[{"scopus_import":"1","issue":"12","publication":"International Mathematics Research Notices","acknowledgement":"Z.H. was supported by SNSF grant 200021-228014. M.K. was supported by ERC Starting Grant “RANDSTRUCT” No. 101076777. L.S. was supported by the Deutsche Forschungsgemeinschaft (DFG, German\r\nResearch Foundation)—CRC 1720–539309657. This research was conducted during the period M.S. served\r\nas a Clay Research Fellow. This work began when the authors were visiting Mathematisches Forschungsinstitut Oberwolfach, which\r\nprovided ideal working conditions. M.S. thanks Vishesh Jain for initial discussions regarding the problem.\r\nWe also thank the anonymous referee for helpful comments.","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"OA_type":"hybrid","OA_place":"publisher","language":[{"iso":"eng"}],"author":[{"full_name":"Hunter, Zach","first_name":"Zach","last_name":"Hunter"},{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan","last_name":"Kwan","full_name":"Kwan, Matthew Alan","orcid":"0000-0002-4003-7567"},{"last_name":"Sauermann","first_name":"Lisa","full_name":"Sauermann, Lisa"},{"full_name":"Sawhney, Mehtaab","first_name":"Mehtaab","last_name":"Sawhney"}],"date_created":"2026-06-28T22:01:35Z","status":"public","title":"On random matrices with large corank","_id":"22147","abstract":[{"lang":"eng","text":"Let 1 ≤ k ≤ n and M be a random n × n matrix with independent uniformly random {±1}-entries. We\r\nshow that there exists an absolute constant c > 0 such that\r\nP[rank(M) ≤ n − k] ≤ exp(−cnk).\r\nThis confirms a well-known prediction in the area, extending a result of Rudelson (who previously\r\nproved this same result under the restriction k ≤ √n, via different methods)."}],"oa_version":"Published Version","type":"journal_article","article_type":"original","citation":{"mla":"Hunter, Zach, et al. “On Random Matrices with Large Corank.” International Mathematics Research Notices, vol. 2026, no. 12, rnag126, Oxford University Press, 2026, doi:10.1093/imrn/rnag126.","ama":"Hunter Z, Kwan MA, Sauermann L, Sawhney M. On random matrices with large corank. International Mathematics Research Notices. 2026;2026(12). doi:10.1093/imrn/rnag126","ieee":"Z. Hunter, M. A. Kwan, L. Sauermann, and M. Sawhney, “On random matrices with large corank,” International Mathematics Research Notices, vol. 2026, no. 12. Oxford University Press, 2026.","short":"Z. Hunter, M.A. Kwan, L. Sauermann, M. Sawhney, International Mathematics Research Notices 2026 (2026).","ista":"Hunter Z, Kwan MA, Sauermann L, Sawhney M. 2026. On random matrices with large corank. International Mathematics Research Notices. 2026(12), rnag126.","chicago":"Hunter, Zach, Matthew Alan Kwan, Lisa Sauermann, and Mehtaab Sawhney. “On Random Matrices with Large Corank.” International Mathematics Research Notices. Oxford University Press, 2026. https://doi.org/10.1093/imrn/rnag126.","apa":"Hunter, Z., Kwan, M. A., Sauermann, L., & Sawhney, M. (2026). On random matrices with large corank. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnag126"},"project":[{"_id":"bd95085b-d553-11ed-ba76-e55d3349be45","name":"Randomness and structure in combinatorics","grant_number":"101076777"}],"license":"https://creativecommons.org/licenses/by/4.0/","PlanS_conform":"1","supplementarymaterial":"no","date_updated":"2026-06-29T09:19:14Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","oa":1,"day":"01","publisher":"Oxford University Press","month":"06","department":[{"_id":"MaKw"}],"external_id":{"arxiv":["2510.12933"]},"article_number":"rnag126","doi":"10.1093/imrn/rnag126","researchdata_availability":"no","file":[{"checksum":"396b47d0532d7ea509f8cd30f11392a8","date_created":"2026-06-29T09:15:15Z","success":1,"creator":"dernst","relation":"main_file","access_level":"open_access","file_id":"22151","file_size":524993,"file_name":"2026_IMRN_Hunter.pdf","date_updated":"2026-06-29T09:15:15Z","content_type":"application/pdf"}],"volume":2026,"ddc":["500"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"intvolume":" 2026","publication_status":"published","quality_controlled":"1","year":"2026","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","file_date_updated":"2026-06-29T09:15:15Z","date_published":"2026-06-01T00:00:00Z","arxiv":1,"das_tickbox":"0","fulldoi":"https://doi.org/10.1093/imrn/rnag126"},{"quality_controlled":"1","year":"2026","publication_status":"published","intvolume":" 2026","date_published":"2026-02-01T00:00:00Z","article_processing_charge":"No","fulldoi":"https://doi.org/10.1093/imrn/rnag018","arxiv":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2506.15582","open_access":"1"}],"day":"01","oa":1,"external_id":{"arxiv":["2506.15582"]},"month":"02","publisher":"Oxford University Press","article_number":"rnag018","volume":2026,"doi":"10.1093/imrn/rnag018","_id":"22183","title":"Is it easy to regularize a hypergraph with easy links?","date_created":"2026-06-29T12:02:25Z","author":[{"last_name":"Gishboliner","first_name":"Lior","full_name":"Gishboliner, Lior"},{"full_name":"Shapira, Asaf","first_name":"Asaf","last_name":"Shapira"},{"id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","last_name":"Wigderson","first_name":"Yuval","full_name":"Wigderson, Yuval"}],"status":"public","article_type":"original","oa_version":"Preprint","type":"journal_article","extern":"1","abstract":[{"text":"A partition of a (hyper)graph is ε-homogeneous if the edge densities between almost all clusters are\r\neither at most ε or at least 1 − ε. Suppose a 3-graph has the property that the link of every vertex has\r\nan ε-homogeneous partition of size poly(1/ε). Does this guarantee that the 3-graph also has a small\r\nhomogeneous partition? Terry and Wolf proved that such a 3-graph has an ε-homogeneous partition\r\nof size given by a wowzer-type function. Terry recently improved this to a double exponential bound,\r\nand conjectured that this bound is tight. Our first result in this paper disproves this conjecture by\r\ngiving an improved (single) exponential bound, which is best possible. We further obtain an analogous\r\nresult for k-graphs of all uniformities k 3. The above problem is part of a much broader programme,\r\nwhich seeks to understand the conditions under which a (hyper)graph has small ε-regular partitions.\r\nWhile this problem is fairly well understood for graphs, the situation is (as always) much more\r\ninvolved already for 3-graphs. For example, it is natural to ask if one can strengthen our first result\r\nby only requiring each link to have ε-regular partitions of size poly(1/ε). Our second result shows that\r\nsurprisingly the answer is “no”, namely, a 3-graph might only have regular partitions of tower-type size,\r\neven though the link of every vertex has an ε-regular partition of polynomial size.","lang":"eng"}],"citation":{"mla":"Gishboliner, Lior, et al. “Is It Easy to Regularize a Hypergraph with Easy Links?” International Mathematics Research Notices, vol. 2026, no. 4, rnag018, Oxford University Press, 2026, doi:10.1093/imrn/rnag018.","ama":"Gishboliner L, Shapira A, Wigderson Y. Is it easy to regularize a hypergraph with easy links? International Mathematics Research Notices. 2026;2026(4). doi:10.1093/imrn/rnag018","short":"L. Gishboliner, A. Shapira, Y. Wigderson, International Mathematics Research Notices 2026 (2026).","ieee":"L. Gishboliner, A. Shapira, and Y. Wigderson, “Is it easy to regularize a hypergraph with easy links?,” International Mathematics Research Notices, vol. 2026, no. 4. Oxford University Press, 2026.","ista":"Gishboliner L, Shapira A, Wigderson Y. 2026. Is it easy to regularize a hypergraph with easy links? International Mathematics Research Notices. 2026(4), rnag018.","chicago":"Gishboliner, Lior, Asaf Shapira, and Yuval Wigderson. “Is It Easy to Regularize a Hypergraph with Easy Links?” International Mathematics Research Notices. Oxford University Press, 2026. https://doi.org/10.1093/imrn/rnag018.","apa":"Gishboliner, L., Shapira, A., & Wigderson, Y. (2026). Is it easy to regularize a hypergraph with easy links? International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnag018"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-07-14T09:25:22Z","publication":"International Mathematics Research Notices","issue":"4","scopus_import":"1","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"OA_type":"green","OA_place":"repository","language":[{"iso":"eng"}]},{"publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"acknowledgement":"This work was supported by a DOC Fellowship of the Austrian Academy of Sciences at the Institute of Science and Technology Austria (ISTA) and by an Erasmus+ staff mobility training. It took place during the author’s visit to Laboratoire de Mathématiques d’Orsay in the course of his PhD at the Institute of Science and Technology Austria. First and foremost, I would like to thank Matthew Morrow for discussions, explanations and ideas without which this work would not have been carried out. I would further like to thank Brian Conrad for providing an amazing reference on projective cones in appropriate generality, to Vova Sosnilo for carefully discussing – among other things – the derived nilinvariance for quotients by any linearly reductive group, and to Adeel Khan, Timo Richarz, Matthias Wendt and Xinwen Zhu for helpful conversations\r\nabout the results. I would moreover like to thank the referee for the very useful comments.","issue":"7","scopus_import":"1","publication":"International Mathematics Research Notices","language":[{"iso":"eng"}],"OA_place":"publisher","OA_type":"hybrid","abstract":[{"text":"We define a certain class of simple varieties over a field k by a constructive recipe and show how to control their (equivariant) truncating invariants. Consequently, we prove that on simple varieties: (i) if k = k and char k = p, the p-adic cyclotomic trace is an equivalence; (ii) if k = Q, the Goodwillie–Jones trace is an isomorphism in degree zero; (iii) we can control homotopy invariant K-theory KH, which is equivariantly formal and determined by its topological counterparts. Simple varieties are quite special, but encompass important singular examples appearing in geometric representation theory. We, in particular, show that both finite and affine Schubert varieties for GLn lie in this class, so all the above results hold for them. ","lang":"eng"}],"article_type":"original","oa_version":"Published Version","type":"journal_article","date_created":"2026-04-19T22:07:48Z","author":[{"first_name":"Jakub","last_name":"Löwit","id":"e3b80ae2-eb8e-11eb-b029-9aef4a9108a0","full_name":"Löwit, Jakub"}],"status":"public","_id":"21751","title":"Equivariant localizing invariants of simple varieties","PlanS_conform":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-08-26T06:53:54Z","project":[{"grant_number":"27004","_id":"901e2a43-16d5-11f0-9cad-9cead34748d6","name":"Arithmetic, geometry, topology and representation theory arising from the affine Grassmannian"}],"citation":{"chicago":"Löwit, Jakub. “Equivariant Localizing Invariants of Simple Varieties.” International Mathematics Research Notices. Oxford University Press, 2026. https://doi.org/10.1093/imrn/rnag058.","apa":"Löwit, J. (2026). Equivariant localizing invariants of simple varieties. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnag058","ama":"Löwit J. Equivariant localizing invariants of simple varieties. International Mathematics Research Notices. 2026;2026(7). doi:10.1093/imrn/rnag058","mla":"Löwit, Jakub. “Equivariant Localizing Invariants of Simple Varieties.” International Mathematics Research Notices, vol. 2026, no. 7, rnag058, Oxford University Press, 2026, doi:10.1093/imrn/rnag058.","short":"J. Löwit, International Mathematics Research Notices 2026 (2026).","ieee":"J. Löwit, “Equivariant localizing invariants of simple varieties,” International Mathematics Research Notices, vol. 2026, no. 7. Oxford University Press, 2026.","ista":"Löwit J. 2026. Equivariant localizing invariants of simple varieties. International Mathematics Research Notices. 2026(7), rnag058."},"related_material":{"record":[{"relation":"dissertation_contains","id":"22694","status":"public"}]},"month":"04","department":[{"_id":"TaHa"}],"publisher":"Oxford University Press","external_id":{"arxiv":["2507.09392"]},"corr_author":"1","oa":1,"day":"01","file":[{"success":1,"date_created":"2026-05-06T06:35:05Z","checksum":"306f4567b7b2dcf38e23f7b55a27514e","access_level":"open_access","relation":"main_file","creator":"dernst","file_id":"21803","content_type":"application/pdf","date_updated":"2026-05-06T06:35:05Z","file_name":"2026_IMRN_Loewit.pdf","file_size":1663246}],"doi":"10.1093/imrn/rnag058","volume":2026,"article_number":"rnag058","intvolume":" 2026","quality_controlled":"1","year":"2026","publication_status":"published","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["510"],"arxiv":1,"fulldoi":"https://doi.org/10.1093/imrn/rnag058","article_processing_charge":"Yes (via OA deal)","file_date_updated":"2026-05-06T06:35:05Z","date_published":"2026-04-01T00:00:00Z","has_accepted_license":"1"},{"file":[{"access_level":"open_access","relation":"main_file","creator":"dernst","success":1,"date_created":"2025-10-21T07:36:56Z","checksum":"016aa4df9453dc180ae7504ac77bf72f","date_updated":"2025-10-21T07:36:56Z","content_type":"application/pdf","file_name":"2025_IMRN_Jain.pdf","file_size":774323,"file_id":"20511"}],"doi":"10.1093/imrn/rnaf273","volume":2025,"article_number":"rnaf273","isi":1,"department":[{"_id":"MaKw"}],"month":"09","publisher":"Oxford University Press","external_id":{"isi":["001575137400001"],"arxiv":["2505.03954"]},"oa":1,"corr_author":"1","day":"11","arxiv":1,"fulldoi":"https://doi.org/10.1093/imrn/rnaf273","article_processing_charge":"Yes (via OA deal)","date_published":"2025-09-11T00:00:00Z","file_date_updated":"2025-10-21T07:36:56Z","has_accepted_license":"1","intvolume":" 2025","quality_controlled":"1","year":"2025","publication_status":"published","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["510"],"language":[{"iso":"eng"}],"OA_type":"hybrid","OA_place":"publisher","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"acknowledgement":"This work was supported by NSF CAREER award DMS-2237646 [to V.J.], ERC Starting Grant “RANDSTRUCT” [no. 101076777 to M.K.], NSF grant DMS-2153576 [to D.M.], and the National Key Research and Development Program of China [2023YFA101020 to T.T.].\r\nWe would like to thank Lisa Sauermann for her helpful comments. We would also like to thank Alex Grebennikov for identifying an oversight in the application of Theorem 7.1 (in a previous version of this paper).","issue":"18","scopus_import":"1","publication":"International Mathematics Research Notices","PlanS_conform":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2025-12-01T13:00:35Z","project":[{"name":"Randomness and structure in combinatorics","_id":"bd95085b-d553-11ed-ba76-e55d3349be45","grant_number":"101076777"}],"citation":{"mla":"Jain, Vishesh, et al. “The Edge-Statistics Conjecture for Hypergraphs.” International Mathematics Research Notices, vol. 2025, no. 18, rnaf273, Oxford University Press, 2025, doi:10.1093/imrn/rnaf273.","ama":"Jain V, Kwan MA, Mubayi D, Tran T. The edge-statistics conjecture for hypergraphs. International Mathematics Research Notices. 2025;2025(18). doi:10.1093/imrn/rnaf273","ieee":"V. Jain, M. A. Kwan, D. Mubayi, and T. Tran, “The edge-statistics conjecture for hypergraphs,” International Mathematics Research Notices, vol. 2025, no. 18. Oxford University Press, 2025.","short":"V. Jain, M.A. Kwan, D. Mubayi, T. Tran, International Mathematics Research Notices 2025 (2025).","ista":"Jain V, Kwan MA, Mubayi D, Tran T. 2025. The edge-statistics conjecture for hypergraphs. International Mathematics Research Notices. 2025(18), rnaf273.","chicago":"Jain, Vishesh, Matthew Alan Kwan, Dhruv Mubayi, and Tuan Tran. “The Edge-Statistics Conjecture for Hypergraphs.” International Mathematics Research Notices. Oxford University Press, 2025. https://doi.org/10.1093/imrn/rnaf273.","apa":"Jain, V., Kwan, M. A., Mubayi, D., & Tran, T. (2025). The edge-statistics conjecture for hypergraphs. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnaf273"},"abstract":[{"text":"Let r, k, be integers such that 0 ≤ ≤ (k/r). Given a large r-uniform hypergraph G, we consider the\r\nfraction of k-vertex subsets that span exactly edges. If is 0 or (k/r), this fraction can be exactly 1 (by taking G to be empty or complete), but for all other values of , one might suspect that this fraction is always significantly smaller than 1.\r\nIn this paper we prove an essentially optimal result along these lines: if is not 0 or (k/r), then this\r\nfraction is at most (1/e) + ε, assuming k is sufficiently large in terms of r and ε > 0, and G is sufficiently large in terms of k. Previously, this was only known for a very limited range of values of r, k, (due to Kwan–Sudakov–Tran, Fox–Sauermann, and Martinsson–Mousset–Noever–Trujic). Our result answers a question of Alon–Hefetz–Krivelevich–Tyomkyn, who suggested this as a hypergraph generalization of their edge-statistics conjecture. We also prove a much stronger bound when is far from 0 and (k/r).","lang":"eng"}],"article_type":"original","oa_version":"Published Version","type":"journal_article","author":[{"first_name":"Vishesh","last_name":"Jain","full_name":"Jain, Vishesh"},{"full_name":"Kwan, Matthew Alan","orcid":"0000-0002-4003-7567","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","last_name":"Kwan","first_name":"Matthew Alan"},{"first_name":"Dhruv","last_name":"Mubayi","full_name":"Mubayi, Dhruv"},{"full_name":"Tran, Tuan","last_name":"Tran","first_name":"Tuan"}],"date_created":"2025-10-20T11:08:57Z","status":"public","_id":"20504","title":"The edge-statistics conjecture for hypergraphs"},{"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."}],"article_type":"original","type":"journal_article","oa_version":"Preprint","status":"public","date_created":"2026-02-17T07:45:45Z","author":[{"id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","first_name":"Victor","last_name":"Wang","full_name":"Wang, Victor","orcid":"0000-0002-0704-7026"},{"full_name":"Xu, Max Wenqiang","last_name":"Xu","first_name":"Max Wenqiang"}],"_id":"21265","title":"Harper’s beyond square-root conjecture","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","supplementarymaterial":"no","date_updated":"2026-07-16T08:57:40Z","project":[{"grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"citation":{"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.","short":"V. Wang, M.W. Xu, International Mathematics Research Notices 2025 (2025).","ista":"Wang V, Xu MW. 2025. Harper’s beyond square-root conjecture. International Mathematics Research Notices. 2025(18), rnaf279.","ama":"Wang V, Xu MW. Harper’s beyond square-root conjecture. International Mathematics Research Notices. 2025;2025(18). doi:10.1093/imrn/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."},"publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"ec_funded":1,"acknowledgement":"The first author is supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101034413. The second author is supported by a Simons Junior Fellowship from Simons Foundation. We thank Paul Bourgade and Kannan Soundararajan for discussions on random matrices and probability, Alexandra Florea for helpful comments on the Ratios Conjecture, and Joni Teräväinen for providing several references. We are also grateful to Alexandra Florea, Adam Harper, Joni Teräväinen, and the referee for helpful comments on earlier drafts.","issue":"18","scopus_import":"1","publication":"International Mathematics Research Notices","language":[{"iso":"eng"}],"OA_place":"repository","OA_type":"green","intvolume":" 2025","year":"2025","quality_controlled":"1","publication_status":"published","arxiv":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2405.04094","open_access":"1"}],"fulldoi":"https://doi.org/10.1093/imrn/rnaf279","das_tickbox":"0","article_processing_charge":"No","date_published":"2025-09-01T00:00:00Z","department":[{"_id":"TiBr"}],"month":"09","publisher":"Oxford University Press","external_id":{"arxiv":["2405.04094"]},"oa":1,"day":"01","doi":"10.1093/imrn/rnaf279","researchdata_availability":"no","volume":2025,"article_number":"rnaf279"},{"department":[{"_id":"TiBr"}],"month":"08","publisher":"Oxford University Press","external_id":{"arxiv":["2503.19451"],"isi":["001549126000001"]},"corr_author":"1","oa":1,"day":"01","file":[{"date_updated":"2025-09-02T07:55:05Z","content_type":"application/pdf","file_name":"2025_IMRN_Verzobio.pdf","file_size":540263,"file_id":"20275","access_level":"open_access","relation":"main_file","creator":"dernst","success":1,"date_created":"2025-09-02T07:55:05Z","checksum":"482ae2be98841ee446cf2bdfcd79f86f"}],"researchdata_availability":"no","doi":"10.1093/imrn/rnaf249","volume":2025,"article_number":"rnaf249","isi":1,"intvolume":" 2025","year":"2025","quality_controlled":"1","publication_status":"published","ddc":["510"],"tmp":{"image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"arxiv":1,"fulldoi":"https://doi.org/10.1093/imrn/rnaf249","das_tickbox":"0","article_processing_charge":"Yes (via OA deal)","date_published":"2025-08-01T00:00:00Z","file_date_updated":"2025-09-02T07:55:05Z","has_accepted_license":"1","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"acknowledgement":"While working on this paper, the author was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101034413. The author is very grateful to Tim Browning for suggesting the problem and for many useful discussions. We thank the anonymous referees for their many helpful comments, which improved the exposition of the paper. We are also grateful to Gal Binyamini for their interest in this work and for drawing our attention to the aforementioned paper [1].\r\nWe shared an early version of this paper with Per Salberger, who mentioned that he announced a new bound for smooth threefolds in P4 during a talk in 2019 (see [7] for the abstract). This result has not been published.","ec_funded":1,"issue":"16","scopus_import":"1","publication":"International Mathematics Research Notices","language":[{"iso":"eng"}],"OA_place":"publisher","OA_type":"hybrid","abstract":[{"text":"Let X be a smooth projective hypersurface defined over Q. We provide new bounds for rational points of bounded height on X. In particular, we show that if X is a smooth projective hypersurface in Pn with n 4 and degree d 50, then the set of rational points on X of height bounded by B have cardinality On,d,ε (Bn−2+ε ). If X is smooth and has degree d 6, we improve the dimension growth conjecture bound. We achieve an analogue result for affine hypersurfaces whose projective closure is smooth.","lang":"eng"}],"article_type":"original","type":"journal_article","oa_version":"Published Version","status":"public","author":[{"orcid":"0000-0002-0854-0306","full_name":"Verzobio, Matteo","last_name":"Verzobio","first_name":"Matteo","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb"}],"date_created":"2025-08-24T22:01:31Z","_id":"20222","title":"Counting rational points on smooth hypersurfaces with high degree","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_updated":"2026-07-17T11:55:00Z","supplementarymaterial":"no","project":[{"grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"citation":{"ama":"Verzobio M. Counting rational points on smooth hypersurfaces with high degree. International Mathematics Research Notices. 2025;2025(16). doi:10.1093/imrn/rnaf249","mla":"Verzobio, Matteo. “Counting Rational Points on Smooth Hypersurfaces with High Degree.” International Mathematics Research Notices, vol. 2025, no. 16, rnaf249, Oxford University Press, 2025, doi:10.1093/imrn/rnaf249.","short":"M. Verzobio, International Mathematics Research Notices 2025 (2025).","ista":"Verzobio M. 2025. Counting rational points on smooth hypersurfaces with high degree. International Mathematics Research Notices. 2025(16), rnaf249.","ieee":"M. Verzobio, “Counting rational points on smooth hypersurfaces with high degree,” International Mathematics Research Notices, vol. 2025, no. 16. Oxford University Press, 2025.","chicago":"Verzobio, Matteo. “Counting Rational Points on Smooth Hypersurfaces with High Degree.” International Mathematics Research Notices. Oxford University Press, 2025. https://doi.org/10.1093/imrn/rnaf249.","apa":"Verzobio, M. (2025). Counting rational points on smooth hypersurfaces with high degree. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnaf249"},"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/"},{"date_updated":"2025-07-10T11:51:44Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"S. Chan, International Mathematics Research Notices 2024 (2024) 7571–7593.","ieee":"S. Chan, “The 3-isogeny selmer groups of the elliptic curves y2=x3+n2,” International Mathematics Research Notices, vol. 2024, no. 9. Oxford University Press, pp. 7571–7593, 2024.","ista":"Chan S. 2024. The 3-isogeny selmer groups of the elliptic curves y2=x3+n2. International Mathematics Research Notices. 2024(9), 7571–7593.","mla":"Chan, Stephanie. “The 3-Isogeny Selmer Groups of the Elliptic Curves Y2=x3+n2.” International Mathematics Research Notices, vol. 2024, no. 9, Oxford University Press, 2024, pp. 7571–93, doi:10.1093/imrn/rnad266.","ama":"Chan S. The 3-isogeny selmer groups of the elliptic curves y2=x3+n2. International Mathematics Research Notices. 2024;2024(9):7571-7593. doi:10.1093/imrn/rnad266","apa":"Chan, S. (2024). The 3-isogeny selmer groups of the elliptic curves y2=x3+n2. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnad266","chicago":"Chan, Stephanie. “The 3-Isogeny Selmer Groups of the Elliptic Curves Y2=x3+n2.” International Mathematics Research Notices. Oxford University Press, 2024. https://doi.org/10.1093/imrn/rnad266."},"page":"7571-7593","abstract":[{"text":"Consider the family of elliptic curves En:y2=x3+n2, where n varies over positive cubefree integers. There is a rational 3-isogeny ϕ from En to E^n:y2=x3−27n2 and a dual isogeny ϕ^:E^n→En. We show that for almost all n, the rank of Selϕ(En) is 0, and the rank of Selϕ^(E^n) is determined by the number of prime factors of n that are congruent to 2mod3 and the congruence class of nmod9.","lang":"eng"}],"extern":"1","oa_version":"Preprint","type":"journal_article","article_type":"original","status":"public","date_created":"2025-04-05T10:50:33Z","author":[{"first_name":"Yik Tung","last_name":"Chan","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","full_name":"Chan, Yik Tung","orcid":"0000-0001-8467-4106"}],"title":"The 3-isogeny selmer groups of the elliptic curves y2=x3+n2","_id":"19486","language":[{"iso":"eng"}],"OA_type":"green","OA_place":"repository","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"acknowledgement":"The author would like to thank Peter Koymans and Carlo Pagano for helpful discussions.","scopus_import":"1","issue":"9","publication":"International Mathematics Research Notices","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2211.06062"}],"arxiv":1,"fulldoi":"https://doi.org/10.1093/imrn/rnad266","article_processing_charge":"No","date_published":"2024-05-01T00:00:00Z","intvolume":" 2024","publication_status":"published","quality_controlled":"1","year":"2024","doi":"10.1093/imrn/rnad266","volume":2024,"publisher":"Oxford University Press","month":"05","external_id":{"arxiv":["2211.06062"]},"oa":1,"day":"01"},{"das_tickbox":"0","fulldoi":"https://doi.org/10.1093/imrn/rnae066","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","file_date_updated":"2025-02-18T07:56:36Z","date_published":"2024-07-01T00:00:00Z","intvolume":" 2024","publication_status":"published","quality_controlled":"1","year":"2024","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["510"],"researchdata_availability":"no","doi":"10.1093/imrn/rnae066","file":[{"file_id":"19052","file_size":205750,"content_type":"application/pdf","date_updated":"2025-02-18T07:56:36Z","file_name":"2024_IMRN_Browning.pdf","checksum":"b625b8adf018d2a97591813c1fc17b96","date_created":"2025-02-18T07:56:36Z","success":1,"creator":"dernst","relation":"main_file","access_level":"open_access"}],"volume":2024,"isi":1,"publisher":"Oxford University Press","month":"07","department":[{"_id":"TiBr"}],"external_id":{"isi":["001196957300001"]},"oa":1,"corr_author":"1","day":"01","supplementarymaterial":"no","date_updated":"2026-07-29T09:59:57Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"chicago":"Browning, Timothy D. “The Polynomial Sieve and Equal Sums of like Polynomials.” International Mathematics Research Notices. Oxford University Press, 2024. https://doi.org/10.1093/imrn/rnae066.","apa":"Browning, T. D. (2024). The polynomial sieve and equal sums of like polynomials. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnae066","ama":"Browning TD. The polynomial sieve and equal sums of like polynomials. International Mathematics Research Notices. 2024;2024(13):10165-10168. doi:10.1093/imrn/rnae066","mla":"Browning, Timothy D. “The Polynomial Sieve and Equal Sums of like Polynomials.” International Mathematics Research Notices, vol. 2024, no. 13, Oxford University Press, 2024, pp. 10165–68, doi:10.1093/imrn/rnae066.","ieee":"T. D. Browning, “The polynomial sieve and equal sums of like polynomials,” International Mathematics Research Notices, vol. 2024, no. 13. Oxford University Press, pp. 10165–10168, 2024.","short":"T.D. Browning, International Mathematics Research Notices 2024 (2024) 10165–10168.","ista":"Browning TD. 2024. The polynomial sieve and equal sums of like polynomials. International Mathematics Research Notices. 2024(13), 10165–10168."},"page":"10165-10168","related_material":{"record":[{"relation":"earlier_version","id":"254","status":"public"}]},"abstract":[{"text":"This paper corrects an error in an earlier work of the author.","lang":"eng"}],"type":"journal_article","oa_version":"Published Version","article_type":"original","author":[{"first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177"}],"status":"public","date_created":"2025-02-18T07:15:50Z","title":"The polynomial sieve and equal sums of like polynomials","_id":"19051","language":[{"iso":"eng"}],"OA_type":"hybrid","OA_place":"publisher","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"scopus_import":"1","issue":"13","publication":"International Mathematics Research Notices"},{"type":"journal_article","oa_version":"Published Version","article_type":"original","abstract":[{"text":"We prove that certain closable derivations on the GNS Hilbert space associated with a non-tracial weight on a von Neumann algebra give rise to GNS-symmetric semigroups of contractive completely positive maps on the von Neumann algebra.","lang":"eng"}],"title":"Modular completely Dirichlet forms as squares of derivations","_id":"18900","author":[{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","first_name":"Melchior","last_name":"Wirth","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior"}],"status":"public","date_created":"2025-01-27T12:36:10Z","date_updated":"2026-10-02T12:21:50Z","supplementarymaterial":"no","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"chicago":"Wirth, Melchior. “Modular Completely Dirichlet Forms as Squares of Derivations.” International Mathematics Research Notices. Oxford University Press, 2024. https://doi.org/10.1093/imrn/rnae092.","apa":"Wirth, M. (2024). Modular completely Dirichlet forms as squares of derivations. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnae092","mla":"Wirth, Melchior. “Modular Completely Dirichlet Forms as Squares of Derivations.” International Mathematics Research Notices, vol. 2024, no. 14, Oxford University Press, 2024, pp. 10597–614, doi:10.1093/imrn/rnae092.","ama":"Wirth M. Modular completely Dirichlet forms as squares of derivations. International Mathematics Research Notices. 2024;2024(14):10597-10614. doi:10.1093/imrn/rnae092","short":"M. Wirth, International Mathematics Research Notices 2024 (2024) 10597–10614.","ieee":"M. Wirth, “Modular completely Dirichlet forms as squares of derivations,” International Mathematics Research Notices, vol. 2024, no. 14. Oxford University Press, pp. 10597–10614, 2024.","ista":"Wirth M. 2024. Modular completely Dirichlet forms as squares of derivations. International Mathematics Research Notices. 2024(14), 10597–10614."},"page":"10597-10614","project":[{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups","grant_number":"ESP156_N"}],"acknowledgement":"The author was funded by the Austrian Science Fund under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. ","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"publication":"International Mathematics Research Notices","scopus_import":"1","issue":"14","language":[{"iso":"eng"}],"OA_type":"hybrid","OA_place":"publisher","publication_status":"published","quality_controlled":"1","year":"2024","intvolume":" 2024","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["510"],"das_tickbox":"0","fulldoi":"https://doi.org/10.1093/imrn/rnae092","has_accepted_license":"1","file_date_updated":"2025-01-27T12:38:10Z","date_published":"2024-07-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["001222279400001"]},"publisher":"Oxford University Press","month":"07","department":[{"_id":"JaMa"}],"day":"01","oa":1,"corr_author":"1","volume":2024,"doi":"10.1093/imrn/rnae092","researchdata_availability":"no","file":[{"file_size":689984,"file_name":"2024_IMRN_Wirth.pdf","date_updated":"2025-01-27T12:38:10Z","content_type":"application/pdf","file_id":"18901","relation":"main_file","creator":"dernst","access_level":"open_access","checksum":"3e1f80d58ada0c60a58f35df8080967e","date_created":"2025-01-27T12:38:10Z","success":1}],"isi":1},{"fulldoi":"https://doi.org/10.1093/imrn/rnae062","das_tickbox":"0","article_processing_charge":"Yes (via OA deal)","file_date_updated":"2024-07-22T06:40:19Z","date_published":"2024-07-01T00:00:00Z","has_accepted_license":"1","intvolume":" 2024","year":"2024","quality_controlled":"1","publication_status":"published","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["510"],"file":[{"file_size":1233508,"date_updated":"2024-07-22T06:40:19Z","content_type":"application/pdf","file_name":"2024_IMRN_Campbell.pdf","file_id":"17288","creator":"dernst","relation":"main_file","access_level":"open_access","date_created":"2024-07-22T06:40:19Z","checksum":"f36a7dbf53f23d5833db711052e69b49","success":1}],"doi":"10.1093/imrn/rnae062","researchdata_availability":"no","volume":2024,"isi":1,"month":"07","department":[{"_id":"LaEr"}],"publisher":"Oxford University Press","external_id":{"isi":["001198019500001"]},"corr_author":"1","oa":1,"day":"01","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_updated":"2026-10-16T08:32:45Z","supplementarymaterial":"yes","page":"10189-10218","citation":{"apa":"Campbell, A. J., O’Rourke, S., & Renfrew, D. T. (2024). The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnae062","chicago":"Campbell, Andrew J, Sean O’Rourke, and David T Renfrew. “The Fractional Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated Differentiation.” International Mathematics Research Notices. Oxford University Press, 2024. https://doi.org/10.1093/imrn/rnae062.","short":"A.J. Campbell, S. O’Rourke, D.T. Renfrew, International Mathematics Research Notices 2024 (2024) 10189–10218.","ieee":"A. J. Campbell, S. O’Rourke, and D. T. Renfrew, “The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation,” International Mathematics Research Notices, vol. 2024, no. 13. Oxford University Press, pp. 10189–10218, 2024.","ista":"Campbell AJ, O’Rourke S, Renfrew DT. 2024. The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. International Mathematics Research Notices. 2024(13), 10189–10218.","mla":"Campbell, Andrew J., et al. “The Fractional Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated Differentiation.” International Mathematics Research Notices, vol. 2024, no. 13, Oxford University Press, 2024, pp. 10189–218, doi:10.1093/imrn/rnae062.","ama":"Campbell AJ, O’Rourke S, Renfrew DT. The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. International Mathematics Research Notices. 2024;2024(13):10189-10218. doi:10.1093/imrn/rnae062"},"abstract":[{"lang":"eng","text":"We extend the free convolution of Brown measures of R-diagonal elements introduced by Kösters and Tikhomirov [ 28] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit theorem-type behavior and discuss stable distributions."}],"article_type":"original","type":"journal_article","oa_version":"Published Version","author":[{"full_name":"Campbell, Andrew J","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4","last_name":"Campbell","first_name":"Andrew J"},{"first_name":"Sean","last_name":"O'Rourke","full_name":"O'Rourke, Sean"},{"first_name":"David T","last_name":"Renfrew","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3493-121X","full_name":"Renfrew, David T"}],"status":"public","date_created":"2024-07-21T22:01:01Z","_id":"17281","title":"The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"acknowledgement":"This work was supported by the National Science Foundation [Grant No. DMS-2143142 to S.O.]; and the European Research Council [Grant No. 101020331].The third author acknowledges the support of the University of Colorado Boulder, where a portion of this work was completed. The authors thank Martin Auer, Vadim Gorin, Brian Hall, and Noah Williams for comments, corrections, and references. The authors also wish to thank the anonymous referees for useful feedback and corrections.","issue":"13","scopus_import":"1","publication":"International Mathematics Research Notices"},{"article_processing_charge":"Yes (via OA deal)","keyword":["General Mathematics"],"has_accepted_license":"1","date_published":"2024-04-01T00:00:00Z","file_date_updated":"2024-07-22T11:41:57Z","arxiv":1,"das_tickbox":"0","fulldoi":"https://doi.org/10.1093/imrn/rnae005","ddc":["510"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"intvolume":" 2024","publication_status":"published","year":"2024","quality_controlled":"1","isi":1,"doi":"10.1093/imrn/rnae005","researchdata_availability":"no","file":[{"creator":"dernst","relation":"main_file","access_level":"open_access","date_created":"2024-07-22T11:41:57Z","checksum":"e3cd31ebb2e79b5b1f34d1c4ac9f5b0f","success":1,"file_size":1488981,"file_name":"2024_IMRN_Shen.pdf","content_type":"application/pdf","date_updated":"2024-07-22T11:41:57Z","file_id":"17308"}],"volume":2024,"corr_author":"1","oa":1,"day":"01","publisher":"Oxford University Press","department":[{"_id":"TaHa"}],"month":"04","external_id":{"isi":["001157898100001"],"arxiv":["1810.12491"]},"page":"6176-6208","citation":{"apa":"Shen, S. (2024). Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnae005","chicago":"Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” International Mathematics Research Notices. Oxford University Press, 2024. https://doi.org/10.1093/imrn/rnae005.","ista":"Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. 2024(7), 6176–6208.","short":"S. Shen, International Mathematics Research Notices 2024 (2024) 6176–6208.","ieee":"S. Shen, “Tamely ramified geometric Langlands correspondence in positive characteristic,” International Mathematics Research Notices, vol. 2024, no. 7. Oxford University Press, pp. 6176–6208, 2024.","ama":"Shen S. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. 2024;2024(7):6176-6208. doi:10.1093/imrn/rnae005","mla":"Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” International Mathematics Research Notices, vol. 2024, no. 7, Oxford University Press, 2024, pp. 6176–208, doi:10.1093/imrn/rnae005."},"project":[{"grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"PlanS_conform":"1","supplementarymaterial":"no","date_updated":"2026-10-21T10:56:48Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2024-02-14T12:16:17Z","status":"public","author":[{"full_name":"Shen, Shiyu","orcid":"0000-0002-4444-8718","last_name":"Shen","first_name":"Shiyu","id":"544cccd3-9005-11ec-87bc-94aef1c5b814"}],"title":"Tamely ramified geometric Langlands correspondence in positive characteristic","_id":"14986","abstract":[{"lang":"eng","text":"We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for GLn(k). Let k be an algebraically closed field of characteristic p>n. Let X be a smooth projective curve over k with marked points, and fix a parabolic subgroup of GLn(k) at each marked point. We denote by Bunn,P the moduli stack of (quasi-)parabolic vector bundles on X, and by Locn,P the moduli stack of parabolic flat connections such that the residue is nilpotent with respect to the parabolic reduction at each marked point. We construct an equivalence between the bounded derived category Db(Qcoh(Loc0n,P)) of quasi-coherent sheaves on an open substack Loc0n,P⊂Locn,P, and the bounded derived category Db(D0Bunn,P-mod) of D0Bunn,P-modules, where D0Bunn,P is a localization of DBunn,P the sheaf of crystalline differential operators on Bunn,P. Thus we extend the work of Bezrukavnikov-Braverman to the tamely ramified case. We also prove a correspondence between flat connections on X with regular singularities and meromorphic Higgs bundles on the Frobenius twist X(1) of X with first order poles ."}],"oa_version":"Published Version","type":"journal_article","article_type":"original","OA_type":"hybrid","OA_place":"publisher","language":[{"iso":"eng"}],"scopus_import":"1","issue":"7","publication":"International Mathematics Research Notices","ec_funded":1,"acknowledgement":"This work was supported by the NSF [DMS-1502125to S.S.]; and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement [101034413 to S.S.].\r\nI would like to thank my advisor Tom Nevins for many helpful discussions on this subject and for his comments on this paper. I would like to thank Christopher Dodd, Michael Groechenig, and Tamas Hausel for helpful conversations. I would like to thank Tsao-Hsien Chen for useful comments on an earlier version of this paper.","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]}},{"month":"12","department":[{"_id":"UlWa"}],"publisher":"Oxford University Press","external_id":{"arxiv":["2212.11781"],"isi":["001184146800001"]},"corr_author":"1","oa":1,"day":"01","file":[{"file_id":"14738","file_size":815777,"content_type":"application/pdf","date_updated":"2024-01-08T09:53:09Z","file_name":"2023_IMRN_Ivanov.pdf","checksum":"353666cea80633beb0f1ffd342dff6d4","date_created":"2024-01-08T09:53:09Z","success":1,"relation":"main_file","creator":"dernst","access_level":"open_access"}],"doi":"10.1093/imrn/rnad210","volume":2023,"isi":1,"intvolume":" 2023","year":"2023","quality_controlled":"1","publication_status":"published","ddc":["510"],"tmp":{"image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"arxiv":1,"fulldoi":"https://doi.org/10.1093/imrn/rnad210","keyword":["General Mathematics"],"article_processing_charge":"Yes (via OA deal)","file_date_updated":"2024-01-08T09:53:09Z","date_published":"2023-12-01T00:00:00Z","has_accepted_license":"1","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"acknowledgement":"We thank Alexander Litvak for the many discussions on Theorem 1.1. Igor Tsiutsiurupa participated in the early stage of this project. To our deep regret, Igor chose another road for his life and stopped working with us.\r\nThis work was supported by the János Bolyai Scholarship of the Hungarian Academy of Sciences [to M.N.]; the National Research, Development, and Innovation Fund (NRDI) [K119670 and K131529 to M.N.]; and the ÚNKP-22-5 New National Excellence Program of the Ministry for Innovation and Technology from the source of the NRDI [to M.N.].","issue":"23","scopus_import":"1","publication":"International Mathematics Research Notices","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"John’s fundamental theorem characterizing the largest volume ellipsoid contained in a convex body $K$ in $\\mathbb{R}^{d}$ has seen several generalizations and extensions. One direction, initiated by V. Milman is to replace ellipsoids by positions (affine images) of another body $L$. Another, more recent direction is to consider logarithmically concave functions on $\\mathbb{R}^{d}$ instead of convex bodies: we designate some special, radially symmetric log-concave function $g$ as the analogue of the Euclidean ball, and want to find its largest integral position under the constraint that it is pointwise below some given log-concave function $f$. We follow both directions simultaneously: we consider the functional question, and allow essentially any meaningful function to play the role of $g$ above. Our general theorems jointly extend known results in both directions. The dual problem in the setting of convex bodies asks for the smallest volume ellipsoid, called Löwner’s ellipsoid, containing $K$. We consider the analogous problem for functions: we characterize the solutions of the optimization problem of finding a smallest integral position of some log-concave function $g$ under the constraint that it is pointwise above $f$. It turns out that in the functional setting, the relationship between the John and the Löwner problems is more intricate than it is in the setting of convex bodies."}],"article_type":"original","type":"journal_article","oa_version":"Published Version","date_created":"2024-01-08T09:48:56Z","status":"public","author":[{"first_name":"Grigory","last_name":"Ivanov","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory"},{"first_name":"Márton","last_name":"Naszódi","full_name":"Naszódi, Márton"}],"_id":"14737","title":"Functional John and Löwner conditions for pairs of log-concave functions","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_updated":"2025-09-09T14:08:25Z","page":"20613-20669","citation":{"mla":"Ivanov, Grigory, and Márton Naszódi. “Functional John and Löwner Conditions for Pairs of Log-Concave Functions.” International Mathematics Research Notices, vol. 2023, no. 23, Oxford University Press, 2023, pp. 20613–69, doi:10.1093/imrn/rnad210.","ama":"Ivanov G, Naszódi M. Functional John and Löwner conditions for pairs of log-concave functions. International Mathematics Research Notices. 2023;2023(23):20613-20669. doi:10.1093/imrn/rnad210","ieee":"G. Ivanov and M. Naszódi, “Functional John and Löwner conditions for pairs of log-concave functions,” International Mathematics Research Notices, vol. 2023, no. 23. Oxford University Press, pp. 20613–20669, 2023.","short":"G. Ivanov, M. Naszódi, International Mathematics Research Notices 2023 (2023) 20613–20669.","ista":"Ivanov G, Naszódi M. 2023. Functional John and Löwner conditions for pairs of log-concave functions. International Mathematics Research Notices. 2023(23), 20613–20669.","chicago":"Ivanov, Grigory, and Márton Naszódi. “Functional John and Löwner Conditions for Pairs of Log-Concave Functions.” International Mathematics Research Notices. Oxford University Press, 2023. https://doi.org/10.1093/imrn/rnad210.","apa":"Ivanov, G., & Naszódi, M. (2023). Functional John and Löwner conditions for pairs of log-concave functions. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnad210"}},{"doi":"10.1093/imrn/rnab374","volume":2023,"oa":1,"day":"01","month":"03","publisher":"Oxford University Press","external_id":{"arxiv":["2106.13333"]},"article_processing_charge":"No","date_published":"2023-03-01T00:00:00Z","arxiv":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.13333"}],"fulldoi":"https://doi.org/10.1093/imrn/rnab374","das_tickbox":"1","intvolume":" 2023","year":"2023","quality_controlled":"1","publication_status":"published","OA_place":"repository","OA_type":"green","language":[{"iso":"eng"}],"issue":"6","scopus_import":"1","publication":"International Mathematics Research Notices","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"page":"4601-4642","citation":{"chicago":"Harrop-Griffiths, Benjamin, Rowan Killip, and Monica Vişan. “Large-Data Equicontinuity for the Derivative NLS.” International Mathematics Research Notices. Oxford University Press, 2023. https://doi.org/10.1093/imrn/rnab374.","apa":"Harrop-Griffiths, B., Killip, R., & Vişan, M. (2023). Large-data equicontinuity for the derivative NLS. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnab374","ama":"Harrop-Griffiths B, Killip R, Vişan M. Large-data equicontinuity for the derivative NLS. International Mathematics Research Notices. 2023;2023(6):4601-4642. doi:10.1093/imrn/rnab374","mla":"Harrop-Griffiths, Benjamin, et al. “Large-Data Equicontinuity for the Derivative NLS.” International Mathematics Research Notices, vol. 2023, no. 6, Oxford University Press, 2023, pp. 4601–42, doi:10.1093/imrn/rnab374.","short":"B. Harrop-Griffiths, R. Killip, M. Vişan, International Mathematics Research Notices 2023 (2023) 4601–4642.","ieee":"B. Harrop-Griffiths, R. Killip, and M. Vişan, “Large-data equicontinuity for the derivative NLS,” International Mathematics Research Notices, vol. 2023, no. 6. Oxford University Press, pp. 4601–4642, 2023.","ista":"Harrop-Griffiths B, Killip R, Vişan M. 2023. Large-data equicontinuity for the derivative NLS. International Mathematics Research Notices. 2023(6), 4601–4642."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-06-30T10:56:42Z","status":"public","author":[{"first_name":"Benjamin","last_name":"Harrop-Griffiths","full_name":"Harrop-Griffiths, Benjamin"},{"full_name":"Killip, Rowan","first_name":"Rowan","last_name":"Killip"},{"full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan","first_name":"Monica"}],"date_created":"2026-06-19T08:22:03Z","_id":"22072","title":"Large-data equicontinuity for the derivative NLS","abstract":[{"lang":"eng","text":"We consider the derivative nonlinear Schrödinger equation in one spatial dimension, which is known to be completely integrable. We prove that the orbits of L^2 bounded and equicontinuous sets of initial data remain bounded and equicontinuous, not only under this flow, but also under the entire hierarchy. This allows us to remove the small-data restriction from prior conservation laws and global well-posedness results."}],"extern":"1","article_type":"original","type":"journal_article","oa_version":"Preprint"},{"date_updated":"2026-07-29T10:43:18Z","supplementarymaterial":"no","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","page":"6780-6808","citation":{"chicago":"Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Log Fano Threefold.” International Mathematics Research Notices. Oxford University Press, 2023. https://doi.org/10.1093/imrn/rnac048.","apa":"Wilsch, F. A. (2023). Integral points of bounded height on a log Fano threefold. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnac048","mla":"Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Log Fano Threefold.” International Mathematics Research Notices, vol. 2023, no. 8, Oxford University Press, 2023, pp. 6780–808, doi:10.1093/imrn/rnac048.","ama":"Wilsch FA. Integral points of bounded height on a log Fano threefold. International Mathematics Research Notices. 2023;2023(8):6780-6808. doi:10.1093/imrn/rnac048","ieee":"F. A. Wilsch, “Integral points of bounded height on a log Fano threefold,” International Mathematics Research Notices, vol. 2023, no. 8. Oxford University Press, pp. 6780–6808, 2023.","ista":"Wilsch FA. 2023. Integral points of bounded height on a log Fano threefold. International Mathematics Research Notices. 2023(8), 6780–6808.","short":"F.A. Wilsch, International Mathematics Research Notices 2023 (2023) 6780–6808."},"type":"journal_article","oa_version":"Preprint","article_type":"original","abstract":[{"text":"We determine an asymptotic formula for the number of integral points of bounded height on a blow-up of P3 outside certain planes using universal torsors.","lang":"eng"}],"title":"Integral points of bounded height on a log Fano threefold","_id":"9034","status":"public","date_created":"2021-01-22T09:31:09Z","author":[{"first_name":"Florian Alexander","last_name":"Wilsch","id":"560601DA-8D36-11E9-A136-7AC1E5697425","orcid":"0000-0001-7302-8256","full_name":"Wilsch, Florian Alexander"}],"language":[{"iso":"eng"}],"acknowledgement":"This work was supported by the German Academic Exchange Service. Parts of this article were prepared at the Institut de Mathémathiques de Jussieu—Paris Rive Gauche. I wish to thank Antoine Chambert-Loir for his remarks and the institute for its hospitality, as well as the anonymous referee for several useful remarks and suggestions for improvements.","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"publication":"International Mathematics Research Notices","scopus_import":"1","issue":"8","das_tickbox":"0","fulldoi":"https://doi.org/10.1093/imrn/rnac048","main_file_link":[{"url":"https://arxiv.org/abs/1901.08503","open_access":"1"}],"arxiv":1,"date_published":"2023-04-01T00:00:00Z","article_processing_charge":"No","publication_status":"published","year":"2023","quality_controlled":"1","intvolume":" 2023","volume":2023,"doi":"10.1093/imrn/rnac048","researchdata_availability":"no","isi":1,"external_id":{"arxiv":["1901.08503"],"isi":["000773116000001"]},"publisher":"Oxford University Press","department":[{"_id":"TiBr"}],"month":"04","day":"01","corr_author":"1","oa":1},{"article_processing_charge":"No","date_published":"2022-05-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1912.05437"}],"arxiv":1,"fulldoi":"https://doi.org/10.1093/imrn/rnaa318","intvolume":" 2022","publication_status":"published","year":"2022","quality_controlled":"1","doi":"10.1093/imrn/rnaa318","volume":2022,"oa":1,"day":"01","publisher":"Oxford University Press","month":"05","external_id":{"arxiv":["1912.05437"]},"citation":{"apa":"Chen, X. (2022). Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants of symplectic six-folds. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnaa318","chicago":"Chen, Xujia. “Solomon-Tukachinsky’s versus Welschinger’s Open Gromov-Witten Invariants of Symplectic Six-Folds.” International Mathematics Research Notices. Oxford University Press, 2022. https://doi.org/10.1093/imrn/rnaa318.","ista":"Chen X. 2022. Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants of symplectic six-folds. International Mathematics Research Notices. 2022(9), 7021–7055.","ieee":"X. Chen, “Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants of symplectic six-folds,” International Mathematics Research Notices, vol. 2022, no. 9. Oxford University Press, pp. 7021–7055, 2022.","short":"X. Chen, International Mathematics Research Notices 2022 (2022) 7021–7055.","ama":"Chen X. Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants of symplectic six-folds. International Mathematics Research Notices. 2022;2022(9):7021-7055. doi:10.1093/imrn/rnaa318","mla":"Chen, Xujia. “Solomon-Tukachinsky’s versus Welschinger’s Open Gromov-Witten Invariants of Symplectic Six-Folds.” International Mathematics Research Notices, vol. 2022, no. 9, Oxford University Press, 2022, pp. 7021–55, doi:10.1093/imrn/rnaa318."},"page":"7021-7055","date_updated":"2025-11-10T14:57:33Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","date_created":"2025-11-10T08:40:57Z","author":[{"full_name":"Chen, Xujia","id":"968ad14a-fd86-11ee-a420-ea29715511a3","first_name":"Xujia","last_name":"Chen"}],"title":"Solomon-Tukachinsky’s versus Welschinger’s open Gromov-Witten invariants of symplectic six-folds","_id":"20617","abstract":[{"lang":"eng","text":"Our previous paper describes a geometric translation of the construction of open Gromov–Witten invariants by Solomon and Tukachinsky from a perspective of $A_{\\infty }$-algebras of differential forms. We now use this geometric perspective to show that these invariants reduce to Welschinger’s open Gromov–Witten invariants in dimension 6, inline with their and Tian’s expectations. As an immediate corollary, we obtain a translation of Solomon–Tukachinsky’s open WDVV equations into relations for Welschinger’s invariants."}],"extern":"1","oa_version":"Preprint","type":"journal_article","article_type":"original","OA_place":"repository","OA_type":"green","language":[{"iso":"eng"}],"scopus_import":"1","issue":"9","publication":"International Mathematics Research Notices","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]}},{"publication":"International Mathematics Research Notices","issue":"3","scopus_import":"1","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036.","language":[{"iso":"eng"}],"_id":"10867","title":"Waist of balls in hyperbolic and spherical spaces","status":"public","author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"date_created":"2022-03-18T11:39:30Z","article_type":"original","type":"journal_article","oa_version":"Preprint","abstract":[{"text":"In this paper we find a tight estimate for Gromov’s waist of the balls in spaces of constant curvature, deduce the estimates for the balls in Riemannian manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar result for normed spaces.","lang":"eng"}],"page":"669-697","citation":{"ama":"Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020;2020(3):669-697. doi:10.1093/imrn/rny037","mla":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices, vol. 2020, no. 3, Oxford University Press, 2020, pp. 669–97, doi:10.1093/imrn/rny037.","ieee":"A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,” International Mathematics Research Notices, vol. 2020, no. 3. Oxford University Press, pp. 669–697, 2020.","ista":"Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697.","short":"A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697.","chicago":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices. Oxford University Press, 2020. https://doi.org/10.1093/imrn/rny037.","apa":"Akopyan, A., & Karasev, R. (2020). Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rny037"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_updated":"2023-08-24T14:19:55Z","day":"01","oa":1,"external_id":{"isi":["000522852700002"],"arxiv":["1702.07513"]},"department":[{"_id":"HeEd"}],"month":"02","publisher":"Oxford University Press","isi":1,"volume":2020,"doi":"10.1093/imrn/rny037","year":"2020","quality_controlled":"1","publication_status":"published","intvolume":" 2020","date_published":"2020-02-01T00:00:00Z","keyword":["General Mathematics"],"article_processing_charge":"No","fulldoi":"https://doi.org/10.1093/imrn/rny037","arxiv":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1702.07513"}]},{"intvolume":" 2020","quality_controlled":"1","year":"2020","publication_status":"published","arxiv":1,"main_file_link":[{"open_access":"1","url":"http://arxiv-export-lb.library.cornell.edu/abs/1810.07462"}],"fulldoi":"https://doi.org/10.1093/imrn/rnaa004","article_processing_charge":"No","date_published":"2020-11-01T00:00:00Z","month":"11","publisher":"Oxford University Press","external_id":{"arxiv":["1810.07462"]},"oa":1,"day":"01","doi":"10.1093/imrn/rnaa004","volume":2020,"abstract":[{"lang":"eng","text":"In 1989, Rota made the following conjecture. Given n bases B1,…,Bn in an n-dimensional vector space V⁠, one can always find n disjoint bases of V⁠, each containing exactly one element from each Bi (we call such bases transversal bases). Rota’s basis conjecture remains wide open despite its apparent simplicity and the efforts of many researchers (e.g., the conjecture was recently the subject of the collaborative “Polymath” project). In this paper we prove that one can always find (1/2−o(1))n disjoint transversal bases, improving on the previous best bound of Ω(n/logn)⁠. Our results also apply to the more general setting of matroids."}],"extern":"1","article_type":"original","oa_version":"Preprint","type":"journal_article","date_created":"2021-06-21T08:12:30Z","status":"public","author":[{"last_name":"Bucić","first_name":"Matija","full_name":"Bucić, Matija"},{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","last_name":"Kwan","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","full_name":"Kwan, Matthew Alan"},{"last_name":"Pokrovskiy","first_name":"Alexey","full_name":"Pokrovskiy, Alexey"},{"full_name":"Sudakov, Benny","last_name":"Sudakov","first_name":"Benny"}],"_id":"9576","title":"Halfway to Rota’s basis conjecture","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","date_updated":"2023-02-23T14:01:30Z","citation":{"chicago":"Bucić, Matija, Matthew Alan Kwan, Alexey Pokrovskiy, and Benny Sudakov. “Halfway to Rota’s Basis Conjecture.” International Mathematics Research Notices. Oxford University Press, 2020. https://doi.org/10.1093/imrn/rnaa004.","apa":"Bucić, M., Kwan, M. A., Pokrovskiy, A., & Sudakov, B. (2020). Halfway to Rota’s basis conjecture. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnaa004","mla":"Bucić, Matija, et al. “Halfway to Rota’s Basis Conjecture.” International Mathematics Research Notices, vol. 2020, no. 21, Oxford University Press, 2020, pp. 8007–26, doi:10.1093/imrn/rnaa004.","ama":"Bucić M, Kwan MA, Pokrovskiy A, Sudakov B. Halfway to Rota’s basis conjecture. International Mathematics Research Notices. 2020;2020(21):8007-8026. doi:10.1093/imrn/rnaa004","short":"M. Bucić, M.A. Kwan, A. Pokrovskiy, B. Sudakov, International Mathematics Research Notices 2020 (2020) 8007–8026.","ista":"Bucić M, Kwan MA, Pokrovskiy A, Sudakov B. 2020. Halfway to Rota’s basis conjecture. International Mathematics Research Notices. 2020(21), 8007–8026.","ieee":"M. Bucić, M. A. Kwan, A. Pokrovskiy, and B. Sudakov, “Halfway to Rota’s basis conjecture,” International Mathematics Research Notices, vol. 2020, no. 21. Oxford University Press, pp. 8007–8026, 2020."},"page":"8007-8026","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"issue":"21","scopus_import":"1","publication":"International Mathematics Research Notices","language":[{"iso":"eng"}]},{"doi":"10.1093/imrn/rny064","volume":2020,"oa":1,"day":"01","publisher":"Oxford University Press","month":"03","external_id":{"arxiv":["1711.02937"]},"article_processing_charge":"No","date_published":"2020-03-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1093/imrn/rny064"}],"arxiv":1,"fulldoi":"https://doi.org/10.1093/imrn/rny064","intvolume":" 2020","publication_status":"published","year":"2020","quality_controlled":"1","OA_place":"publisher","OA_type":"hybrid","language":[{"iso":"eng"}],"scopus_import":"1","issue":"6","publication":"International Mathematics Research Notices","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"page":"1621–1638","citation":{"ama":"Kwan MA, Sudakov B. Ramsey graphs induce subgraphs of quadratically many sizes. International Mathematics Research Notices. 2020;2020(6):1621–1638. doi:10.1093/imrn/rny064","mla":"Kwan, Matthew Alan, and Benny Sudakov. “Ramsey Graphs Induce Subgraphs of Quadratically Many Sizes.” International Mathematics Research Notices, vol. 2020, no. 6, Oxford University Press, 2020, pp. 1621–1638, doi:10.1093/imrn/rny064.","short":"M.A. Kwan, B. Sudakov, International Mathematics Research Notices 2020 (2020) 1621–1638.","ieee":"M. A. Kwan and B. Sudakov, “Ramsey graphs induce subgraphs of quadratically many sizes,” International Mathematics Research Notices, vol. 2020, no. 6. Oxford University Press, pp. 1621–1638, 2020.","ista":"Kwan MA, Sudakov B. 2020. Ramsey graphs induce subgraphs of quadratically many sizes. International Mathematics Research Notices. 2020(6), 1621–1638.","chicago":"Kwan, Matthew Alan, and Benny Sudakov. “Ramsey Graphs Induce Subgraphs of Quadratically Many Sizes.” International Mathematics Research Notices. Oxford University Press, 2020. https://doi.org/10.1093/imrn/rny064.","apa":"Kwan, M. A., & Sudakov, B. (2020). Ramsey graphs induce subgraphs of quadratically many sizes. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rny064"},"date_updated":"2024-10-16T12:20:07Z","user_id":"0043cee0-e5fc-11ee-9736-f83bc23afbf0","author":[{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","last_name":"Kwan","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","full_name":"Kwan, Matthew Alan"},{"full_name":"Sudakov, Benny","first_name":"Benny","last_name":"Sudakov"}],"date_created":"2021-06-21T08:30:12Z","status":"public","title":"Ramsey graphs induce subgraphs of quadratically many sizes","_id":"9577","extern":"1","abstract":[{"lang":"eng","text":"An n-vertex graph is called C-Ramsey if it has no clique or independent set of size Clogn⁠. All known constructions of Ramsey graphs involve randomness in an essential way, and there is an ongoing line of research towards showing that in fact all Ramsey graphs must obey certain “richness” properties characteristic of random graphs. Motivated by an old problem of Erd̋s and McKay, recently Narayanan, Sahasrabudhe, and Tomon conjectured that for any fixed C, every n-vertex C-Ramsey graph induces subgraphs of Θ(n2) different sizes. In this paper we prove this conjecture."}],"type":"journal_article","oa_version":"Published Version","article_type":"original"},{"intvolume":" 2019","year":"2019","quality_controlled":"1","publication_status":"published","article_processing_charge":"No","date_published":"2019-03-01T00:00:00Z","arxiv":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1606.09467","open_access":"1"}],"fulldoi":"https://doi.org/10.1093/imrn/rnx152","das_tickbox":"1","oa":1,"day":"01","month":"03","publisher":"Oxford University Press","external_id":{"arxiv":["1606.09467"]},"doi":"10.1093/imrn/rnx152","volume":2019,"author":[{"last_name":"Killip","first_name":"Rowan","full_name":"Killip, Rowan"},{"last_name":"Visan","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","full_name":"Visan, Monica"},{"last_name":"Zhang","first_name":"Xiaoyi","full_name":"Zhang, Xiaoyi"}],"date_created":"2026-06-19T07:50:08Z","status":"public","_id":"22048","title":"Symplectic non-squeezing for the cubic NLS on the line","abstract":[{"lang":"eng","text":"We prove symplectic non-squeezing for the cubic nonlinear Schrödinger equation on the line via finite-dimensional approximation."}],"extern":"1","article_type":"original","type":"journal_article","oa_version":"Preprint","page":"1312-1332","citation":{"short":"R. Killip, M. Vişan, X. Zhang, International Mathematics Research Notices 2019 (2019) 1312–1332.","ieee":"R. Killip, M. Vişan, and X. Zhang, “Symplectic non-squeezing for the cubic NLS on the line,” International Mathematics Research Notices, vol. 2019, no. 5. Oxford University Press, pp. 1312–1332, 2019.","ista":"Killip R, Vişan M, Zhang X. 2019. Symplectic non-squeezing for the cubic NLS on the line. International Mathematics Research Notices. 2019(5), 1312–1332.","ama":"Killip R, Vişan M, Zhang X. Symplectic non-squeezing for the cubic NLS on the line. International Mathematics Research Notices. 2019;2019(5):1312-1332. doi:10.1093/imrn/rnx152","mla":"Killip, Rowan, et al. “Symplectic Non-Squeezing for the Cubic NLS on the Line.” International Mathematics Research Notices, vol. 2019, no. 5, Oxford University Press, 2019, pp. 1312–32, doi:10.1093/imrn/rnx152.","apa":"Killip, R., Vişan, M., & Zhang, X. (2019). Symplectic non-squeezing for the cubic NLS on the line. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnx152","chicago":"Killip, Rowan, Monica Vişan, and Xiaoyi Zhang. “Symplectic Non-Squeezing for the Cubic NLS on the Line.” International Mathematics Research Notices. Oxford University Press, 2019. https://doi.org/10.1093/imrn/rnx152."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-06-25T08:08:21Z","issue":"5","scopus_import":"1","publication":"International Mathematics Research Notices","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"OA_type":"green","OA_place":"repository","language":[{"iso":"eng"}]},{"project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"page":"3255-3298","citation":{"apa":"Erdös, L., & Schröder, D. J. (2018). Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnw330","chicago":"Erdös, László, and Dominik J Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research Notices. Oxford University Press, 2018. https://doi.org/10.1093/imrn/rnw330.","ista":"Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10), 3255–3298.","short":"L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018 (2018) 3255–3298.","ieee":"L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues,” International Mathematics Research Notices, vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018.","mla":"Erdös, László, and Dominik J. Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research Notices, vol. 2018, no. 10, Oxford University Press, 2018, pp. 3255–98, doi:10.1093/imrn/rnw330.","ama":"Erdös L, Schröder DJ. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018;2018(10):3255-3298. doi:10.1093/imrn/rnw330"},"related_material":{"record":[{"relation":"dissertation_contains","id":"6179","status":"public"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-07-29T13:46:19Z","status":"public","author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2018-12-11T11:49:41Z","_id":"1012","title":"Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues","abstract":[{"lang":"eng","text":"We prove a new central limit theorem (CLT) for the difference of linear eigenvalue statistics of a Wigner random matrix H and its minor H and find that the fluctuation is much smaller than the fluctuations of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of H and H. In particular, our theorem identifies the fluctuation of Kerov's rectangular Young diagrams, defined by the interlacing eigenvalues ofH and H, around their asymptotic shape, the Vershik'Kerov'Logan'Shepp curve. Young diagrams equipped with the Plancherel measure follow the same limiting shape. For this, algebraically motivated, ensemble a CLT has been obtained in Ivanov and Olshanski [20] which is structurally similar to our result but the variance is different, indicating that the analogy between the two models has its limitations. Moreover, our theorem shows that Borodin's result [7] on the convergence of the spectral distribution of Wigner matrices to a Gaussian free field also holds in derivative sense."}],"type":"journal_article","oa_version":"Preprint","language":[{"iso":"eng"}],"publist_id":"6383","issue":"10","scopus_import":"1","publication":"International Mathematics Research Notices","publication_identifier":{"issn":["1073-7928"]},"ec_funded":1,"article_processing_charge":"No","date_published":"2018-05-18T00:00:00Z","arxiv":1,"main_file_link":[{"url":"https://arxiv.org/abs/1608.05163","open_access":"1"}],"fulldoi":"https://doi.org/10.1093/imrn/rnw330","intvolume":" 2018","year":"2018","quality_controlled":"1","publication_status":"published","isi":1,"doi":"10.1093/imrn/rnw330","volume":2018,"oa":1,"day":"18","department":[{"_id":"LaEr"}],"month":"05","publisher":"Oxford University Press","external_id":{"isi":["000441668300009"],"arxiv":["1608.05163"]}}]