823-112d-11f0-a3f5-c264f852e697","first_name":"Vivian Zieve"}],"OA_type":"green","article_type":"original","_id":"22201","extern":"1","month":"06","publication_identifier":{"eissn":["1565-8511"],"issn":["0021-2172"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2305.02662"}],"page":"437-461","status":"public","quality_controlled":"1","year":"2025","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2305.02662"]},"title":"Lower bounds on weighted moments of primes in short intervals in number fields","oa_version":"Preprint","date_published":"2025-06-01T00:00:00Z","date_created":"2026-06-29T13:00:06Z"},{"quality_controlled":"1","year":"2025","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2312.09021"}],"month":"07","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1460-244X"],"issn":["0024-6115"]},"_id":"22203","extern":"1","date_published":"2025-07-01T00:00:00Z","date_created":"2026-06-29T13:00:46Z","mathsc":["11N69","11N05","14G05"],"external_id":{"arxiv":["2312.09021"]},"title":"Odd moments and adding fractions","oa_version":"Preprint","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"T. F. Bloom and V. Z. Kuperberg, “Odd moments and adding fractions,” <i>Proceedings of the London Mathematical Society</i>, vol. 131, no. 1. Wiley, 2025.","apa":"Bloom, T. F., &#38; Kuperberg, V. Z. (2025). Odd moments and adding fractions. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/plms.70068\">https://doi.org/10.1112/plms.70068</a>","chicago":"Bloom, Thomas F., and Vivian Zieve Kuperberg. “Odd Moments and Adding Fractions.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2025. <a href=\"https://doi.org/10.1112/plms.70068\">https://doi.org/10.1112/plms.70068</a>.","short":"T.F. Bloom, V.Z. Kuperberg, Proceedings of the London Mathematical Society 131 (2025).","ista":"Bloom TF, Kuperberg VZ. 2025. Odd moments and adding fractions. Proceedings of the London Mathematical Society. 131(1), e70068.","ama":"Bloom TF, Kuperberg VZ. Odd moments and adding fractions. <i>Proceedings of the London Mathematical Society</i>. 2025;131(1). doi:<a href=\"https://doi.org/10.1112/plms.70068\">10.1112/plms.70068</a>","mla":"Bloom, Thomas F., and Vivian Zieve Kuperberg. “Odd Moments and Adding Fractions.” <i>Proceedings of the London Mathematical Society</i>, vol. 131, no. 1, e70068, Wiley, 2025, doi:<a href=\"https://doi.org/10.1112/plms.70068\">10.1112/plms.70068</a>."},"article_number":"e70068","issue":"1","type":"journal_article","volume":131,"publication":"Proceedings of the London Mathematical Society","oa":1,"scopus_import":"1","publisher":"Wiley","doi":"10.1112/plms.70068","date_updated":"2026-07-14T11:45:18Z","intvolume":"       131","article_type":"original","author":[{"full_name":"Bloom, Thomas F.","first_name":"Thomas F.","last_name":"Bloom"},{"last_name":"Kuperberg","first_name":"Vivian Zieve","full_name":"Kuperberg, Vivian Zieve","id":"c3bac823-112d-11f0-a3f5-c264f852e697"}],"OA_type":"green","publication_status":"published","arxiv":1,"day":"01","abstract":[{"lang":"eng","text":"We prove near-optimal upper bounds for the oddmoments of the distribution of coprime residues inshort intervals, confirming a conjecture of Montgomeryand Vaughan. As an application, we prove near-optimalupper bounds for the average of the refined singularseries in the Hardy–Littlewood conjectures concerningthe number of prime 𝑘-tuples for 𝑘 odd. The mainnew ingredient is a near-optimal upper bound for thenumber of solutions to ∑1 ⩽𝑖 ⩽𝑘𝑎 𝑖𝑞𝑖∈ ℤ when 𝑘 is odd,with gcd(𝑎𝑖 , 𝑞𝑖 ) = 1 and restrictions on the size of thenumerators and denominators, which is of indepen-dent interest."}],"OA_place":"repository","fulldoi":"https://doi.org/10.1112/plms.70068"},{"oa":1,"publisher":"Cambridge University Press","scopus_import":"1","doi":"10.1017/s1474748025000131","intvolume":"        24","date_updated":"2026-07-14T11:50:36Z","citation":{"ama":"Kimmel N, Kuperberg VZ. Positive density for consecutive runs of sums of two squares. <i>Journal of the Institute of Mathematics of Jussieu</i>. 2025;24(5):1995-2046. doi:<a href=\"https://doi.org/10.1017/s1474748025000131\">10.1017/s1474748025000131</a>","mla":"Kimmel, Noam, and Vivian Zieve Kuperberg. “Positive Density for Consecutive Runs of Sums of Two Squares.” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 24, no. 5, Cambridge University Press, 2025, pp. 1995–2046, doi:<a href=\"https://doi.org/10.1017/s1474748025000131\">10.1017/s1474748025000131</a>.","short":"N. Kimmel, V.Z. Kuperberg, Journal of the Institute of Mathematics of Jussieu 24 (2025) 1995–2046.","ista":"Kimmel N, Kuperberg VZ. 2025. Positive density for consecutive runs of sums of two squares. Journal of the Institute of Mathematics of Jussieu. 24(5), 1995–2046.","chicago":"Kimmel, Noam, and Vivian Zieve Kuperberg. “Positive Density for Consecutive Runs of Sums of Two Squares.” <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/s1474748025000131\">https://doi.org/10.1017/s1474748025000131</a>.","apa":"Kimmel, N., &#38; Kuperberg, V. Z. (2025). Positive density for consecutive runs of sums of two squares. <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s1474748025000131\">https://doi.org/10.1017/s1474748025000131</a>","ieee":"N. Kimmel and V. Z. Kuperberg, “Positive density for consecutive runs of sums of two squares,” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 24, no. 5. Cambridge University Press, pp. 1995–2046, 2025."},"issue":"5","type":"journal_article","volume":24,"publication":"Journal of the Institute of Mathematics of Jussieu","day":"01","publication_status":"published","arxiv":1,"abstract":[{"text":"We study the distribution of consecutive sums of two squares in arithmetic progressions. We\r\nshow that for any odd squarefree modulus q, any two reduced congruence classes a1 and a2 mod q,\r\nand any r1,r2 ≥ 1, a positive density of sums of two squares begin a chain of r1 consecutive sums of\r\ntwo squares, all of which are a1 mod q, followed immediately by a chain of r2 consecutive sums of two\r\nsquares, all of which are a2 mod q. This is an analog of the result of Maynard for the sequence of primes,\r\nshowing that for any reduced congruence class a mod q and for any r ≥ 1, a positive density of primes\r\nbegin a sequence of r consecutive primes, all of which are a mod q","lang":"eng"}],"OA_place":"repository","fulldoi":"https://doi.org/10.1017/s1474748025000131","article_type":"original","author":[{"full_name":"Kimmel, Noam","first_name":"Noam","last_name":"Kimmel"},{"first_name":"Vivian Zieve","id":"c3bac823-112d-11f0-a3f5-c264f852e697","full_name":"Kuperberg, Vivian Zieve","last_name":"Kuperberg"}],"OA_type":"green","month":"09","publication_identifier":{"eissn":["1475-3030"],"issn":["1474-7480"]},"language":[{"iso":"eng"}],"_id":"22204","extern":"1","year":"2025","status":"public","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2406.04174","open_access":"1"}],"page":"1995-2046","external_id":{"arxiv":["2406.04174"]},"title":"Positive density for consecutive runs of sums of two squares","oa_version":"Preprint","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2025-09-01T00:00:00Z","date_created":"2026-06-29T13:01:08Z"},{"publication_identifier":{"issn":["2160-3308"]},"language":[{"iso":"eng"}],"has_accepted_license":"1","month":"08","extern":"1","_id":"22213","status":"public","year":"2025","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.1103/8csn-71jk","open_access":"1"}],"oa_version":"Published Version","title":"Synthetic quorum sensing and absorbing phase transitions in colloidal active matter","external_id":{"arxiv":["2502.13919"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","date_created":"2026-06-30T06:32:31Z","date_published":"2025-08-22T00:00:00Z","ddc":["530"],"scopus_import":"1","publisher":"American Physical Society","oa":1,"intvolume":"        15","date_updated":"2026-07-15T07:21:38Z","doi":"10.1103/8csn-71jk","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_number":"031050","citation":{"ista":"Lefranc T, Dinelli A, Fernández-Rico C, Dullens RPA, Tailleur J, Bartolo D. 2025. Synthetic quorum sensing and absorbing phase transitions in colloidal active matter. Physical Review X. 15(3), 031050.","short":"T. Lefranc, A. Dinelli, C. Fernández-Rico, R.P.A. Dullens, J. Tailleur, D. Bartolo, Physical Review X 15 (2025).","ama":"Lefranc T, Dinelli A, Fernández-Rico C, Dullens RPA, Tailleur J, Bartolo D. Synthetic quorum sensing and absorbing phase transitions in colloidal active matter. <i>Physical Review X</i>. 2025;15(3). doi:<a href=\"https://doi.org/10.1103/8csn-71jk\">10.1103/8csn-71jk</a>","mla":"Lefranc, Thibault, et al. “Synthetic Quorum Sensing and Absorbing Phase Transitions in Colloidal Active Matter.” <i>Physical Review X</i>, vol. 15, no. 3, 031050, American Physical Society, 2025, doi:<a href=\"https://doi.org/10.1103/8csn-71jk\">10.1103/8csn-71jk</a>.","chicago":"Lefranc, Thibault, Alberto Dinelli, Carla Fernández-Rico, Roel P. A. Dullens, Julien Tailleur, and Denis Bartolo. “Synthetic Quorum Sensing and Absorbing Phase Transitions in Colloidal Active Matter.” <i>Physical Review X</i>. American Physical Society, 2025. <a href=\"https://doi.org/10.1103/8csn-71jk\">https://doi.org/10.1103/8csn-71jk</a>.","apa":"Lefranc, T., Dinelli, A., Fernández-Rico, C., Dullens, R. P. A., Tailleur, J., &#38; Bartolo, D. (2025). Synthetic quorum sensing and absorbing phase transitions in colloidal active matter. <i>Physical Review X</i>. American Physical Society. <a href=\"https://doi.org/10.1103/8csn-71jk\">https://doi.org/10.1103/8csn-71jk</a>","ieee":"T. Lefranc, A. Dinelli, C. Fernández-Rico, R. P. A. Dullens, J. Tailleur, and D. Bartolo, “Synthetic quorum sensing and absorbing phase transitions in colloidal active matter,” <i>Physical Review X</i>, vol. 15, no. 3. American Physical Society, 2025."},"publication":"Physical Review X","volume":15,"type":"journal_article","issue":"3","arxiv":1,"publication_status":"published","day":"22","fulldoi":"https://doi.org/10.1103/8csn-71jk","OA_place":"publisher","abstract":[{"text":"Unlike biological active matter that constantly adapt to their environment, the motors of synthetic active particles are typically agnostic to their surroundings and merely operate at constant force. Here, we design colloidal active rods capable of modulating their inner activity in response to crowding, thereby enforcing a primitive form of quorum sensing interactions. Through experiments, simulations, and theory we elucidate the impact of these interactions on the phase behavior of isotropic active matter. We demonstrate that, when conditioned to density, motility regulation can either lead to an absorbing phase transition, where all particles freeze their dynamics, or to atypical phase separation, where flat interfaces supporting a net pressure drop are in mechanical equilibrium. Fully active and fully arrested particles can then form heterogeneous patterns ruled by the competition between quorum sensing and mechanical interactions. Beyond the specifics of motile colloids, we expect our findings to apply broadly to adaptive active matter assembled from living or synthetic units.","lang":"eng"}],"article_type":"original","OA_type":"hybrid","author":[{"last_name":"Lefranc","first_name":"Thibault","full_name":"Lefranc, Thibault"},{"first_name":"Alberto","full_name":"Dinelli, Alberto","last_name":"Dinelli"},{"last_name":"Fernández-Rico","id":"492def71-6250-11f0-b278-d41dbd241b62","first_name":"Carla","full_name":"Fernández-Rico, Carla"},{"last_name":"Dullens","first_name":"Roel P. A.","full_name":"Dullens, Roel P. A."},{"last_name":"Tailleur","first_name":"Julien","full_name":"Tailleur, Julien"},{"first_name":"Denis","full_name":"Bartolo, Denis","last_name":"Bartolo"}]},{"citation":{"apa":"Fojo, J., Subert, R., Rodríguez-Arco, L., López-López, M. T., Dijkstra, M., Fernández-Rico, C., &#38; Alvarez, L. (2025). Field-driven reversible networks from colloidal rods. <i>Soft Matter</i>. Royal Society of Chemistry. <a href=\"https://doi.org/10.1039/d5sm00218d\">https://doi.org/10.1039/d5sm00218d</a>","ieee":"J. Fojo <i>et al.</i>, “Field-driven reversible networks from colloidal rods,” <i>Soft Matter</i>, vol. 21, no. 23. Royal Society of Chemistry, pp. 4596–4605, 2025.","mla":"Fojo, José, et al. “Field-Driven Reversible Networks from Colloidal Rods.” <i>Soft Matter</i>, vol. 21, no. 23, Royal Society of Chemistry, 2025, pp. 4596–605, doi:<a href=\"https://doi.org/10.1039/d5sm00218d\">10.1039/d5sm00218d</a>.","ama":"Fojo J, Subert R, Rodríguez-Arco L, et al. Field-driven reversible networks from colloidal rods. <i>Soft Matter</i>. 2025;21(23):4596-4605. doi:<a href=\"https://doi.org/10.1039/d5sm00218d\">10.1039/d5sm00218d</a>","ista":"Fojo J, Subert R, Rodríguez-Arco L, López-López MT, Dijkstra M, Fernández-Rico C, Alvarez L. 2025. Field-driven reversible networks from colloidal rods. Soft Matter. 21(23), 4596–4605.","short":"J. Fojo, R. Subert, L. Rodríguez-Arco, M.T. López-López, M. Dijkstra, C. Fernández-Rico, L. Alvarez, Soft Matter 21 (2025) 4596–4605.","chicago":"Fojo, José, Rodolfo Subert, Laura Rodríguez-Arco, Modesto T. López-López, Marjolein Dijkstra, Carla Fernández-Rico, and Laura Alvarez. “Field-Driven Reversible Networks from Colloidal Rods.” <i>Soft Matter</i>. Royal Society of Chemistry, 2025. <a href=\"https://doi.org/10.1039/d5sm00218d\">https://doi.org/10.1039/d5sm00218d</a>."},"issue":"23","type":"journal_article","publication":"Soft Matter","volume":21,"pmid":1,"publisher":"Royal Society of Chemistry","scopus_import":"1","doi":"10.1039/d5sm00218d","date_updated":"2026-07-15T07:37:27Z","intvolume":"        21","article_type":"original","author":[{"first_name":"José","full_name":"Fojo, José","last_name":"Fojo"},{"last_name":"Subert","first_name":"Rodolfo","full_name":"Subert, Rodolfo"},{"first_name":"Laura","full_name":"Rodríguez-Arco, Laura","last_name":"Rodríguez-Arco"},{"last_name":"López-López","first_name":"Modesto T.","full_name":"López-López, Modesto T."},{"first_name":"Marjolein","full_name":"Dijkstra, Marjolein","last_name":"Dijkstra"},{"full_name":"Fernández-Rico, Carla","first_name":"Carla","id":"492def71-6250-11f0-b278-d41dbd241b62","last_name":"Fernández-Rico"},{"first_name":"Laura","full_name":"Alvarez, Laura","last_name":"Alvarez"}],"OA_type":"closed access","day":"21","publication_status":"published","abstract":[{"lang":"eng","text":"Highly interconnected percolated networks are interesting structures for materials with enhanced transport and mechanical properties. While percolated networks of anisotropic particles have been explored at the nanoscale, achieving highly interconnected structures at the microscale remains challenging. In this work, we explore the controlled assembly of rod-like polymer colloids under external fields leading to reversible quasi-2D networks. By varying voltage and frequency, we modulate the pore size and thickness of the network. We find that field-driven attractive interactions enable percolation at lower area fractions than predicted for non-interacting rods. Monte Carlo simulations incorporating dipolar interactions and electrostatic boundary conditions confirm the field-induced transition from isotropic to aligned rod configurations, supporting the emergence of percolated networks. This work presents a simple and robust approach for assembling reconfigurable colloidal networks with controlled connectivity, offering new strategies for designing adaptive soft materials."}],"fulldoi":"https://doi.org/10.1039/d5sm00218d","year":"2025","quality_controlled":"1","status":"public","page":"4596-4605","month":"06","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1744-6848"],"issn":["1744-683X"]},"_id":"22214","extern":"1","date_published":"2025-06-21T00:00:00Z","date_created":"2026-06-30T06:32:50Z","external_id":{"pmid":["40314070"]},"title":"Field-driven reversible networks from colloidal rods","oa_version":"None","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"OA_type":"hybrid","author":[{"first_name":"Bartosz","full_name":"Naskręcki, Bartosz","last_name":"Naskręcki"},{"last_name":"Verzobio","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","full_name":"Verzobio, Matteo","first_name":"Matteo","orcid":"0000-0002-0854-0306"}],"article_type":"original","file_date_updated":"2025-12-30T06:45:47Z","OA_place":"publisher","corr_author":"1","fulldoi":"https://doi.org/10.1017/prm.2024.7","abstract":[{"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.","lang":"eng"}],"researchdata_availability":"no","arxiv":1,"publication_status":"published","day":"01","keyword":["Elliptic curves","Néron models","division polynomials","height functions","discrete valuation rings"],"type":"journal_article","volume":155,"publication":"Proceedings of the Royal Society of Edinburgh Section A: Mathematics","das_tickbox":"0","issue":"5","citation":{"ieee":"B. Naskręcki and M. Verzobio, “Common valuations of division polynomials,” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>, vol. 155, no. 5. Cambridge University Press, pp. 1646–1660, 2025.","apa":"Naskręcki, B., &#38; Verzobio, M. (2025). Common valuations of division polynomials. <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/prm.2024.7\">https://doi.org/10.1017/prm.2024.7</a>","chicago":"Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/prm.2024.7\">https://doi.org/10.1017/prm.2024.7</a>.","mla":"Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>, vol. 155, no. 5, Cambridge University Press, 2025, pp. 1646–60, doi:<a href=\"https://doi.org/10.1017/prm.2024.7\">10.1017/prm.2024.7</a>.","ama":"Naskręcki B, Verzobio M. Common valuations of division polynomials. <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. 2025;155(5):1646-1660. doi:<a href=\"https://doi.org/10.1017/prm.2024.7\">10.1017/prm.2024.7</a>","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.","short":"B. Naskręcki, M. Verzobio, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 155 (2025) 1646–1660."},"intvolume":"       155","date_updated":"2026-07-16T08:43:40Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"PlanS_conform":"1","doi":"10.1017/prm.2024.7","scopus_import":"1","publisher":"Cambridge University Press","oa":1,"supplementarymaterial":"no","department":[{"_id":"TiBr"}],"ddc":["510"],"file":[{"date_created":"2025-12-30T06:45:47Z","success":1,"checksum":"c5ec6e29aca2fb4533cb95fac409a0b2","file_name":"2025_ProceedingsRoyalSocEdinburghA_Naskrecki.pdf","creator":"dernst","file_size":477624,"relation":"main_file","content_type":"application/pdf","date_updated":"2025-12-30T06:45:47Z","file_id":"20878","access_level":"open_access"}],"date_created":"2023-01-16T11:45:22Z","date_published":"2025-10-01T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_processing_charge":"Yes (via OA deal)","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.","title":"Common valuations of division polynomials","oa_version":"Published Version","external_id":{"isi":["001174907100001"],"arxiv":["2203.02015"]},"isi":1,"page":"1646-1660","project":[{"name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"quality_controlled":"1","year":"2025","status":"public","ec_funded":1,"_id":"12311","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0308-2105"],"eissn":["1473-7124"]},"month":"10","has_accepted_license":"1"},{"_id":"20797","has_accepted_license":"1","month":"08","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2331-7019"]},"year":"2025","status":"public","quality_controlled":"1","article_processing_charge":"Yes (in subscription journal)","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","external_id":{"arxiv":["2412.08694"]},"oa_version":"Published Version","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).","title":"Surpassing the loss-noise robustness trade-off in quantum key distribution","ddc":["530"],"department":[{"_id":"OnHo"}],"date_published":"2025-08-29T00:00:00Z","date_created":"2025-12-11T10:46:28Z","file":[{"creator":"dernst","file_name":"2025_PhysReviewApplied_Seabrook.pdf","checksum":"12ddb0414780f65b8e690fe0e6cfb95e","date_created":"2025-12-15T09:39:12Z","success":1,"access_level":"open_access","date_updated":"2025-12-15T09:39:12Z","content_type":"application/pdf","file_id":"20824","file_size":3028735,"relation":"main_file"}],"doi":"10.1103/xq2l-r4r7","PlanS_conform":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"intvolume":"        24","date_updated":"2026-07-16T08:27:32Z","supplementarymaterial":"no","oa":1,"publisher":"American Physical Society","scopus_import":"1","issue":"2","das_tickbox":"1","publication":"Physical Review Applied","volume":24,"type":"journal_article","article_number":"024072","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  ","citation":{"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.” <i>Physical Review Applied</i>. American Physical Society, 2025. <a href=\"https://doi.org/10.1103/xq2l-r4r7\">https://doi.org/10.1103/xq2l-r4r7</a>.","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.","short":"H. Seabrook, E. Lavie, K.T. Strömberg, M.P. Stafford, G. Rubino, Physical Review Applied 24 (2025).","mla":"Seabrook, Hannah, et al. “Surpassing the Loss-Noise Robustness Trade-off in Quantum Key Distribution.” <i>Physical Review Applied</i>, vol. 24, no. 2, 024072, American Physical Society, 2025, doi:<a href=\"https://doi.org/10.1103/xq2l-r4r7\">10.1103/xq2l-r4r7</a>.","ama":"Seabrook H, Lavie E, Strömberg KT, Stafford MP, Rubino G. Surpassing the loss-noise robustness trade-off in quantum key distribution. <i>Physical Review Applied</i>. 2025;24(2). doi:<a href=\"https://doi.org/10.1103/xq2l-r4r7\">10.1103/xq2l-r4r7</a>","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,” <i>Physical Review Applied</i>, vol. 24, no. 2. American Physical Society, 2025.","apa":"Seabrook, H., Lavie, E., Strömberg, K. T., Stafford, M. P., &#38; Rubino, G. (2025). Surpassing the loss-noise robustness trade-off in quantum key distribution. <i>Physical Review Applied</i>. American Physical Society. <a href=\"https://doi.org/10.1103/xq2l-r4r7\">https://doi.org/10.1103/xq2l-r4r7</a>"},"abstract":[{"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.","lang":"eng"}],"fulldoi":"https://doi.org/10.1103/xq2l-r4r7","file_date_updated":"2025-12-15T09:39:12Z","OA_place":"publisher","day":"29","publication_status":"published","arxiv":1,"researchdata_availability":"yes","author":[{"last_name":"Seabrook","full_name":"Seabrook, Hannah","first_name":"Hannah"},{"last_name":"Lavie","first_name":"Emilien","full_name":"Lavie, Emilien"},{"last_name":"Strömberg","first_name":"Karl T","full_name":"Strömberg, Karl T","id":"68011cd2-da32-11ee-a930-b2774c7aba5f"},{"full_name":"Stafford, Matthew P.","first_name":"Matthew P.","last_name":"Stafford"},{"last_name":"Rubino","full_name":"Rubino, Giulia","first_name":"Giulia"}],"OA_type":"hybrid","article_type":"original"},{"citation":{"apa":"Browning, T. D., Lyczak, J., &#38; Smeets, A. (2025). Paucity of rational points on fibrations with multiple fibres. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2025.19.2049\">https://doi.org/10.2140/ant.2025.19.2049</a>","ieee":"T. D. Browning, J. Lyczak, and A. Smeets, “Paucity of rational points on fibrations with multiple fibres,” <i>Algebra &#38; Number Theory</i>, vol. 19, no. 10. Mathematical Sciences Publishers, pp. 2049–2090, 2025.","short":"T.D. Browning, J. Lyczak, A. Smeets, Algebra &#38; Number Theory 19 (2025) 2049–2090.","ista":"Browning TD, Lyczak J, Smeets A. 2025. Paucity of rational points on fibrations with multiple fibres. Algebra &#38; Number Theory. 19(10), 2049–2090.","mla":"Browning, Timothy D., et al. “Paucity of Rational Points on Fibrations with Multiple Fibres.” <i>Algebra &#38; Number Theory</i>, vol. 19, no. 10, Mathematical Sciences Publishers, 2025, pp. 2049–90, doi:<a href=\"https://doi.org/10.2140/ant.2025.19.2049\">10.2140/ant.2025.19.2049</a>.","ama":"Browning TD, Lyczak J, Smeets A. Paucity of rational points on fibrations with multiple fibres. <i>Algebra &#38; Number Theory</i>. 2025;19(10):2049-2090. doi:<a href=\"https://doi.org/10.2140/ant.2025.19.2049\">10.2140/ant.2025.19.2049</a>","chicago":"Browning, Timothy D, Julian Lyczak, and Arne Smeets. “Paucity of Rational Points on Fibrations with Multiple Fibres.” <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2025. <a href=\"https://doi.org/10.2140/ant.2025.19.2049\">https://doi.org/10.2140/ant.2025.19.2049</a>."},"das_tickbox":"0","issue":"10","type":"journal_article","publication":"Algebra & Number Theory","volume":19,"supplementarymaterial":"no","oa":1,"publisher":"Mathematical Sciences Publishers","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"doi":"10.2140/ant.2025.19.2049","PlanS_conform":"1","date_updated":"2026-07-16T08:52:36Z","intvolume":"        19","article_type":"original","author":[{"last_name":"Browning","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","first_name":"Timothy D"},{"last_name":"Lyczak","full_name":"Lyczak, Julian","first_name":"Julian"},{"first_name":"Arne","full_name":"Smeets, Arne","last_name":"Smeets"}],"OA_type":"diamond","publication_status":"published","day":"05","arxiv":1,"researchdata_availability":"no","abstract":[{"text":"Given a family of varieties over the projective line, we study the density of fibres that are everywhere locally soluble in the case that components of higher multiplicity are allowed. We use log geometry to formulate a new sparsity criterion for the existence of everywhere locally soluble fibres and formulate new conjectures that generalise previous work of Loughran and Smeets. These conjectures involve geometric invariants of the associated multiplicity orbifolds on the base of the fibration in the spirit of Campana. We give evidence for the conjectures by providing an assortment of bounds using Chebotarev’s theorem and sieve methods, with most of the evidence involving upper bounds. ","lang":"eng"}],"file_date_updated":"2026-02-17T11:56:20Z","OA_place":"publisher","corr_author":"1","fulldoi":"https://doi.org/10.2140/ant.2025.19.2049","project":[{"call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","name":"New frontiers of the Manin conjecture"}],"quality_controlled":"1","status":"public","year":"2025","page":"2049-2090","month":"09","has_accepted_license":"1","publication_identifier":{"eissn":["1944-7833"],"issn":["1937-0652"]},"language":[{"iso":"eng"}],"_id":"21244","date_published":"2025-09-05T00:00:00Z","file":[{"access_level":"open_access","file_id":"21300","date_updated":"2026-02-17T11:56:20Z","content_type":"application/pdf","file_size":1505580,"relation":"main_file","creator":"dernst","file_name":"2025_AlgebraNumberTheory_Browning.pdf","checksum":"e50a60a4303b81563f7adbcadbe2e986","success":1,"date_created":"2026-02-17T11:56:20Z"}],"date_created":"2026-02-16T15:22:19Z","ddc":["510"],"department":[{"_id":"TiBr"}],"external_id":{"arxiv":["2310.01135"]},"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.","title":"Paucity of rational points on fibrations with multiple fibres","oa_version":"Published Version","article_processing_charge":"No","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345"},{"_id":"20850","publication_identifier":{"issn":["1246-7405"],"eissn":["2118-8572"]},"language":[{"iso":"eng"}],"has_accepted_license":"1","month":"11","page":"973-988","license":"https://creativecommons.org/licenses/by-nd/4.0/","year":"2025","quality_controlled":"1","status":"public","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_processing_charge":"Yes (in subscription journal)","oa_version":"Published Version","title":"Class numbers and integer points on some Pellian surfaces","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.","external_id":{"arxiv":["2408.03774"]},"department":[{"_id":"TiBr"}],"ddc":["510"],"file":[{"file_id":"20861","content_type":"application/pdf","date_updated":"2025-12-29T10:05:22Z","access_level":"open_access","file_size":766196,"relation":"main_file","file_name":"2025_JTNB_Diao.pdf","creator":"dernst","success":1,"date_created":"2025-12-29T10:05:22Z","checksum":"67aa0afbc0b5bcbff5341f4d25e6ba20"}],"date_created":"2025-12-21T23:01:35Z","date_published":"2025-11-27T00:00:00Z","intvolume":"        37","date_updated":"2026-07-16T08:45:12Z","doi":"10.5802/jtnb.1348","tmp":{"short":"CC BY-ND (4.0)","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)"},"scopus_import":"1","publisher":"Université de Bordeaux","oa":1,"supplementarymaterial":"no","publication":"Journal de theorie des nombres de Bordeaux","volume":37,"type":"journal_article","issue":"3","das_tickbox":"0","citation":{"chicago":"Diao, Yijie. “Class Numbers and Integer Points on Some Pellian Surfaces.” <i>Journal de Theorie Des Nombres de Bordeaux</i>. Université de Bordeaux, 2025. <a href=\"https://doi.org/10.5802/jtnb.1348\">https://doi.org/10.5802/jtnb.1348</a>.","short":"Y. Diao, Journal de Theorie Des Nombres de Bordeaux 37 (2025) 973–988.","ista":"Diao Y. 2025. Class numbers and integer points on some Pellian surfaces. Journal de theorie des nombres de Bordeaux. 37(3), 973–988.","ama":"Diao Y. Class numbers and integer points on some Pellian surfaces. <i>Journal de theorie des nombres de Bordeaux</i>. 2025;37(3):973-988. doi:<a href=\"https://doi.org/10.5802/jtnb.1348\">10.5802/jtnb.1348</a>","mla":"Diao, Yijie. “Class Numbers and Integer Points on Some Pellian Surfaces.” <i>Journal de Theorie Des Nombres de Bordeaux</i>, vol. 37, no. 3, Université de Bordeaux, 2025, pp. 973–88, doi:<a href=\"https://doi.org/10.5802/jtnb.1348\">10.5802/jtnb.1348</a>.","ieee":"Y. Diao, “Class numbers and integer points on some Pellian surfaces,” <i>Journal de theorie des nombres de Bordeaux</i>, vol. 37, no. 3. Université de Bordeaux, pp. 973–988, 2025.","apa":"Diao, Y. (2025). Class numbers and integer points on some Pellian surfaces. <i>Journal de Theorie Des Nombres de Bordeaux</i>. Université de Bordeaux. <a href=\"https://doi.org/10.5802/jtnb.1348\">https://doi.org/10.5802/jtnb.1348</a>"},"fulldoi":"https://doi.org/10.5802/jtnb.1348","OA_place":"publisher","corr_author":"1","file_date_updated":"2025-12-29T10:05:22Z","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."}],"researchdata_availability":"no","day":"27","publication_status":"published","arxiv":1,"OA_type":"hybrid","author":[{"last_name":"Diao","orcid":"0000-0002-4989-5330","first_name":"Yijie","full_name":"Diao, Yijie","id":"7b7eb4ca-eb2c-11ec-b98b-accec0b20c3b"}],"article_type":"original"},{"date_published":"2025-09-01T00:00:00Z","date_created":"2026-01-18T23:02:44Z","file":[{"checksum":"3d38e850b40f3e1abbfd30073bd4388a","date_created":"2026-02-12T07:50:47Z","success":1,"creator":"dernst","file_name":"2025_DiscreteAnalysis_Browning.pdf","relation":"main_file","file_size":393625,"access_level":"open_access","date_updated":"2026-02-12T07:50:47Z","content_type":"application/pdf","file_id":"21214"}],"ddc":["510"],"department":[{"_id":"TiBr"}],"external_id":{"arxiv":["2408.11453"]},"oa_version":"Published Version","title":"Counting integer points on affine surfaces with a side condition","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_processing_charge":"No","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2025","status":"public","project":[{"name":"Rational curves via function field analytic number theory","grant_number":"P36278","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3"},{"grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"has_accepted_license":"1","month":"09","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2397-3129"]},"_id":"21003","ec_funded":1,"article_type":"original","author":[{"last_name":"Browning","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","first_name":"Timothy D"},{"orcid":"0000-0002-0854-0306","first_name":"Matteo","full_name":"Verzobio, Matteo","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","last_name":"Verzobio"}],"OA_type":"diamond","arxiv":1,"publication_status":"published","day":"01","researchdata_availability":"no","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."}],"fulldoi":"https://doi.org/10.19086/da.143787","OA_place":"publisher","file_date_updated":"2026-02-12T07:50:47Z","corr_author":"1","article_number":"12","citation":{"apa":"Browning, T. D., &#38; Verzobio, M. (2025). Counting integer points on affine surfaces with a side condition. <i>Discrete Analysis</i>. Cambridge: Alliance of Diamond Open Access Journals. <a href=\"https://doi.org/10.19086/da.143787\">https://doi.org/10.19086/da.143787</a>","ieee":"T. D. Browning and M. Verzobio, “Counting integer points on affine surfaces with a side condition,” <i>Discrete Analysis</i>, vol. 2025. Cambridge: Alliance of Diamond Open Access Journals, 2025.","ama":"Browning TD, Verzobio M. Counting integer points on affine surfaces with a side condition. <i>Discrete Analysis</i>. 2025;2025. doi:<a href=\"https://doi.org/10.19086/da.143787\">10.19086/da.143787</a>","mla":"Browning, Timothy D., and Matteo Verzobio. “Counting Integer Points on Affine Surfaces with a Side Condition.” <i>Discrete Analysis</i>, vol. 2025, 12, Cambridge: Alliance of Diamond Open Access Journals, 2025, doi:<a href=\"https://doi.org/10.19086/da.143787\">10.19086/da.143787</a>.","ista":"Browning TD, Verzobio M. 2025. Counting integer points on affine surfaces with a side condition. Discrete Analysis. 2025, 12.","short":"T.D. Browning, M. Verzobio, Discrete Analysis 2025 (2025).","chicago":"Browning, Timothy D, and Matteo Verzobio. “Counting Integer Points on Affine Surfaces with a Side Condition.” <i>Discrete Analysis</i>. Cambridge: Alliance of Diamond Open Access Journals, 2025. <a href=\"https://doi.org/10.19086/da.143787\">https://doi.org/10.19086/da.143787</a>."},"das_tickbox":"0","volume":2025,"publication":"Discrete Analysis","type":"journal_article","supplementarymaterial":"no","oa":1,"scopus_import":"1","publisher":"Cambridge: Alliance of Diamond Open Access Journals","doi":"10.19086/da.143787","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"intvolume":"      2025","date_updated":"2026-07-16T08:48:35Z"},{"citation":{"apa":"Yao Xiao, S., &#38; Yamagishi, S. (2025). Quartic polynomials in two variables do not represent all non-negative integers. <i>Journal of the European Mathematical Society</i>. EMS Press. <a href=\"https://doi.org/10.4171/jems/1697\">https://doi.org/10.4171/jems/1697</a>","ieee":"S. Yao Xiao and S. Yamagishi, “Quartic polynomials in two variables do not represent all non-negative integers,” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025.","short":"S. Yao Xiao, S. Yamagishi, Journal of the European Mathematical Society (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.” <i>Journal of the European Mathematical Society</i>, EMS Press, 2025, doi:<a href=\"https://doi.org/10.4171/jems/1697\">10.4171/jems/1697</a>.","ama":"Yao Xiao S, Yamagishi S. Quartic polynomials in two variables do not represent all non-negative integers. <i>Journal of the European Mathematical Society</i>. 2025. doi:<a href=\"https://doi.org/10.4171/jems/1697\">10.4171/jems/1697</a>","chicago":"Yao Xiao, Stanley, and Shuntaro Yamagishi. “Quartic Polynomials in Two Variables Do Not Represent All Non-Negative Integers.” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/jems/1697\">https://doi.org/10.4171/jems/1697</a>."},"type":"journal_article","publication":"Journal of the European Mathematical Society","das_tickbox":"0","publisher":"EMS Press","oa":1,"supplementarymaterial":"no","date_updated":"2026-07-16T08:54:37Z","doi":"10.4171/jems/1697","article_type":"original","OA_type":"diamond","author":[{"first_name":"Stanley","full_name":"Yao Xiao, Stanley","last_name":"Yao Xiao"},{"last_name":"Yamagishi","full_name":"Yamagishi, Shuntaro","first_name":"Shuntaro","id":"0c3fbc5c-f7a6-11ec-8d70-9485e75b416b"}],"researchdata_availability":"no","publication_status":"epub_ahead","arxiv":1,"day":"06","OA_place":"publisher","corr_author":"1","fulldoi":"https://doi.org/10.4171/jems/1697","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."}],"project":[{"call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","name":"New frontiers of the Manin conjecture"}],"quality_controlled":"1","year":"2025","status":"public","main_file_link":[{"url":"https://doi.org/10.4171/JEMS/1697","open_access":"1"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1435-9855"],"eissn":["1435-9863"]},"month":"08","_id":"21260","date_created":"2026-02-16T16:00:02Z","date_published":"2025-08-06T00:00:00Z","department":[{"_id":"TiBr"}],"ddc":["500"],"title":"Quartic polynomials in two variables do not represent all non-negative integers","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.","oa_version":"Published Version","external_id":{"arxiv":["2307.05712"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_processing_charge":"No"}]