[{"file":[{"file_size":1218719,"file_id":"14500","date_created":"2023-11-07T09:16:23Z","creator":"dernst","file_name":"2023_ForumMathematics_Kwan.pdf","date_updated":"2023-11-07T09:16:23Z","checksum":"54b824098d59073cc87a308d458b0a3e","content_type":"application/pdf","success":1,"relation":"main_file","access_level":"open_access"}],"acknowledgement":"Kwan was supported for part of this work by ERC Starting Grant ‘RANDSTRUCT’ No. 101076777. Sah and Sawhney were supported by NSF Graduate Research Fellowship Program DGE-2141064. Sah was supported by the PD Soros Fellowship. Sauermann was supported by NSF Award DMS-2100157, and for part of this work by a Sloan Research Fellowship.","oa":1,"publication_identifier":{"issn":["2050-5086"]},"keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Analysis"],"author":[{"orcid":"0000-0002-4003-7567","full_name":"Kwan, Matthew Alan","last_name":"Kwan","first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3"},{"first_name":"Ashwin","full_name":"Sah, Ashwin","last_name":"Sah"},{"first_name":"Lisa","last_name":"Sauermann","full_name":"Sauermann, Lisa"},{"first_name":"Mehtaab","last_name":"Sawhney","full_name":"Sawhney, Mehtaab"}],"scopus_import":"1","file_date_updated":"2023-11-07T09:16:23Z","publication":"Forum of Mathematics, Pi","intvolume":"        11","isi":1,"volume":11,"quality_controlled":"1","license":"https://creativecommons.org/licenses/by/4.0/","abstract":[{"text":"An n-vertex graph is called C-Ramsey if it has no clique or independent set of size Clog2n (i.e., if it has near-optimal Ramsey behavior). In this paper, we study edge statistics in Ramsey graphs, in particular obtaining very precise control of the distribution of the number of edges in a random vertex subset of a C-Ramsey graph. This brings together two ongoing lines of research: the study of ‘random-like’ properties of Ramsey graphs and the study of small-ball probability for low-degree polynomials of independent random variables.\r\n\r\nThe proof proceeds via an ‘additive structure’ dichotomy on the degree sequence and involves a wide range of different tools from Fourier analysis, random matrix theory, the theory of Boolean functions, probabilistic combinatorics and low-rank approximation. In particular, a key ingredient is a new sharpened version of the quadratic Carbery–Wright theorem on small-ball probability for polynomials of Gaussians, which we believe is of independent interest. One of the consequences of our result is the resolution of an old conjecture of Erdős and McKay, for which Erdős reiterated in several of his open problem collections and for which he offered one of his notorious monetary prizes.","lang":"eng"}],"article_number":"e21","publication_status":"published","external_id":{"isi":["001123866200001"],"arxiv":["2208.02874"]},"department":[{"_id":"MaKw"}],"date_created":"2023-11-07T09:02:48Z","corr_author":"1","language":[{"iso":"eng"}],"status":"public","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"day":"24","type":"journal_article","publisher":"Cambridge University Press","has_accepted_license":"1","project":[{"grant_number":"101076777","_id":"bd95085b-d553-11ed-ba76-e55d3349be45","name":"Randomness and structure in combinatorics"}],"date_published":"2023-08-24T00:00:00Z","oa_version":"Published Version","year":"2023","date_updated":"2025-09-09T13:16:15Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"14499","title":"Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture","month":"08","article_processing_charge":"Yes","citation":{"ista":"Kwan MA, Sah A, Sauermann L, Sawhney M. 2023. Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. Forum of Mathematics, Pi. 11, e21.","chicago":"Kwan, Matthew Alan, Ashwin Sah, Lisa Sauermann, and Mehtaab Sawhney. “Anticoncentration in Ramsey Graphs and a Proof of the Erdős–McKay Conjecture.” <i>Forum of Mathematics, Pi</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/fmp.2023.17\">https://doi.org/10.1017/fmp.2023.17</a>.","apa":"Kwan, M. A., Sah, A., Sauermann, L., &#38; Sawhney, M. (2023). Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. <i>Forum of Mathematics, Pi</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fmp.2023.17\">https://doi.org/10.1017/fmp.2023.17</a>","ama":"Kwan MA, Sah A, Sauermann L, Sawhney M. Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. <i>Forum of Mathematics, Pi</i>. 2023;11. doi:<a href=\"https://doi.org/10.1017/fmp.2023.17\">10.1017/fmp.2023.17</a>","ieee":"M. A. Kwan, A. Sah, L. Sauermann, and M. Sawhney, “Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture,” <i>Forum of Mathematics, Pi</i>, vol. 11. Cambridge University Press, 2023.","short":"M.A. Kwan, A. Sah, L. Sauermann, M. Sawhney, Forum of Mathematics, Pi 11 (2023).","mla":"Kwan, Matthew Alan, et al. “Anticoncentration in Ramsey Graphs and a Proof of the Erdős–McKay Conjecture.” <i>Forum of Mathematics, Pi</i>, vol. 11, e21, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/fmp.2023.17\">10.1017/fmp.2023.17</a>."},"arxiv":1,"ddc":["510"],"doi":"10.1017/fmp.2023.17","article_type":"original"},{"month":"01","title":"Local criteria for triangulating general manifolds","_id":"12287","citation":{"ama":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. Local criteria for triangulating general manifolds. <i>Discrete &#38; Computational Geometry</i>. 2023;69:156-191. doi:<a href=\"https://doi.org/10.1007/s00454-022-00431-7\">10.1007/s00454-022-00431-7</a>","apa":"Boissonnat, J.-D., Dyer, R., Ghosh, A., &#38; Wintraecken, M. (2023). Local criteria for triangulating general manifolds. <i>Discrete &#38; Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-022-00431-7\">https://doi.org/10.1007/s00454-022-00431-7</a>","chicago":"Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, and Mathijs Wintraecken. “Local Criteria for Triangulating General Manifolds.” <i>Discrete &#38; Computational Geometry</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00454-022-00431-7\">https://doi.org/10.1007/s00454-022-00431-7</a>.","ista":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. 2023. Local criteria for triangulating general manifolds. Discrete &#38; Computational Geometry. 69, 156–191.","mla":"Boissonnat, Jean-Daniel, et al. “Local Criteria for Triangulating General Manifolds.” <i>Discrete &#38; Computational Geometry</i>, vol. 69, Springer Nature, 2023, pp. 156–91, doi:<a href=\"https://doi.org/10.1007/s00454-022-00431-7\">10.1007/s00454-022-00431-7</a>.","short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, M. Wintraecken, Discrete &#38; Computational Geometry 69 (2023) 156–191.","ieee":"J.-D. Boissonnat, R. Dyer, A. Ghosh, and M. Wintraecken, “Local criteria for triangulating general manifolds,” <i>Discrete &#38; Computational Geometry</i>, vol. 69. Springer Nature, pp. 156–191, 2023."},"article_processing_charge":"No","ddc":["510"],"article_type":"original","doi":"10.1007/s00454-022-00431-7","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"status":"public","type":"journal_article","day":"01","publisher":"Springer Nature","date_updated":"2025-04-14T07:44:00Z","oa_version":"Published Version","year":"2023","has_accepted_license":"1","date_published":"2023-01-01T00:00:00Z","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"name":"Learning and triangulating manifolds via collapses","grant_number":"M03073","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"page":"156-191","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","volume":69,"abstract":[{"text":"We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use.","lang":"eng"}],"publication_status":"published","language":[{"iso":"eng"}],"corr_author":"1","date_created":"2023-01-16T10:04:06Z","external_id":{"isi":["000862193600001"]},"department":[{"_id":"HeEd"}],"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"oa":1,"file":[{"file_name":"2023_DiscreteCompGeometry_Boissonnat.pdf","creator":"dernst","date_created":"2023-02-02T11:01:10Z","file_id":"12488","file_size":582850,"content_type":"application/pdf","checksum":"46352e0ee71e460848f88685ca852681","date_updated":"2023-02-02T11:01:10Z","success":1,"access_level":"open_access","relation":"main_file"}],"acknowledgement":"This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). Arijit Ghosh is supported by Ramanujan Fellowship (No. SB/S2/RJN-064/2015). Part of this work was done when Arijit Ghosh was a Researcher at Max-Planck-Institute for Informatics, Germany, supported by the IndoGerman Max Planck Center for Computer Science (IMPECS). Mathijs Wintraecken also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Austrian Science Fund (FWF): M-3073. A part of the results described in this paper were presented at SoCG 2018 and in [3]. \r\nOpen access funding provided by the Austrian Science Fund (FWF).","intvolume":"        69","isi":1,"ec_funded":1,"author":[{"first_name":"Jean-Daniel","last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel"},{"last_name":"Dyer","full_name":"Dyer, Ramsay","first_name":"Ramsay"},{"last_name":"Ghosh","full_name":"Ghosh, Arijit","first_name":"Arijit"},{"full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","orcid":"0000-0002-7472-2220"}],"scopus_import":"1","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"publication":"Discrete & Computational Geometry","file_date_updated":"2023-02-02T11:01:10Z"},{"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"oa":1,"file":[{"file_size":1747581,"file_id":"12345","date_created":"2023-01-23T11:10:03Z","file_name":"2022_DiscreteCompGeometry_Wagner.pdf","creator":"dernst","date_updated":"2023-01-23T11:10:03Z","checksum":"307e879d09e52eddf5b225d0aaa9213a","content_type":"application/pdf","success":1,"relation":"main_file","access_level":"open_access"}],"acknowledgement":"This is a full and revised version of [38] (on partial triangulations) in Proceedings of the 36th Annual International Symposium on Computational Geometry (SoCG‘20) and of some of the results in [37] (on full triangulations) in Proceedings of the 31st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA‘20).\r\nThis research started at the 11th Gremo’s Workshop on Open Problems (GWOP), Alp Sellamatt, Switzerland, June 24–28, 2013, motivated by a question posed by Filip Mori´c on full triangulations. Research was supported by the Swiss National Science Foundation within the collaborative DACH project Arrangements and Drawings as SNSF Project 200021E-171681, and by IST Austria and Berlin Free University during a sabbatical stay of the second author. We thank Michael Joswig, Jesús De Loera, and Francisco Santos for helpful discussions on the topics of this paper, and Daniel Bertschinger and Valentin Stoppiello for carefully reading earlier versions and for many helpful comments.\r\nOpen access funding provided by the Swiss Federal Institute of Technology Zürich","intvolume":"        68","isi":1,"author":[{"full_name":"Wagner, Uli","last_name":"Wagner","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568"},{"full_name":"Welzl, Emo","last_name":"Welzl","first_name":"Emo"}],"keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"scopus_import":"1","publication":"Discrete & Computational Geometry","file_date_updated":"2023-01-23T11:10:03Z","abstract":[{"text":"Given a finite point set P in general position in the plane, a full triangulation of P is a maximal straight-line embedded plane graph on P. A partial triangulation of P is a full triangulation of some subset P′ of P containing all extreme points in P. A bistellar flip on a partial triangulation either flips an edge (called edge flip), removes a non-extreme point of degree 3, or adds a point in P∖P′ as vertex of degree 3. The bistellar flip graph has all partial triangulations as vertices, and a pair of partial triangulations is adjacent if they can be obtained from one another by a bistellar flip. The edge flip graph is defined with full triangulations as vertices, and edge flips determining the adjacencies. Lawson showed in the early seventies that these graphs are connected. The goal of this paper is to investigate the structure of these graphs, with emphasis on their vertex connectivity. For sets P of n points in the plane in general position, we show that the edge flip graph is ⌈n/2−2⌉-vertex connected, and the bistellar flip graph is (n−3)-vertex connected; both results are tight. The latter bound matches the situation for the subfamily of regular triangulations (i.e., partial triangulations obtained by lifting the points to 3-space and projecting back the lower convex hull), where (n−3)-vertex connectivity has been known since the late eighties through the secondary polytope due to Gelfand, Kapranov, & Zelevinsky and Balinski’s Theorem. For the edge flip-graph, we additionally show that the vertex connectivity is at least as large as (and hence equal to) the minimum degree (i.e., the minimum number of flippable edges in any full triangulation), provided that n is large enough. Our methods also yield several other results: (i) The edge flip graph can be covered by graphs of polytopes of dimension ⌈n/2−2⌉ (products of associahedra) and the bistellar flip graph can be covered by graphs of polytopes of dimension n−3 (products of secondary polytopes). (ii) A partial triangulation is regular, if it has distance n−3 in the Hasse diagram of the partial order of partial subdivisions from the trivial subdivision. (iii) All partial triangulations of a point set are regular iff the partial order of partial subdivisions has height n−3. (iv) There are arbitrarily large sets P with non-regular partial triangulations and such that every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular triangulations.","lang":"eng"}],"quality_controlled":"1","volume":68,"corr_author":"1","language":[{"iso":"eng"}],"date_created":"2023-01-12T12:02:28Z","external_id":{"isi":["000883222200003"]},"department":[{"_id":"UlWa"}],"publication_status":"published","issue":"4","day":"14","publisher":"Springer Nature","type":"journal_article","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"status":"public","page":"1227-1284","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_updated":"2025-07-10T11:54:56Z","oa_version":"Published Version","year":"2022","has_accepted_license":"1","date_published":"2022-11-14T00:00:00Z","related_material":{"record":[{"id":"7807","status":"public","relation":"earlier_version"},{"status":"public","relation":"earlier_version","id":"7990"}]},"citation":{"ieee":"U. Wagner and E. Welzl, “Connectivity of triangulation flip graphs in the plane,” <i>Discrete &#38; Computational Geometry</i>, vol. 68, no. 4. Springer Nature, pp. 1227–1284, 2022.","mla":"Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane.” <i>Discrete &#38; Computational Geometry</i>, vol. 68, no. 4, Springer Nature, 2022, pp. 1227–84, doi:<a href=\"https://doi.org/10.1007/s00454-022-00436-2\">10.1007/s00454-022-00436-2</a>.","short":"U. Wagner, E. Welzl, Discrete &#38; Computational Geometry 68 (2022) 1227–1284.","ista":"Wagner U, Welzl E. 2022. Connectivity of triangulation flip graphs in the plane. Discrete &#38; Computational Geometry. 68(4), 1227–1284.","chicago":"Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane.” <i>Discrete &#38; Computational Geometry</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00454-022-00436-2\">https://doi.org/10.1007/s00454-022-00436-2</a>.","apa":"Wagner, U., &#38; Welzl, E. (2022). Connectivity of triangulation flip graphs in the plane. <i>Discrete &#38; Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-022-00436-2\">https://doi.org/10.1007/s00454-022-00436-2</a>","ama":"Wagner U, Welzl E. Connectivity of triangulation flip graphs in the plane. <i>Discrete &#38; Computational Geometry</i>. 2022;68(4):1227-1284. doi:<a href=\"https://doi.org/10.1007/s00454-022-00436-2\">10.1007/s00454-022-00436-2</a>"},"article_processing_charge":"No","month":"11","title":"Connectivity of triangulation flip graphs in the plane","_id":"12129","article_type":"original","doi":"10.1007/s00454-022-00436-2","ddc":["510"]},{"citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>.","mla":"Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e96, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022."},"article_processing_charge":"No","title":"Rank-uniform local law for Wigner matrices","month":"10","_id":"12148","doi":"10.1017/fms.2022.86","article_type":"original","ddc":["510"],"type":"journal_article","day":"27","publisher":"Cambridge University Press","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2022","oa_version":"Published Version","date_updated":"2025-04-14T07:57:18Z","has_accepted_license":"1","project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"date_published":"2022-10-27T00:00:00Z","abstract":[{"lang":"eng","text":"We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables."}],"article_number":"e96","quality_controlled":"1","volume":10,"language":[{"iso":"eng"}],"corr_author":"1","department":[{"_id":"LaEr"}],"external_id":{"isi":["000873719200001"]},"date_created":"2023-01-12T12:07:30Z","publication_status":"published","oa":1,"publication_identifier":{"issn":["2050-5094"]},"file":[{"access_level":"open_access","relation":"main_file","success":1,"checksum":"94a049aeb1eea5497aa097712a73c400","content_type":"application/pdf","date_updated":"2023-01-24T10:02:40Z","creator":"dernst","file_name":"2022_ForumMath_Cipolloni.pdf","date_created":"2023-01-24T10:02:40Z","file_id":"12356","file_size":817089}],"acknowledgement":"L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331. D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","ec_funded":1,"isi":1,"intvolume":"        10","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"author":[{"orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"publication":"Forum of Mathematics, Sigma","scopus_import":"1","file_date_updated":"2023-01-24T10:02:40Z"},{"file":[{"success":1,"relation":"main_file","access_level":"open_access","file_size":441184,"date_created":"2023-01-27T08:08:39Z","file_id":"12415","creator":"dernst","file_name":"2022_LinearAlgebra_Carlen.pdf","date_updated":"2023-01-27T08:08:39Z","content_type":"application/pdf","checksum":"cf3cb7e7e34baa967849f01d8f0c1ae4"}],"acknowledgement":"Work partially supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.","publication_identifier":{"issn":["0024-3795"]},"oa":1,"file_date_updated":"2023-01-27T08:08:39Z","keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Numerical Analysis","Algebra and Number Theory"],"publication":"Linear Algebra and its Applications","scopus_import":"1","author":[{"last_name":"Carlen","full_name":"Carlen, Eric A.","first_name":"Eric A."},{"first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan","last_name":"Zhang"}],"isi":1,"intvolume":"       654","volume":654,"quality_controlled":"1","abstract":[{"text":"Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The latter says that quantum operations can never increase the relative entropy. The monotonicity versions often have many advantages, and often have direct physical application, as in the example just mentioned. Moreover, the monotonicity results are often valid for a larger class of maps than, say, quantum operations (which are completely positive). In this paper we prove several new monotonicity results, the first of which is a monotonicity theorem that has as a simple corollary a celebrated concavity theorem of Epstein. Our starting points are the monotonicity versions of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs of these in their general forms using interpolation. We then prove our new monotonicity theorems by several duality arguments.","lang":"eng"}],"publication_status":"published","date_created":"2023-01-16T09:46:38Z","department":[{"_id":"JaMa"}],"external_id":{"isi":["000860689600014"]},"corr_author":"1","language":[{"iso":"eng"}],"status":"public","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"publisher":"Elsevier","day":"01","type":"journal_article","has_accepted_license":"1","date_published":"2022-12-01T00:00:00Z","project":[{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","grant_number":"M03337","name":"Curvature-dimension in noncommutative analysis"}],"date_updated":"2025-04-14T13:05:27Z","oa_version":"Published Version","year":"2022","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","page":"289-310","_id":"12216","month":"12","title":"Monotonicity versions of Epstein's concavity theorem and related inequalities","article_processing_charge":"Yes (via OA deal)","citation":{"apa":"Carlen, E. A., &#38; Zhang, H. (2022). Monotonicity versions of Epstein’s concavity theorem and related inequalities. <i>Linear Algebra and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">https://doi.org/10.1016/j.laa.2022.09.001</a>","ama":"Carlen EA, Zhang H. Monotonicity versions of Epstein’s concavity theorem and related inequalities. <i>Linear Algebra and its Applications</i>. 2022;654:289-310. doi:<a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">10.1016/j.laa.2022.09.001</a>","ista":"Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and its Applications. 654, 289–310.","chicago":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” <i>Linear Algebra and Its Applications</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">https://doi.org/10.1016/j.laa.2022.09.001</a>.","mla":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” <i>Linear Algebra and Its Applications</i>, vol. 654, Elsevier, 2022, pp. 289–310, doi:<a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">10.1016/j.laa.2022.09.001</a>.","short":"E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310.","ieee":"E. A. Carlen and H. Zhang, “Monotonicity versions of Epstein’s concavity theorem and related inequalities,” <i>Linear Algebra and its Applications</i>, vol. 654. Elsevier, pp. 289–310, 2022."},"ddc":["510"],"article_type":"original","doi":"10.1016/j.laa.2022.09.001"},{"title":"Loose cores and cycles in random hypergraphs","month":"10","_id":"12286","citation":{"ama":"Cooley O, Kang M, Zalla J. Loose cores and cycles in random hypergraphs. <i>The Electronic Journal of Combinatorics</i>. 2022;29(4). doi:<a href=\"https://doi.org/10.37236/10794\">10.37236/10794</a>","apa":"Cooley, O., Kang, M., &#38; Zalla, J. (2022). Loose cores and cycles in random hypergraphs. <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal of Combinatorics. <a href=\"https://doi.org/10.37236/10794\">https://doi.org/10.37236/10794</a>","chicago":"Cooley, Oliver, Mihyun Kang, and Julian Zalla. “Loose Cores and Cycles in Random Hypergraphs.” <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal of Combinatorics, 2022. <a href=\"https://doi.org/10.37236/10794\">https://doi.org/10.37236/10794</a>.","ista":"Cooley O, Kang M, Zalla J. 2022. Loose cores and cycles in random hypergraphs. The Electronic Journal of Combinatorics. 29(4), P4.13.","mla":"Cooley, Oliver, et al. “Loose Cores and Cycles in Random Hypergraphs.” <i>The Electronic Journal of Combinatorics</i>, vol. 29, no. 4, P4.13, The Electronic Journal of Combinatorics, 2022, doi:<a href=\"https://doi.org/10.37236/10794\">10.37236/10794</a>.","short":"O. Cooley, M. Kang, J. Zalla, The Electronic Journal of Combinatorics 29 (2022).","ieee":"O. Cooley, M. Kang, and J. Zalla, “Loose cores and cycles in random hypergraphs,” <i>The Electronic Journal of Combinatorics</i>, vol. 29, no. 4. The Electronic Journal of Combinatorics, 2022."},"article_processing_charge":"No","ddc":["510"],"doi":"10.37236/10794","article_type":"original","tmp":{"name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode"},"status":"public","type":"journal_article","day":"21","publisher":"The Electronic Journal of Combinatorics","issue":"4","year":"2022","oa_version":"Published Version","date_updated":"2023-08-04T10:29:18Z","date_published":"2022-10-21T00:00:00Z","has_accepted_license":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","volume":29,"abstract":[{"text":"Inspired by the study of loose cycles in hypergraphs, we define the loose core in hypergraphs as a structurewhich mirrors the close relationship between cycles and $2$-cores in graphs. We prove that in the $r$-uniform binomial random hypergraph $H^r(n,p)$, the order of the loose core undergoes a phase transition at a certain critical threshold and determine this order, as well as the number of edges, asymptotically in the subcritical and supercritical regimes.&#x0D;\r\nOur main tool is an algorithm called CoreConstruct, which enables us to analyse a peeling process for the loose core. By analysing this algorithm we determine the asymptotic degree distribution of vertices in the loose core and in particular how many vertices and edges the loose core contains. As a corollary we obtain an improved upper bound on the length of the longest loose cycle in $H^r(n,p)$.","lang":"eng"}],"license":"https://creativecommons.org/licenses/by-nd/4.0/","article_number":"P4.13","publication_status":"published","language":[{"iso":"eng"}],"department":[{"_id":"MaKw"}],"external_id":{"isi":["000876763300001"]},"date_created":"2023-01-16T10:03:57Z","oa":1,"publication_identifier":{"eissn":["1077-8926"]},"file":[{"success":1,"access_level":"open_access","relation":"main_file","file_size":626953,"file_name":"2022_ElecJournCombinatorics_Cooley_Kang_Zalla.pdf","creator":"dernst","date_created":"2023-01-30T11:45:13Z","file_id":"12462","date_updated":"2023-01-30T11:45:13Z","content_type":"application/pdf","checksum":"00122b2459f09b5ae43073bfba565e94"}],"acknowledgement":"Supported by Austrian Science Fund (FWF): I3747, W1230.","intvolume":"        29","isi":1,"publication":"The Electronic Journal of Combinatorics","author":[{"first_name":"Oliver","id":"43f4ddd0-a46b-11ec-8df6-ef3703bd721d","last_name":"Cooley","full_name":"Cooley, Oliver"},{"first_name":"Mihyun","full_name":"Kang, Mihyun","last_name":"Kang"},{"first_name":"Julian","full_name":"Zalla, Julian","last_name":"Zalla"}],"file_date_updated":"2023-01-30T11:45:13Z","scopus_import":"1","keyword":["Computational Theory and Mathematics","Geometry and Topology","Theoretical Computer Science","Applied Mathematics","Discrete Mathematics and Combinatorics"]},{"scopus_import":"1","author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X"},{"first_name":"Stefan","full_name":"Teufel, Stefan","last_name":"Teufel"}],"keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"file_date_updated":"2022-01-19T09:27:43Z","publication":"Forum of Mathematics, Sigma","intvolume":"        10","isi":1,"ec_funded":1,"acknowledgement":"J.H. acknowledges partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen is gratefully acknowledged.","file":[{"content_type":"application/pdf","checksum":"87592a755adcef22ea590a99dc728dd3","date_updated":"2022-01-19T09:27:43Z","file_name":"2022_ForumMathSigma_Henheik.pdf","creator":"cchlebak","file_id":"10646","date_created":"2022-01-19T09:27:43Z","file_size":705323,"access_level":"open_access","relation":"main_file","success":1}],"publication_identifier":{"eissn":["2050-5094"]},"oa":1,"date_created":"2022-01-18T16:18:51Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"external_id":{"arxiv":["2012.15239"],"isi":["000743615000001"]},"corr_author":"1","language":[{"iso":"eng"}],"publication_status":"published","article_number":"e4","abstract":[{"lang":"eng","text":"We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n"}],"volume":10,"quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2022-01-18T00:00:00Z","has_accepted_license":"1","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"date_updated":"2025-04-14T07:57:17Z","oa_version":"Published Version","year":"2022","day":"18","type":"journal_article","publisher":"Cambridge University Press","status":"public","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_type":"original","doi":"10.1017/fms.2021.80","ddc":["510"],"arxiv":1,"article_processing_charge":"Yes","citation":{"ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2021.80\">https://doi.org/10.1017/fms.2021.80</a>.","apa":"Henheik, S. J., &#38; Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.80\">https://doi.org/10.1017/fms.2021.80</a>","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2021.80\">10.1017/fms.2021.80</a>","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022.","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e4, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2021.80\">10.1017/fms.2021.80</a>.","short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022)."},"_id":"10643","month":"01","title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk"},{"article_type":"original","doi":"10.1142/s2010326322500368","arxiv":1,"article_processing_charge":"No","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"17164"}]},"citation":{"apa":"Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated entries. <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s2010326322500368\">https://doi.org/10.1142/s2010326322500368</a>","ama":"Reker J. On the operator norm of a Hermitian random matrix with correlated entries. <i>Random Matrices: Theory and Applications</i>. 2022;11(4). doi:<a href=\"https://doi.org/10.1142/s2010326322500368\">10.1142/s2010326322500368</a>","ista":"Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 11(4), 2250036.","chicago":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing, 2022. <a href=\"https://doi.org/10.1142/s2010326322500368\">https://doi.org/10.1142/s2010326322500368</a>.","mla":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4, 2250036, World Scientific Publishing, 2022, doi:<a href=\"https://doi.org/10.1142/s2010326322500368\">10.1142/s2010326322500368</a>.","short":"J. Reker, Random Matrices: Theory and Applications 11 (2022).","ieee":"J. Reker, “On the operator norm of a Hermitian random matrix with correlated entries,” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4. World Scientific Publishing, 2022."},"_id":"11135","month":"10","title":"On the operator norm of a Hermitian random matrix with correlated entries","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2022-10-01T00:00:00Z","date_updated":"2026-04-07T13:02:12Z","year":"2022","oa_version":"Preprint","issue":"4","publisher":"World Scientific Publishing","type":"journal_article","day":"01","status":"public","date_created":"2022-04-08T07:11:12Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"external_id":{"arxiv":["2103.03906"],"isi":["000848873800001"]},"language":[{"iso":"eng"}],"corr_author":"1","publication_status":"published","article_number":"2250036","abstract":[{"text":"We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one.","lang":"eng"}],"volume":11,"quality_controlled":"1","publication":"Random Matrices: Theory and Applications","scopus_import":"1","keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"author":[{"first_name":"Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","full_name":"Reker, Jana","last_name":"Reker"}],"intvolume":"        11","isi":1,"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2103.03906"}],"publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"oa":1},{"volume":66,"quality_controlled":"1","abstract":[{"text":"Suppose that n is not a prime power and not twice a prime power. We prove that for any Hausdorff compactum X with a free action of the symmetric group Sn, there exists an Sn-equivariant map X→Rn whose image avoids the diagonal {(x,x,…,x)∈Rn∣x∈R}. Previously, the special cases of this statement for certain X were usually proved using the equivartiant obstruction theory. Such calculations are difficult and may become infeasible past the first (primary) obstruction. We take a different approach which allows us to prove the vanishing of all obstructions simultaneously. The essential step in the proof is classifying the possible degrees of Sn-equivariant maps from the boundary ∂Δn−1 of (n−1)-simplex to itself. Existence of equivariant maps between spaces is important for many questions arising from discrete mathematics and geometry, such as Kneser’s conjecture, the Square Peg conjecture, the Splitting Necklace problem, and the Topological Tverberg conjecture, etc. We demonstrate the utility of our result applying it to one such question, a specific instance of envy-free division problem.","lang":"eng"}],"publication_status":"published","date_created":"2022-06-17T08:45:15Z","external_id":{"arxiv":["1910.12628"]},"corr_author":"1","language":[{"iso":"eng"}],"acknowledgement":"S. Avvakumov has received funding from the European Research Council under the European Union’s Seventh Framework Programme ERC Grant agreement ERC StG 716424–CASe. S. Kudrya was supported by the Austrian Academic Exchange Service (OeAD), ICM-2019-13577.","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"author":[{"orcid":"0000-0002-7840-5062","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","full_name":"Avvakumov, Sergey","last_name":"Avvakumov"},{"first_name":"Sergey","id":"ecf01965-d252-11ea-95a5-8ada5f6c6a67","last_name":"Kudrya","full_name":"Kudrya, Sergey"}],"scopus_import":"1","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"publication":"Discrete & Computational Geometry","intvolume":"        66","_id":"11446","month":"10","title":"Vanishing of all equivariant obstructions and the mapping degree","article_processing_charge":"No","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"8182"}]},"citation":{"ieee":"S. Avvakumov and S. Kudrya, “Vanishing of all equivariant obstructions and the mapping degree,” <i>Discrete &#38; Computational Geometry</i>, vol. 66, no. 3. Springer Nature, pp. 1202–1216, 2021.","short":"S. Avvakumov, S. Kudrya, Discrete &#38; Computational Geometry 66 (2021) 1202–1216.","mla":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” <i>Discrete &#38; Computational Geometry</i>, vol. 66, no. 3, Springer Nature, 2021, pp. 1202–16, doi:<a href=\"https://doi.org/10.1007/s00454-021-00299-z\">10.1007/s00454-021-00299-z</a>.","chicago":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” <i>Discrete &#38; Computational Geometry</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00454-021-00299-z\">https://doi.org/10.1007/s00454-021-00299-z</a>.","ista":"Avvakumov S, Kudrya S. 2021. Vanishing of all equivariant obstructions and the mapping degree. Discrete &#38; Computational Geometry. 66(3), 1202–1216.","ama":"Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. <i>Discrete &#38; Computational Geometry</i>. 2021;66(3):1202-1216. doi:<a href=\"https://doi.org/10.1007/s00454-021-00299-z\">10.1007/s00454-021-00299-z</a>","apa":"Avvakumov, S., &#38; Kudrya, S. (2021). Vanishing of all equivariant obstructions and the mapping degree. <i>Discrete &#38; Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-021-00299-z\">https://doi.org/10.1007/s00454-021-00299-z</a>"},"arxiv":1,"article_type":"original","doi":"10.1007/s00454-021-00299-z","status":"public","issue":"3","day":"01","publisher":"Springer Nature","type":"journal_article","date_published":"2021-10-01T00:00:00Z","date_updated":"2025-04-14T09:10:06Z","oa_version":"Preprint","year":"2021","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"1202-1216","extern":"1"},{"issue":"6","publisher":"Springer Nature","day":"20","type":"journal_article","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"803-813","date_published":"2021-11-20T00:00:00Z","date_updated":"2024-04-09T10:40:08Z","year":"2021","oa_version":"Preprint","article_processing_charge":"No","citation":{"ama":"Fox J, Pach J, Suk A. Bounded VC-dimension implies the Schur-Erdős conjecture. <i>Combinatorica</i>. 2021;41(6):803-813. doi:<a href=\"https://doi.org/10.1007/s00493-021-4530-9\">10.1007/s00493-021-4530-9</a>","apa":"Fox, J., Pach, J., &#38; Suk, A. (2021). Bounded VC-dimension implies the Schur-Erdős conjecture. <i>Combinatorica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00493-021-4530-9\">https://doi.org/10.1007/s00493-021-4530-9</a>","chicago":"Fox, Jacob, János Pach, and Andrew Suk. “Bounded VC-Dimension Implies the Schur-Erdős Conjecture.” <i>Combinatorica</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00493-021-4530-9\">https://doi.org/10.1007/s00493-021-4530-9</a>.","ista":"Fox J, Pach J, Suk A. 2021. Bounded VC-dimension implies the Schur-Erdős conjecture. Combinatorica. 41(6), 803–813.","short":"J. Fox, J. Pach, A. Suk, Combinatorica 41 (2021) 803–813.","mla":"Fox, Jacob, et al. “Bounded VC-Dimension Implies the Schur-Erdős Conjecture.” <i>Combinatorica</i>, vol. 41, no. 6, Springer Nature, 2021, pp. 803–13, doi:<a href=\"https://doi.org/10.1007/s00493-021-4530-9\">10.1007/s00493-021-4530-9</a>.","ieee":"J. Fox, J. Pach, and A. Suk, “Bounded VC-dimension implies the Schur-Erdős conjecture,” <i>Combinatorica</i>, vol. 41, no. 6. Springer Nature, pp. 803–813, 2021."},"_id":"15275","month":"11","title":"Bounded VC-dimension implies the Schur-Erdős conjecture","article_type":"original","doi":"10.1007/s00493-021-4530-9","arxiv":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1912.02342","open_access":"1"}],"oa":1,"publication_identifier":{"issn":["0209-9683"],"eissn":["1439-6912"]},"publication":"Combinatorica","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics"],"author":[{"first_name":"Jacob","full_name":"Fox, Jacob","last_name":"Fox"},{"first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János","last_name":"Pach"},{"last_name":"Suk","full_name":"Suk, Andrew","first_name":"Andrew"}],"intvolume":"        41","abstract":[{"lang":"eng","text":"In 1916, Schur introduced the Ramsey number r(3; m), which is the minimum integer n > 1 such that for any m-coloring of the edges of the complete graph Kn, there is a monochromatic copy of K3. He showed that r(3; m) ≤ O(m!), and a simple construction demonstrates that r(3; m) ≥ 2Ω(m). An old conjecture of Erdős states that r(3; m) = 2Θ(m). In this note, we prove the conjecture for m-colorings with bounded VC-dimension, that is, for m-colorings with the property that the set system induced by the neighborhoods of the vertices with respect to each color class has bounded VC-dimension."}],"volume":41,"quality_controlled":"1","date_created":"2024-04-03T07:59:57Z","external_id":{"arxiv":["1912.02342"]},"department":[{"_id":"HeEd"}],"language":[{"iso":"eng"}],"publication_status":"published"},{"ec_funded":1,"intvolume":"        66","isi":1,"publication":"Discrete & Computational Geometry","file_date_updated":"2021-08-06T09:52:29Z","keyword":["Theoretical Computer Science","Computational Theory and Mathematics","Geometry and Topology","Discrete Mathematics and Combinatorics"],"author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"first_name":"Siargey","last_name":"Kachanovich","full_name":"Kachanovich, Siargey"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220"}],"scopus_import":"1","oa":1,"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"acknowledgement":"This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement Number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). The third author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. Open access funding provided by the Institute of Science and Technology (IST Austria).","file":[{"success":1,"access_level":"open_access","relation":"main_file","file_size":983307,"file_name":"2021_DescreteCompGeopmetry_Boissonnat.pdf","creator":"kschuh","file_id":"9795","date_created":"2021-08-06T09:52:29Z","date_updated":"2021-08-06T09:52:29Z","content_type":"application/pdf","checksum":"c848986091e56699dc12de85adb1e39c"}],"publication_status":"published","language":[{"iso":"eng"}],"corr_author":"1","external_id":{"isi":["000597770300001"]},"department":[{"_id":"HeEd"}],"date_created":"2020-12-12T11:07:02Z","quality_controlled":"1","volume":66,"abstract":[{"text":"We quantise Whitney’s construction to prove the existence of a triangulation for any C^2 manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric.","lang":"eng"}],"year":"2021","oa_version":"Published Version","date_updated":"2025-04-14T07:43:50Z","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"date_published":"2021-07-01T00:00:00Z","has_accepted_license":"1","page":"386-434","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"status":"public","type":"journal_article","day":"01","publisher":"Springer Nature","issue":"1","ddc":["516"],"doi":"10.1007/s00454-020-00250-8","article_type":"original","title":"Triangulating submanifolds: An elementary and quantified version of Whitney’s method","month":"07","_id":"8940","citation":{"chicago":"Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” <i>Discrete &#38; Computational Geometry</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00454-020-00250-8\">https://doi.org/10.1007/s00454-020-00250-8</a>.","ista":"Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete &#38; Computational Geometry. 66(1), 386–434.","ama":"Boissonnat J-D, Kachanovich S, Wintraecken M. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. <i>Discrete &#38; Computational Geometry</i>. 2021;66(1):386-434. doi:<a href=\"https://doi.org/10.1007/s00454-020-00250-8\">10.1007/s00454-020-00250-8</a>","apa":"Boissonnat, J.-D., Kachanovich, S., &#38; Wintraecken, M. (2021). Triangulating submanifolds: An elementary and quantified version of Whitney’s method. <i>Discrete &#38; Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00250-8\">https://doi.org/10.1007/s00454-020-00250-8</a>","ieee":"J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Triangulating submanifolds: An elementary and quantified version of Whitney’s method,” <i>Discrete &#38; Computational Geometry</i>, vol. 66, no. 1. Springer Nature, pp. 386–434, 2021.","mla":"Boissonnat, Jean-Daniel, et al. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” <i>Discrete &#38; Computational Geometry</i>, vol. 66, no. 1, Springer Nature, 2021, pp. 386–434, doi:<a href=\"https://doi.org/10.1007/s00454-020-00250-8\">10.1007/s00454-020-00250-8</a>.","short":"J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, Discrete &#38; Computational Geometry 66 (2021) 386–434."},"article_processing_charge":"Yes (via OA deal)"},{"scopus_import":"1","publication":"Discrete and Continuous Dynamical Systems","keyword":["Applied Mathematics","Discrete Mathematics and Combinatorics","Analysis"],"author":[{"first_name":"Franco","last_name":"Flandoli","full_name":"Flandoli, Franco"},{"first_name":"Enrico","last_name":"Priola","full_name":"Priola, Enrico"},{"first_name":"Giovanni A","id":"47491882-F248-11E8-B48F-1D18A9856A87","full_name":"Zanco, Giovanni A","last_name":"Zanco"}],"isi":1,"intvolume":"        39","main_file_link":[{"url":"https://arxiv.org/abs/1708.04156","open_access":"1"}],"acknowledgement":"The second author has been partially supported by INdAM through the GNAMPA Research\r\nProject (2017) “Sistemi stocastici singolari: buona posizione e problemi di controllo”. The third\r\nauthor was partly funded by the Austrian Science Fund (FWF) project F 65.","oa":1,"publication_identifier":{"issn":["1553-5231"]},"department":[{"_id":"JaMa"}],"external_id":{"arxiv":["1708.04156"],"isi":["000459954800003"]},"date_created":"2022-03-18T12:33:34Z","language":[{"iso":"eng"}],"corr_author":"1","publication_status":"published","abstract":[{"lang":"eng","text":"Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with discontinuous coefficients for the action potential of each neuron and takes into account the (random) spatial configuration of neurons allowing the interaction to depend on it. In the limit as the number of particles tends to infinity, we obtain a nonlinear Fokker-Planck type PDE in two variables, with derivatives only with respect to one variable and discontinuous coefficients. We also study strong well-posedness of the system of SDEs and prove the existence and uniqueness of a weak measure-valued solution to the PDE, obtained as the limit of the laws of the empirical measures for the system of particles."}],"volume":39,"quality_controlled":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","page":"3037-3067","date_published":"2019-06-01T00:00:00Z","project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"oa_version":"Preprint","year":"2019","date_updated":"2025-04-15T08:31:32Z","publisher":"American Institute of Mathematical Sciences","type":"journal_article","day":"01","issue":"6","status":"public","doi":"10.3934/dcds.2019126","article_type":"original","arxiv":1,"article_processing_charge":"No","citation":{"chicago":"Flandoli, Franco, Enrico Priola, and Giovanni A Zanco. “A Mean-Field Model with Discontinuous Coefficients for Neurons with Spatial Interaction.” <i>Discrete and Continuous Dynamical Systems</i>. American Institute of Mathematical Sciences, 2019. <a href=\"https://doi.org/10.3934/dcds.2019126\">https://doi.org/10.3934/dcds.2019126</a>.","ista":"Flandoli F, Priola E, Zanco GA. 2019. A mean-field model with discontinuous coefficients for neurons with spatial interaction. Discrete and Continuous Dynamical Systems. 39(6), 3037–3067.","ama":"Flandoli F, Priola E, Zanco GA. A mean-field model with discontinuous coefficients for neurons with spatial interaction. <i>Discrete and Continuous Dynamical Systems</i>. 2019;39(6):3037-3067. doi:<a href=\"https://doi.org/10.3934/dcds.2019126\">10.3934/dcds.2019126</a>","apa":"Flandoli, F., Priola, E., &#38; Zanco, G. A. (2019). A mean-field model with discontinuous coefficients for neurons with spatial interaction. <i>Discrete and Continuous Dynamical Systems</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/dcds.2019126\">https://doi.org/10.3934/dcds.2019126</a>","ieee":"F. Flandoli, E. Priola, and G. A. Zanco, “A mean-field model with discontinuous coefficients for neurons with spatial interaction,” <i>Discrete and Continuous Dynamical Systems</i>, vol. 39, no. 6. American Institute of Mathematical Sciences, pp. 3037–3067, 2019.","short":"F. Flandoli, E. Priola, G.A. Zanco, Discrete and Continuous Dynamical Systems 39 (2019) 3037–3067.","mla":"Flandoli, Franco, et al. “A Mean-Field Model with Discontinuous Coefficients for Neurons with Spatial Interaction.” <i>Discrete and Continuous Dynamical Systems</i>, vol. 39, no. 6, American Institute of Mathematical Sciences, 2019, pp. 3037–67, doi:<a href=\"https://doi.org/10.3934/dcds.2019126\">10.3934/dcds.2019126</a>."},"_id":"10878","title":"A mean-field model with discontinuous coefficients for neurons with spatial interaction","month":"06"}]