[{"project":[{"_id":"bdb2a702-d553-11ed-ba76-f12e3e5a3bc6","grant_number":"101087907","name":"A quantum hybrid of atoms and milligram-scale pendulums: towards gravitational quantum mechanics"}],"status":"public","publication":"31st International Symposium on Graph Drawing and Network Visualization","acknowledgement":"This work was initiated at the 16th European Research Week on Geometric Graphs in Strobl in 2019. A.W. is supported by the Austrian Science Fund (FWF): W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035]. A preliminary version of this work has been presented at the 38th European Workshop on Computational Geometry (EuroCG 2022) in Perugia [9]. A full version of this paper, which includes appendices but is otherwise identical, is available as a technical report [10].","conference":{"name":"GD: Graph Drawing and Network Visualization","start_date":"2023-09-20","end_date":"2023-09-22","location":"Isola delle Femmine, Palermo, Italy"},"date_published":"2024-01-06T00:00:00Z","year":"2024","external_id":{"arxiv":["2202.12175"]},"page":"18-33","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2202.12175"}],"quality_controlled":"1","doi":"10.1007/978-3-031-49275-4_2","alternative_title":["LNCS"],"article_processing_charge":"No","publisher":"Springer Nature","date_updated":"2025-07-21T07:28:03Z","_id":"14888","type":"conference","oa":1,"language":[{"iso":"eng"}],"citation":{"apa":"De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T., Löffler, M., &#38; Rote, G. (2024). Removing popular faces in curve arrangements. In <i>31st International Symposium on Graph Drawing and Network Visualization</i> (Vol. 14466, pp. 18–33). Isola delle Femmine, Palermo, Italy: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-49275-4_2\">https://doi.org/10.1007/978-3-031-49275-4_2</a>","mla":"De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.” <i>31st International Symposium on Graph Drawing and Network Visualization</i>, vol. 14466, Springer Nature, 2024, pp. 18–33, doi:<a href=\"https://doi.org/10.1007/978-3-031-49275-4_2\">10.1007/978-3-031-49275-4_2</a>.","chicago":"De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová, Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in Curve Arrangements.” In <i>31st International Symposium on Graph Drawing and Network Visualization</i>, 14466:18–33. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/978-3-031-49275-4_2\">https://doi.org/10.1007/978-3-031-49275-4_2</a>.","ista":"De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler M, Rote G. 2024. Removing popular faces in curve arrangements. 31st International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 14466, 18–33.","ieee":"P. De Nooijer <i>et al.</i>, “Removing popular faces in curve arrangements,” in <i>31st International Symposium on Graph Drawing and Network Visualization</i>, Isola delle Femmine, Palermo, Italy, 2024, vol. 14466, pp. 18–33.","short":"P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M. Löffler, G. Rote, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 18–33.","ama":"De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve arrangements. In: <i>31st International Symposium on Graph Drawing and Network Visualization</i>. Vol 14466. Springer Nature; 2024:18-33. doi:<a href=\"https://doi.org/10.1007/978-3-031-49275-4_2\">10.1007/978-3-031-49275-4_2</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"month":"01","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"abstract":[{"text":"A face in a curve arrangement is called popular if it is bounded by the same curve multiple times. Motivated by the automatic generation of curved nonogram puzzles, we investigate possibilities to eliminate the popular faces in an arrangement by inserting a single additional curve. This turns out to be NP-hard; however, it becomes tractable when the number of popular faces is small: We present a probabilistic FPT-approach in the number of popular faces.","lang":"eng"}],"intvolume":"     14466","publication_status":"published","publication_identifier":{"isbn":["9783031492747"],"issn":["0302-9743"],"eissn":["1611-3349"]},"author":[{"first_name":"Phoebe","full_name":"De Nooijer, Phoebe","last_name":"De Nooijer"},{"full_name":"Terziadis, Soeren","last_name":"Terziadis","first_name":"Soeren"},{"first_name":"Alexandra","last_name":"Weinberger","full_name":"Weinberger, Alexandra"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","full_name":"Masárová, Zuzana","last_name":"Masárová","first_name":"Zuzana","orcid":"0000-0002-6660-1322"},{"full_name":"Mchedlidze, Tamara","last_name":"Mchedlidze","first_name":"Tamara"},{"first_name":"Maarten","last_name":"Löffler","full_name":"Löffler, Maarten"},{"full_name":"Rote, Günter","last_name":"Rote","first_name":"Günter"}],"day":"06","scopus_import":"1","title":"Removing popular faces in curve arrangements","oa_version":"Preprint","volume":14466,"date_created":"2024-01-28T23:01:43Z"},{"month":"09","department":[{"_id":"UlWa"}],"file":[{"file_size":623787,"date_created":"2023-10-31T11:20:31Z","creator":"dernst","date_updated":"2023-10-31T11:20:31Z","file_id":"14475","file_name":"2023_IsraelJourMath_Wagner.pdf","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"fbb05619fe4b650f341cc730425dd9c3"}],"oa":1,"language":[{"iso":"eng"}],"issue":"2","citation":{"ama":"Wagner U, Wild P. Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes. <i>Israel Journal of Mathematics</i>. 2023;256(2):675-717. doi:<a href=\"https://doi.org/10.1007/s11856-023-2521-9\">10.1007/s11856-023-2521-9</a>","ieee":"U. Wagner and P. Wild, “Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes,” <i>Israel Journal of Mathematics</i>, vol. 256, no. 2. Springer Nature, pp. 675–717, 2023.","short":"U. Wagner, P. Wild, Israel Journal of Mathematics 256 (2023) 675–717.","ista":"Wagner U, Wild P. 2023. Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes. Israel Journal of Mathematics. 256(2), 675–717.","chicago":"Wagner, Uli, and Pascal Wild. “Coboundary Expansion, Equivariant Overlap, and Crossing Numbers of Simplicial Complexes.” <i>Israel Journal of Mathematics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s11856-023-2521-9\">https://doi.org/10.1007/s11856-023-2521-9</a>.","apa":"Wagner, U., &#38; Wild, P. (2023). Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes. <i>Israel Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11856-023-2521-9\">https://doi.org/10.1007/s11856-023-2521-9</a>","mla":"Wagner, Uli, and Pascal Wild. “Coboundary Expansion, Equivariant Overlap, and Crossing Numbers of Simplicial Complexes.” <i>Israel Journal of Mathematics</i>, vol. 256, no. 2, Springer Nature, 2023, pp. 675–717, doi:<a href=\"https://doi.org/10.1007/s11856-023-2521-9\">10.1007/s11856-023-2521-9</a>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner","full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"},{"id":"4C20D868-F248-11E8-B48F-1D18A9856A87","full_name":"Wild, Pascal","last_name":"Wild","first_name":"Pascal"}],"day":"01","scopus_import":"1","title":"Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes","oa_version":"Published Version","volume":256,"article_type":"original","date_created":"2023-10-22T22:01:14Z","has_accepted_license":"1","abstract":[{"lang":"eng","text":"We prove the following quantitative Borsuk–Ulam-type result (an equivariant analogue of Gromov’s Topological Overlap Theorem): Let X be a free ℤ/2-complex of dimension d with coboundary expansion at least ηk in dimension 0 ≤ k < d. Then for every equivariant map F: X →ℤ/2 ℝd, the fraction of d-simplices σ of X with 0 ∈ F (σ) is at least 2−d Π d−1k=0ηk.\r\n\r\nAs an application, we show that for every sufficiently thick d-dimensional spherical building Y and every map f: Y → ℝ2d, we have f(σ) ∩ f(τ) ≠ ∅ for a constant fraction μd > 0 of pairs {σ, τ} of d-simplices of Y. In particular, such complexes are non-embeddable into ℝ2d, which proves a conjecture of Tancer and Vorwerk for sufficiently thick spherical buildings.\r\n\r\nWe complement these results by upper bounds on the coboundary expansion of two families of simplicial complexes; this indicates some limitations to the bounds one can obtain by straighforward applications of the quantitative Borsuk–Ulam theorem. Specifically, we prove\r\n\r\n• an upper bound of (d + 1)/2d on the normalized (d − 1)-th coboundary expansion constant of complete (d + 1)-partite d-dimensional complexes (under a mild divisibility assumption on the sizes of the parts); and\r\n\r\n• an upper bound of (d + 1)/2d + ε on the normalized (d − 1)-th coboundary expansion of the d-dimensional spherical building associated with GLd+2(Fq) for any ε > 0 and sufficiently large q. This disproves, in a rather strong sense, a conjecture of Lubotzky, Meshulam and Mozes."}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"intvolume":"       256","publication_identifier":{"eissn":["1565-8511"],"issn":["0021-2172"]},"publication_status":"published","file_date_updated":"2023-10-31T11:20:31Z","year":"2023","isi":1,"external_id":{"isi":["001081646400010"]},"status":"public","publication":"Israel Journal of Mathematics","date_published":"2023-09-01T00:00:00Z","doi":"10.1007/s11856-023-2521-9","article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","date_updated":"2023-12-13T13:09:07Z","_id":"14445","type":"journal_article","page":"675-717","ddc":["510"],"quality_controlled":"1"},{"scopus_import":"1","day":"04","author":[{"first_name":"Grigory","full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","last_name":"Ivanov"},{"full_name":"Naszódi, Márton","last_name":"Naszódi","first_name":"Márton"}],"oa_version":"Published Version","title":"Quantitative Steinitz theorem: A polynomial bound","date_created":"2023-12-10T23:00:58Z","article_type":"original","abstract":[{"text":"The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull of a set 𝑆⊂ℝ𝑑, then there are at most 2𝑑 points of 𝑆 whose convex hull contains the origin in the interior. Bárány, Katchalski,and Pach proved the following quantitative version of Steinitz’s theorem. Let 𝑄 be a convex polytope in ℝ𝑑 containing the standard Euclidean unit ball 𝐁𝑑. Then there exist at most 2𝑑 vertices of 𝑄 whose convex hull 𝑄′ satisfies 𝑟𝐁𝑑⊂𝑄′ with 𝑟⩾𝑑−2𝑑. They conjectured that 𝑟⩾𝑐𝑑−1∕2 holds with a universal constant 𝑐>0. We prove 𝑟⩾15𝑑2, the first polynomial lower bound on 𝑟. Furthermore, we show that 𝑟 is not greater than 2/√𝑑.","lang":"eng"}],"publication_status":"epub_ahead","publication_identifier":{"issn":["0024-6093"],"eissn":["1469-2120"]},"month":"12","arxiv":1,"department":[{"_id":"UlWa"}],"oa":1,"language":[{"iso":"eng"}],"citation":{"ista":"Ivanov G, Naszódi M. 2023. Quantitative Steinitz theorem: A polynomial bound. Bulletin of the London Mathematical Society.","chicago":"Ivanov, Grigory, and Márton Naszódi. “Quantitative Steinitz Theorem: A Polynomial Bound.” <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society, 2023. <a href=\"https://doi.org/10.1112/blms.12965\">https://doi.org/10.1112/blms.12965</a>.","mla":"Ivanov, Grigory, and Márton Naszódi. “Quantitative Steinitz Theorem: A Polynomial Bound.” <i>Bulletin of the London Mathematical Society</i>, London Mathematical Society, 2023, doi:<a href=\"https://doi.org/10.1112/blms.12965\">10.1112/blms.12965</a>.","apa":"Ivanov, G., &#38; Naszódi, M. (2023). Quantitative Steinitz theorem: A polynomial bound. <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/blms.12965\">https://doi.org/10.1112/blms.12965</a>","ama":"Ivanov G, Naszódi M. Quantitative Steinitz theorem: A polynomial bound. <i>Bulletin of the London Mathematical Society</i>. 2023. doi:<a href=\"https://doi.org/10.1112/blms.12965\">10.1112/blms.12965</a>","short":"G. Ivanov, M. Naszódi, Bulletin of the London Mathematical Society (2023).","ieee":"G. Ivanov and M. Naszódi, “Quantitative Steinitz theorem: A polynomial bound,” <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society, 2023."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","doi":"10.1112/blms.12965","publisher":"London Mathematical Society","_id":"14660","date_updated":"2023-12-11T10:03:54Z","type":"journal_article","main_file_link":[{"open_access":"1","url":" https://doi.org/10.1112/blms.12965"}],"quality_controlled":"1","year":"2023","external_id":{"arxiv":["2212.04308"]},"status":"public","publication":"Bulletin of the London Mathematical Society","date_published":"2023-12-04T00:00:00Z","acknowledgement":"M.N. was supported by the János Bolyai Scholarship of the Hungarian Academy of Sciences aswell as the National Research, Development and Innovation Fund (NRDI) grants K119670 andK131529, and the ÚNKP-22-5 New National Excellence Program of the Ministry for Innovationand Technology from the source of the NRDI as well as the ELTE TKP 2021-NKTA-62 fundingscheme"},{"status":"public","publication":"International Mathematics Research Notices","date_published":"2023-12-01T00:00:00Z","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.].","external_id":{"arxiv":["2212.11781"]},"year":"2023","keyword":["General Mathematics"],"ddc":["510"],"page":"20613-20669","quality_controlled":"1","publisher":"Oxford University Press","doi":"10.1093/imrn/rnad210","article_processing_charge":"Yes (via OA deal)","type":"journal_article","date_updated":"2024-01-08T09:57:25Z","_id":"14737","language":[{"iso":"eng"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"23","citation":{"ama":"Ivanov G, Naszódi M. Functional John and Löwner conditions for pairs of log-concave functions. <i>International Mathematics Research Notices</i>. 2023;2023(23):20613-20669. doi:<a href=\"https://doi.org/10.1093/imrn/rnad210\">10.1093/imrn/rnad210</a>","ieee":"G. Ivanov and M. Naszódi, “Functional John and Löwner conditions for pairs of log-concave functions,” <i>International Mathematics Research Notices</i>, vol. 2023, no. 23. Oxford University Press, pp. 20613–20669, 2023.","short":"G. Ivanov, M. Naszódi, International Mathematics Research Notices 2023 (2023) 20613–20669.","chicago":"Ivanov, Grigory, and Márton Naszódi. “Functional John and Löwner Conditions for Pairs of Log-Concave Functions.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2023. <a href=\"https://doi.org/10.1093/imrn/rnad210\">https://doi.org/10.1093/imrn/rnad210</a>.","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.","apa":"Ivanov, G., &#38; Naszódi, M. (2023). Functional John and Löwner conditions for pairs of log-concave functions. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnad210\">https://doi.org/10.1093/imrn/rnad210</a>","mla":"Ivanov, Grigory, and Márton Naszódi. “Functional John and Löwner Conditions for Pairs of Log-Concave Functions.” <i>International Mathematics Research Notices</i>, vol. 2023, no. 23, Oxford University Press, 2023, pp. 20613–69, doi:<a href=\"https://doi.org/10.1093/imrn/rnad210\">10.1093/imrn/rnad210</a>."},"arxiv":1,"month":"12","file":[{"creator":"dernst","date_updated":"2024-01-08T09:53:09Z","file_size":815777,"date_created":"2024-01-08T09:53:09Z","file_id":"14738","access_level":"open_access","content_type":"application/pdf","success":1,"file_name":"2023_IMRN_Ivanov.pdf","checksum":"353666cea80633beb0f1ffd342dff6d4","relation":"main_file"}],"department":[{"_id":"UlWa"}],"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","abstract":[{"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.","lang":"eng"}],"tmp":{"image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)"},"intvolume":"      2023","has_accepted_license":"1","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"publication_status":"published","file_date_updated":"2024-01-08T09:53:09Z","oa_version":"Published Version","title":"Functional John and Löwner conditions for pairs of log-concave functions","author":[{"first_name":"Grigory","last_name":"Ivanov","full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E"},{"first_name":"Márton","full_name":"Naszódi, Márton","last_name":"Naszódi"}],"day":"01","article_type":"original","date_created":"2024-01-08T09:48:56Z","volume":2023},{"ddc":["510"],"page":"1059-1089","quality_controlled":"1","publisher":"Springer Nature","article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00454-023-00500-5","type":"journal_article","_id":"13270","date_updated":"2024-01-29T11:16:16Z","publication":"Discrete and Computational Geometry","status":"public","acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria).","date_published":"2023-07-05T00:00:00Z","external_id":{"arxiv":["2107.04112"],"isi":["001023742800003"]},"isi":1,"year":"2023","abstract":[{"text":"Consider a geodesic triangle on a surface of constant curvature and subdivide it recursively into four triangles by joining the midpoints of its edges. We show the existence of a uniform δ>0\r\n such that, at any step of the subdivision, all the triangle angles lie in the interval (δ,π−δ)\r\n. Additionally, we exhibit stabilising behaviours for both angles and lengths as this subdivision progresses.","lang":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"intvolume":"        70","has_accepted_license":"1","file_date_updated":"2024-01-29T11:15:22Z","publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"title":"Iterated medial triangle subdivision in surfaces of constant curvature","oa_version":"Published Version","scopus_import":"1","day":"05","author":[{"last_name":"Brunck","full_name":"Brunck, Florestan R","id":"6ab6e556-f394-11eb-9cf6-9dfb78f00d8d","first_name":"Florestan R"}],"date_created":"2023-07-23T22:01:14Z","article_type":"original","volume":70,"language":[{"iso":"eng"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Brunck FR. Iterated medial triangle subdivision in surfaces of constant curvature. <i>Discrete and Computational Geometry</i>. 2023;70(3):1059-1089. doi:<a href=\"https://doi.org/10.1007/s00454-023-00500-5\">10.1007/s00454-023-00500-5</a>","short":"F.R. Brunck, Discrete and Computational Geometry 70 (2023) 1059–1089.","ieee":"F. R. Brunck, “Iterated medial triangle subdivision in surfaces of constant curvature,” <i>Discrete and Computational Geometry</i>, vol. 70, no. 3. Springer Nature, pp. 1059–1089, 2023.","chicago":"Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00454-023-00500-5\">https://doi.org/10.1007/s00454-023-00500-5</a>.","ista":"Brunck FR. 2023. Iterated medial triangle subdivision in surfaces of constant curvature. Discrete and Computational Geometry. 70(3), 1059–1089.","mla":"Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature.” <i>Discrete and Computational Geometry</i>, vol. 70, no. 3, Springer Nature, 2023, pp. 1059–89, doi:<a href=\"https://doi.org/10.1007/s00454-023-00500-5\">10.1007/s00454-023-00500-5</a>.","apa":"Brunck, F. R. (2023). Iterated medial triangle subdivision in surfaces of constant curvature. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-023-00500-5\">https://doi.org/10.1007/s00454-023-00500-5</a>"},"issue":"3","month":"07","arxiv":1,"file":[{"relation":"main_file","checksum":"865e68daafdd4edcfc280172ec50f5ea","file_name":"2023_DiscreteComputGeometry_Brunck.pdf","success":1,"content_type":"application/pdf","access_level":"open_access","file_id":"14897","file_size":1466020,"date_created":"2024-01-29T11:15:22Z","creator":"dernst","date_updated":"2024-01-29T11:15:22Z"}],"department":[{"_id":"UlWa"}]},{"date_created":"2023-07-31T10:20:55Z","title":"Exterior algebra and combinatorics","oa_version":"Published Version","author":[{"first_name":"Seyda","last_name":"Köse","id":"8ba3170d-dc85-11ea-9058-c4251c96a6eb","full_name":"Köse, Seyda"}],"day":"31","publication_status":"published","publication_identifier":{"issn":["2791-4585"]},"file_date_updated":"2023-08-03T15:28:55Z","abstract":[{"text":"The extension of extremal combinatorics to the setting of exterior algebra is a work\r\nin progress that gained attention recently. In this thesis, we study the combinatorial structure of exterior algebra by introducing a dictionary that translates the notions from the set systems into the framework of exterior algebra. We show both generalizations of celebrated Erdös--Ko--Rado theorem and Hilton--Milner theorem to the setting of exterior algebra in the simplest non-trivial case of two-forms.\r\n","lang":"eng"}],"has_accepted_license":"1","file":[{"creator":"skoese","date_updated":"2023-07-31T10:16:32Z","file_size":28684,"date_created":"2023-07-31T10:16:32Z","file_id":"13333","access_level":"closed","content_type":"application/x-zip-compressed","file_name":"Exterior Algebra and Combinatorics.zip","checksum":"96ee518d796d02af71395622c45de03c","relation":"source_file"},{"file_id":"13480","date_created":"2023-08-03T15:28:55Z","file_size":4953418,"date_updated":"2023-08-03T15:28:55Z","creator":"skoese","relation":"main_file","checksum":"f610f4713f88bc477de576aaa46b114e","success":1,"file_name":"thesis-pdfa.pdf","access_level":"open_access","content_type":"application/pdf"}],"department":[{"_id":"GradSch"},{"_id":"UlWa"}],"month":"07","supervisor":[{"orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"short":"S. Köse, Exterior Algebra and Combinatorics, Institute of Science and Technology Austria, 2023.","ieee":"S. Köse, “Exterior algebra and combinatorics,” Institute of Science and Technology Austria, 2023.","ama":"Köse S. Exterior algebra and combinatorics. 2023. doi:<a href=\"https://doi.org/10.15479/at:ista:13331\">10.15479/at:ista:13331</a>","mla":"Köse, Seyda. <i>Exterior Algebra and Combinatorics</i>. Institute of Science and Technology Austria, 2023, doi:<a href=\"https://doi.org/10.15479/at:ista:13331\">10.15479/at:ista:13331</a>.","apa":"Köse, S. (2023). <i>Exterior algebra and combinatorics</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:13331\">https://doi.org/10.15479/at:ista:13331</a>","chicago":"Köse, Seyda. “Exterior Algebra and Combinatorics.” Institute of Science and Technology Austria, 2023. <a href=\"https://doi.org/10.15479/at:ista:13331\">https://doi.org/10.15479/at:ista:13331</a>.","ista":"Köse S. 2023. Exterior algebra and combinatorics. Institute of Science and Technology Austria."},"language":[{"iso":"eng"}],"oa":1,"type":"dissertation","date_updated":"2023-10-04T11:54:56Z","_id":"13331","publisher":"Institute of Science and Technology Austria","doi":"10.15479/at:ista:13331","alternative_title":["ISTA Master's Thesis"],"article_processing_charge":"No","ddc":["510","516"],"page":"26","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"12680"}]},"year":"2023","date_published":"2023-07-31T00:00:00Z","status":"public","degree_awarded":"MS"},{"file_date_updated":"2023-08-07T08:00:48Z","publication_status":"published","publication_identifier":{"issn":["1526-1719"]},"has_accepted_license":"1","abstract":[{"text":"Bundling crossings is a strategy which can enhance the readability\r\nof graph drawings. In this paper we consider good drawings, i.e., we require that\r\nany two edges have at most one common point which can be a common vertex or a\r\ncrossing. Our main result is that there is a polynomial-time algorithm to compute an\r\n8-approximation of the bundled crossing number of a good drawing with no toothed\r\nhole. In general the number of toothed holes has to be added to the 8-approximation.\r\nIn the special case of circular drawings the approximation factor is 8, this improves\r\nupon the 10-approximation of Fink et al. [14]. Our approach also works with the same\r\napproximation factor for families of pseudosegments, i.e., curves intersecting at most\r\nonce. We also show how to compute a 9/2-approximation when the intersection graph of\r\nthe pseudosegments is bipartite and has no toothed hole.","lang":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"intvolume":"        27","volume":27,"date_created":"2023-08-06T22:01:11Z","article_type":"original","scopus_import":"1","day":"01","author":[{"first_name":"Alan M","orcid":"0000-0003-2401-8670","last_name":"Arroyo Guevara","full_name":"Arroyo Guevara, Alan M","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Felsner, Stefan","last_name":"Felsner","first_name":"Stefan"}],"oa_version":"Published Version","title":"Approximating the bundled crossing number","citation":{"ieee":"A. M. Arroyo Guevara and S. Felsner, “Approximating the bundled crossing number,” <i>Journal of Graph Algorithms and Applications</i>, vol. 27, no. 6. Brown University, pp. 433–457, 2023.","short":"A.M. Arroyo Guevara, S. Felsner, Journal of Graph Algorithms and Applications 27 (2023) 433–457.","ama":"Arroyo Guevara AM, Felsner S. Approximating the bundled crossing number. <i>Journal of Graph Algorithms and Applications</i>. 2023;27(6):433-457. doi:<a href=\"https://doi.org/10.7155/jgaa.00629\">10.7155/jgaa.00629</a>","apa":"Arroyo Guevara, A. M., &#38; Felsner, S. (2023). Approximating the bundled crossing number. <i>Journal of Graph Algorithms and Applications</i>. Brown University. <a href=\"https://doi.org/10.7155/jgaa.00629\">https://doi.org/10.7155/jgaa.00629</a>","mla":"Arroyo Guevara, Alan M., and Stefan Felsner. “Approximating the Bundled Crossing Number.” <i>Journal of Graph Algorithms and Applications</i>, vol. 27, no. 6, Brown University, 2023, pp. 433–57, doi:<a href=\"https://doi.org/10.7155/jgaa.00629\">10.7155/jgaa.00629</a>.","chicago":"Arroyo Guevara, Alan M, and Stefan Felsner. “Approximating the Bundled Crossing Number.” <i>Journal of Graph Algorithms and Applications</i>. Brown University, 2023. <a href=\"https://doi.org/10.7155/jgaa.00629\">https://doi.org/10.7155/jgaa.00629</a>.","ista":"Arroyo Guevara AM, Felsner S. 2023. Approximating the bundled crossing number. Journal of Graph Algorithms and Applications. 27(6), 433–457."},"issue":"6","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"UlWa"}],"file":[{"file_id":"13979","creator":"dernst","date_updated":"2023-08-07T08:00:48Z","file_size":865774,"date_created":"2023-08-07T08:00:48Z","checksum":"9c30d2b8e324cc1c904f2aeec92013a3","relation":"main_file","content_type":"application/pdf","access_level":"open_access","file_name":"2023_JourGraphAlgorithms_Arroyo.pdf","success":1}],"month":"07","arxiv":1,"quality_controlled":"1","page":"433-457","ddc":["510"],"_id":"13969","date_updated":"2023-09-25T10:56:10Z","type":"journal_article","article_processing_charge":"Yes","doi":"10.7155/jgaa.00629","publisher":"Brown University","ec_funded":1,"acknowledgement":"This work was initiated during the Workshop on Geometric Graphs in November 2019 in Strobl, Austria. We would like to thank Oswin Aichholzer, Fabian Klute, Man-Kwun Chiu, Martin Balko, Pavel Valtr for their avid discussions during the workshop. The first author has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 754411. The second author has been supported by the German Research Foundation DFG Project FE 340/12-1. An extended abstract of this paper has been published in the proceedings of WALCOM 2022 in the Springer LNCS series, vol. 13174, pages 383–395.","date_published":"2023-07-01T00:00:00Z","status":"public","publication":"Journal of Graph Algorithms and Applications","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020"}],"year":"2023","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"11185"}]},"external_id":{"arxiv":["2109.14892"]}},{"project":[{"_id":"261FA626-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"M02281","name":"Eliminating intersections in drawings of graphs"}],"publication":"Discrete and Computational Geometry","status":"public","acknowledgement":"Part of the research leading to this paper was done during the 16th Gremo Workshop on Open Problems (GWOP), Waltensburg, Switzerland, June 12–16, 2018. We thank Patrick Schnider for suggesting the problem, and Stefan Felsner, Malte Milatz, and Emo Welzl for fruitful discussions during the workshop. We also thank Stefan Felsner and Manfred Scheucher for finding, communicating the example from Sect. 3.3, and the kind permission to include their visualization of the point set. We thank Dömötör Pálvölgyi, the SoCG reviewers, and DCG reviewers for various helpful comments.\r\nR. Fulek gratefully acknowledges support from Austrian Science Fund (FWF), Project  M2281-N35. A. Kupavskii was supported by the Advanced Postdoc.Mobility Grant no. P300P2_177839 of the Swiss National Science Foundation. Research by P. Valtr was supported by the Grant no. 18-19158 S of the Czech Science Foundation (GAČR).","date_published":"2023-07-27T00:00:00Z","external_id":{"arxiv":["1812.04911"],"isi":["001038546500001"]},"related_material":{"record":[{"id":"6647","relation":"earlier_version","status":"public"}]},"isi":1,"year":"2023","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1812.04911","open_access":"1"}],"publisher":"Springer Nature","doi":"10.1007/s00454-023-00532-x","article_processing_charge":"No","type":"journal_article","date_updated":"2023-12-13T12:03:35Z","_id":"13974","language":[{"iso":"eng"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, and U. Wagner, “The crossing Tverberg theorem,” <i>Discrete and Computational Geometry</i>. Springer Nature, 2023.","short":"R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, U. Wagner, Discrete and Computational Geometry (2023).","ama":"Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. The crossing Tverberg theorem. <i>Discrete and Computational Geometry</i>. 2023. doi:<a href=\"https://doi.org/10.1007/s00454-023-00532-x\">10.1007/s00454-023-00532-x</a>","apa":"Fulek, R., Gärtner, B., Kupavskii, A., Valtr, P., &#38; Wagner, U. (2023). The crossing Tverberg theorem. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-023-00532-x\">https://doi.org/10.1007/s00454-023-00532-x</a>","mla":"Fulek, Radoslav, et al. “The Crossing Tverberg Theorem.” <i>Discrete and Computational Geometry</i>, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00454-023-00532-x\">10.1007/s00454-023-00532-x</a>.","ista":"Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. 2023. The crossing Tverberg theorem. Discrete and Computational Geometry.","chicago":"Fulek, Radoslav, Bernd Gärtner, Andrey Kupavskii, Pavel Valtr, and Uli Wagner. “The Crossing Tverberg Theorem.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00454-023-00532-x\">https://doi.org/10.1007/s00454-023-00532-x</a>."},"month":"07","arxiv":1,"department":[{"_id":"UlWa"}],"abstract":[{"lang":"eng","text":"The Tverberg theorem is one of the cornerstones of discrete geometry. It states that, given a set X of at least (d+1)(r−1)+1 points in Rd, one can find a partition X=X1∪⋯∪Xr of X, such that the convex hulls of the Xi, i=1,…,r, all share a common point. In this paper, we prove a trengthening of this theorem that guarantees a partition which, in addition to the above, has the property that the boundaries of full-dimensional convex hulls have pairwise nonempty intersections. Possible generalizations and algorithmic aspects are also discussed. As a concrete application, we show that any n points in the plane in general position span ⌊n/3⌋ vertex-disjoint triangles that are pairwise crossing, meaning that their boundaries have pairwise nonempty intersections; this number is clearly best possible. A previous result of Álvarez-Rebollar et al. guarantees ⌊n/6⌋pairwise crossing triangles. Our result generalizes to a result about simplices in Rd, d≥2."}],"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"publication_status":"epub_ahead","oa_version":"Preprint","title":"The crossing Tverberg theorem","author":[{"first_name":"Radoslav","orcid":"0000-0001-8485-1774","full_name":"Fulek, Radoslav","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","last_name":"Fulek"},{"first_name":"Bernd","full_name":"Gärtner, Bernd","last_name":"Gärtner"},{"full_name":"Kupavskii, Andrey","last_name":"Kupavskii","first_name":"Andrey"},{"first_name":"Pavel","last_name":"Valtr","full_name":"Valtr, Pavel"},{"first_name":"Uli","orcid":"0000-0002-1494-0568","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli"}],"day":"27","scopus_import":"1","article_type":"original","date_created":"2023-08-06T22:01:12Z"},{"author":[{"last_name":"Dymond","full_name":"Dymond, Michael","first_name":"Michael"},{"id":"21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E","full_name":"Kaluza, Vojtech","last_name":"Kaluza","first_name":"Vojtech","orcid":"0000-0002-2512-8698"}],"day":"17","scopus_import":"1","title":"Divergence of separated nets with respect to displacement equivalence","oa_version":"Published Version","article_type":"original","date_created":"2021-07-14T07:01:27Z","abstract":[{"lang":"eng","text":"We introduce a hierachy of equivalence relations on the set of separated nets of a given Euclidean space, indexed by concave increasing functions ϕ:(0,∞)→(0,∞). Two separated nets are called ϕ-displacement equivalent if, roughly speaking, there is a bijection between them which, for large radii R, displaces points of norm at most R by something of order at most ϕ(R). We show that the spectrum of ϕ-displacement equivalence spans from the established notion of bounded displacement equivalence, which corresponds to bounded ϕ, to the indiscrete equivalence relation, coresponding to ϕ(R)∈Ω(R), in which all separated nets are equivalent. In between the two ends of this spectrum, the notions of ϕ-displacement equivalence are shown to be pairwise distinct with respect to the asymptotic classes of ϕ(R) for R→∞. We further undertake a comparison of our notion of ϕ-displacement equivalence with previously studied relations on separated nets. Particular attention is given to the interaction of the notions of ϕ-displacement equivalence with that of bilipschitz equivalence."}],"publication_identifier":{"issn":["0046-5755"],"eissn":["1572-9168"]},"publication_status":"epub_ahead","month":"11","arxiv":1,"department":[{"_id":"UlWa"}],"article_number":"15","oa":1,"language":[{"iso":"eng"}],"citation":{"ista":"Dymond M, Kaluza V. 2023. Divergence of separated nets with respect to displacement equivalence. Geometriae Dedicata., 15.","chicago":"Dymond, Michael, and Vojtech Kaluza. “Divergence of Separated Nets with Respect to Displacement Equivalence.” <i>Geometriae Dedicata</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s10711-023-00862-3\">https://doi.org/10.1007/s10711-023-00862-3</a>.","mla":"Dymond, Michael, and Vojtech Kaluza. “Divergence of Separated Nets with Respect to Displacement Equivalence.” <i>Geometriae Dedicata</i>, 15, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s10711-023-00862-3\">10.1007/s10711-023-00862-3</a>.","apa":"Dymond, M., &#38; Kaluza, V. (2023). Divergence of separated nets with respect to displacement equivalence. <i>Geometriae Dedicata</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10711-023-00862-3\">https://doi.org/10.1007/s10711-023-00862-3</a>","ama":"Dymond M, Kaluza V. Divergence of separated nets with respect to displacement equivalence. <i>Geometriae Dedicata</i>. 2023. doi:<a href=\"https://doi.org/10.1007/s10711-023-00862-3\">10.1007/s10711-023-00862-3</a>","short":"M. Dymond, V. Kaluza, Geometriae Dedicata (2023).","ieee":"M. Dymond and V. Kaluza, “Divergence of separated nets with respect to displacement equivalence,” <i>Geometriae Dedicata</i>. Springer Nature, 2023."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","doi":"10.1007/s10711-023-00862-3","article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","date_updated":"2024-01-11T13:06:32Z","_id":"9651","type":"journal_article","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s10711-023-00862-3"}],"quality_controlled":"1","isi":1,"year":"2023","external_id":{"isi":["001105681500001"],"arxiv":["2102.13046"]},"publication":"Geometriae Dedicata","status":"public","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). This work was started while both authors were employed at the University of Innsbruck and enjoyed the full support of Austrian Science Fund (FWF): P 30902-N35. It was continued when the first named author was employed at University of Leipzig and the second named author was employed at Institute of Science and Technology of Austria, where he was supported by an IST Fellowship.","date_published":"2023-11-17T00:00:00Z"},{"quality_controlled":"1","ddc":["515","516"],"page":"501-554","type":"journal_article","date_updated":"2023-08-14T11:26:34Z","_id":"9652","publisher":"Springer Nature","doi":"10.1007/s11856-022-2448-6","article_processing_charge":"No","acknowledgement":"This work was done while both authors were employed at the University of Innsbruck and enjoyed the full support of Austrian Science Fund (FWF): P 30902-N35.","date_published":"2023-03-01T00:00:00Z","status":"public","publication":"Israel Journal of Mathematics","keyword":["Lipschitz","bilipschitz","bounded displacement","modulus of continuity","separated net","non-realisable density","Burago--Kleiner construction"],"external_id":{"isi":["000904950300003"],"arxiv":["1903.05923"]},"isi":1,"year":"2023","publication_status":"published","publication_identifier":{"eissn":["1565-8511"]},"file_date_updated":"2021-07-14T07:41:50Z","abstract":[{"text":"In 1998 Burago and Kleiner and (independently) McMullen gave examples of separated nets in Euclidean space which are non-bilipschitz equivalent to the integer lattice. We study weaker notions of equivalence of separated nets and demonstrate that such notions also give rise to distinct equivalence classes. Put differently, we find occurrences of particularly strong divergence of separated nets from the integer lattice. Our approach generalises that of Burago and Kleiner and McMullen which takes place largely in a continuous setting. Existence of irregular separated nets is verified via the existence of non-realisable density functions ρ:[0,1]d→(0,∞). In the present work we obtain stronger types of non-realisable densities.","lang":"eng"}],"intvolume":"       253","has_accepted_license":"1","article_type":"original","date_created":"2021-07-14T07:01:28Z","volume":253,"title":"Highly irregular separated nets","oa_version":"Submitted Version","author":[{"first_name":"Michael","last_name":"Dymond","full_name":"Dymond, Michael"},{"first_name":"Vojtech","orcid":"0000-0002-2512-8698","last_name":"Kaluza","full_name":"Kaluza, Vojtech","id":"21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E"}],"scopus_import":"1","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Dymond M, Kaluza V. 2023. Highly irregular separated nets. Israel Journal of Mathematics. 253, 501–554.","chicago":"Dymond, Michael, and Vojtech Kaluza. “Highly Irregular Separated Nets.” <i>Israel Journal of Mathematics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s11856-022-2448-6\">https://doi.org/10.1007/s11856-022-2448-6</a>.","mla":"Dymond, Michael, and Vojtech Kaluza. “Highly Irregular Separated Nets.” <i>Israel Journal of Mathematics</i>, vol. 253, Springer Nature, 2023, pp. 501–54, doi:<a href=\"https://doi.org/10.1007/s11856-022-2448-6\">10.1007/s11856-022-2448-6</a>.","apa":"Dymond, M., &#38; Kaluza, V. (2023). Highly irregular separated nets. <i>Israel Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11856-022-2448-6\">https://doi.org/10.1007/s11856-022-2448-6</a>","ama":"Dymond M, Kaluza V. Highly irregular separated nets. <i>Israel Journal of Mathematics</i>. 2023;253:501-554. doi:<a href=\"https://doi.org/10.1007/s11856-022-2448-6\">10.1007/s11856-022-2448-6</a>","short":"M. Dymond, V. Kaluza, Israel Journal of Mathematics 253 (2023) 501–554.","ieee":"M. Dymond and V. Kaluza, “Highly irregular separated nets,” <i>Israel Journal of Mathematics</i>, vol. 253. Springer Nature, pp. 501–554, 2023."},"language":[{"iso":"eng"}],"oa":1,"file":[{"date_created":"2021-07-14T07:41:50Z","file_size":900422,"date_updated":"2021-07-14T07:41:50Z","creator":"vkaluza","file_id":"9653","file_name":"separated_nets.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"6fa0a3207dd1d6467c309fd1bcc867d1"}],"department":[{"_id":"UlWa"}],"month":"03","arxiv":1},{"type":"journal_article","date_updated":"2023-08-14T12:51:25Z","_id":"11999","publisher":"Springer Nature","doi":"10.1007/s00454-022-00394-9","article_processing_charge":"Yes (in subscription journal)","quality_controlled":"1","ddc":["510"],"page":"745–770","external_id":{"arxiv":["1909.07347"],"isi":["000840292800001"]},"isi":1,"year":"2023","acknowledgement":"This work was started during the 6th Austrian–Japanese–Mexican–Spanish Workshop on Discrete Geometry in June 2019 in Austria. We thank all the participants for the good atmosphere as well as discussions on the topic. Also, we thank Jan Kynčl for sending us remarks on a preliminary version of this work and an anonymous referee for further helpful comments.Alan Arroyo was funded by the Marie Skłodowska-Curie grant agreement No 754411. Fabian Klute was partially supported by the Netherlands Organisation for Scientific Research (NWO) under project no. 612.001.651 and by the Austrian Science Fund (FWF): J-4510. Irene Parada and Birgit Vogtenhuber were partially supported by the Austrian Science Fund (FWF): W1230 and within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. Irene Parada was also partially supported by the Independent Research Fund Denmark grant 2020-2023 (9131-00044B) Dynamic Network Analysis and by the Margarita Salas Fellowship funded by the Ministry of Universities of Spain and the European Union (NextGenerationEU). Tilo Wiedera was supported by the German Research Foundation (DFG) grant CH 897/2-2.","date_published":"2023-04-01T00:00:00Z","ec_funded":1,"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"publication":"Discrete and Computational Geometry","status":"public","article_type":"original","date_created":"2022-08-28T22:02:01Z","volume":69,"oa_version":"Published Version","title":"Inserting one edge into a simple drawing is hard","author":[{"first_name":"Alan M","orcid":"0000-0003-2401-8670","last_name":"Arroyo Guevara","full_name":"Arroyo Guevara, Alan M","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Klute","full_name":"Klute, Fabian","first_name":"Fabian"},{"first_name":"Irene","last_name":"Parada","full_name":"Parada, Irene"},{"full_name":"Vogtenhuber, Birgit","last_name":"Vogtenhuber","first_name":"Birgit"},{"last_name":"Seidel","full_name":"Seidel, Raimund","first_name":"Raimund"},{"last_name":"Wiedera","full_name":"Wiedera, Tilo","first_name":"Tilo"}],"day":"01","scopus_import":"1","publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"file_date_updated":"2022-08-29T11:23:15Z","abstract":[{"lang":"eng","text":"A simple drawing D(G) of a graph G is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge e in the complement of G can be inserted into D(G) if there exists a simple drawing of G+e extending D(G). As a result of Levi’s Enlargement Lemma, if a drawing is rectilinear (pseudolinear), that is, the edges can be extended into an arrangement of lines (pseudolines), then any edge in the complement of G can be inserted. In contrast, we show that it is NP-complete to decide whether one edge can be inserted into a simple drawing. This remains true even if we assume that the drawing is pseudocircular, that is, the edges can be extended to an arrangement of pseudocircles. On the positive side, we show that, given an arrangement of pseudocircles A and a pseudosegment σ, it can be decided in polynomial time whether there exists a pseudocircle Φσ extending σ for which A∪{Φσ} is again an arrangement of pseudocircles."}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"intvolume":"        69","has_accepted_license":"1","file":[{"checksum":"def7ae3b28d9fd6aec16450e40090302","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_name":"2022_DiscreteandComputionalGeometry_Arroyo.pdf","file_id":"12006","creator":"alisjak","date_updated":"2022-08-29T11:23:15Z","date_created":"2022-08-29T11:23:15Z","file_size":1002218}],"department":[{"_id":"UlWa"}],"arxiv":1,"month":"04","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Arroyo Guevara AM, Klute F, Parada I, Vogtenhuber B, Seidel R, Wiedera T. 2023. Inserting one edge into a simple drawing is hard. Discrete and Computational Geometry. 69, 745–770.","chicago":"Arroyo Guevara, Alan M, Fabian Klute, Irene Parada, Birgit Vogtenhuber, Raimund Seidel, and Tilo Wiedera. “Inserting One Edge into a Simple Drawing Is Hard.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00454-022-00394-9\">https://doi.org/10.1007/s00454-022-00394-9</a>.","mla":"Arroyo Guevara, Alan M., et al. “Inserting One Edge into a Simple Drawing Is Hard.” <i>Discrete and Computational Geometry</i>, vol. 69, Springer Nature, 2023, pp. 745–770, doi:<a href=\"https://doi.org/10.1007/s00454-022-00394-9\">10.1007/s00454-022-00394-9</a>.","apa":"Arroyo Guevara, A. M., Klute, F., Parada, I., Vogtenhuber, B., Seidel, R., &#38; Wiedera, T. (2023). Inserting one edge into a simple drawing is hard. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-022-00394-9\">https://doi.org/10.1007/s00454-022-00394-9</a>","ama":"Arroyo Guevara AM, Klute F, Parada I, Vogtenhuber B, Seidel R, Wiedera T. Inserting one edge into a simple drawing is hard. <i>Discrete and Computational Geometry</i>. 2023;69:745–770. doi:<a href=\"https://doi.org/10.1007/s00454-022-00394-9\">10.1007/s00454-022-00394-9</a>","short":"A.M. Arroyo Guevara, F. Klute, I. Parada, B. Vogtenhuber, R. Seidel, T. Wiedera, Discrete and Computational Geometry 69 (2023) 745–770.","ieee":"A. M. Arroyo Guevara, F. Klute, I. Parada, B. Vogtenhuber, R. Seidel, and T. Wiedera, “Inserting one edge into a simple drawing is hard,” <i>Discrete and Computational Geometry</i>, vol. 69. Springer Nature, pp. 745–770, 2023."},"language":[{"iso":"eng"}],"oa":1},{"oa_version":"Preprint","title":"Topology and adjunction in promise constraint satisfaction","author":[{"first_name":"Andrei","full_name":"Krokhin, Andrei","last_name":"Krokhin"},{"first_name":"Jakub","orcid":"0000-0003-1245-3456","last_name":"Opršal","full_name":"Opršal, Jakub","id":"ec596741-c539-11ec-b829-c79322a91242"},{"last_name":"Wrochna","full_name":"Wrochna, Marcin","first_name":"Marcin"},{"first_name":"Stanislav","last_name":"Živný","full_name":"Živný, Stanislav"}],"scopus_import":"1","day":"01","article_type":"original","date_created":"2023-02-16T07:03:52Z","volume":52,"abstract":[{"lang":"eng","text":"he approximate graph coloring problem, whose complexity is unresolved in most cases, concerns finding a c-coloring of a graph that is promised to be k-colorable, where c≥k. This problem naturally generalizes to promise graph homomorphism problems and further to promise constraint satisfaction problems. The complexity of these problems has recently been studied through an algebraic approach. In this paper, we introduce two new techniques to analyze the complexity of promise CSPs: one is based on topology and the other on adjunction. We apply these techniques, together with the previously introduced algebraic approach, to obtain new unconditional NP-hardness results for a significant class of approximate graph coloring and promise graph homomorphism problems."}],"intvolume":"        52","publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"publication_status":"published","month":"01","arxiv":1,"department":[{"_id":"UlWa"}],"language":[{"iso":"eng"}],"oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"1","citation":{"ieee":"A. Krokhin, J. Opršal, M. Wrochna, and S. Živný, “Topology and adjunction in promise constraint satisfaction,” <i>SIAM Journal on Computing</i>, vol. 52, no. 1. Society for Industrial &#38; Applied Mathematics, pp. 38–79, 2023.","short":"A. Krokhin, J. Opršal, M. Wrochna, S. Živný, SIAM Journal on Computing 52 (2023) 38–79.","ama":"Krokhin A, Opršal J, Wrochna M, Živný S. Topology and adjunction in promise constraint satisfaction. <i>SIAM Journal on Computing</i>. 2023;52(1):38-79. doi:<a href=\"https://doi.org/10.1137/20m1378223\">10.1137/20m1378223</a>","apa":"Krokhin, A., Opršal, J., Wrochna, M., &#38; Živný, S. (2023). Topology and adjunction in promise constraint satisfaction. <i>SIAM Journal on Computing</i>. Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/20m1378223\">https://doi.org/10.1137/20m1378223</a>","mla":"Krokhin, Andrei, et al. “Topology and Adjunction in Promise Constraint Satisfaction.” <i>SIAM Journal on Computing</i>, vol. 52, no. 1, Society for Industrial &#38; Applied Mathematics, 2023, pp. 38–79, doi:<a href=\"https://doi.org/10.1137/20m1378223\">10.1137/20m1378223</a>.","chicago":"Krokhin, Andrei, Jakub Opršal, Marcin Wrochna, and Stanislav Živný. “Topology and Adjunction in Promise Constraint Satisfaction.” <i>SIAM Journal on Computing</i>. Society for Industrial &#38; Applied Mathematics, 2023. <a href=\"https://doi.org/10.1137/20m1378223\">https://doi.org/10.1137/20m1378223</a>.","ista":"Krokhin A, Opršal J, Wrochna M, Živný S. 2023. Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing. 52(1), 38–79."},"publisher":"Society for Industrial & Applied Mathematics","doi":"10.1137/20m1378223","article_processing_charge":"No","type":"journal_article","date_updated":"2023-08-01T13:11:30Z","_id":"12563","page":"38-79","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2003.11351","open_access":"1"}],"external_id":{"isi":["000955000000001"],"arxiv":["2003.11351"]},"year":"2023","isi":1,"keyword":["General Mathematics","General Computer Science"],"project":[{"call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"publication":"SIAM Journal on Computing","status":"public","date_published":"2023-01-01T00:00:00Z","acknowledgement":"Andrei Krokhin and Jakub Opršal were supported by the UK EPSRC grant EP/R034516/1. Jakub Opršal has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 101034413. Stanislav Živný was supported by a Royal Society University Research Fellowship. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714532). The paper re\u001eects only the authors’ views and not the views of the ERC or the European Commission. ","ec_funded":1},{"publication":"Discrete Mathematics","status":"public","date_published":"2023-06-01T00:00:00Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"13331"}]},"external_id":{"arxiv":["2201.10892"]},"year":"2023","quality_controlled":"1","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2201.10892","open_access":"1"}],"publisher":"Elsevier","article_processing_charge":"No","doi":"10.1016/j.disc.2023.113363","type":"journal_article","_id":"12680","date_updated":"2023-10-04T11:54:57Z","language":[{"iso":"eng"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"G. Ivanov and S. Köse, “Erdős-Ko-Rado and Hilton-Milner theorems for two-forms,” <i>Discrete Mathematics</i>, vol. 346, no. 6. Elsevier, 2023.","short":"G. Ivanov, S. Köse, Discrete Mathematics 346 (2023).","ama":"Ivanov G, Köse S. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. <i>Discrete Mathematics</i>. 2023;346(6). doi:<a href=\"https://doi.org/10.1016/j.disc.2023.113363\">10.1016/j.disc.2023.113363</a>","apa":"Ivanov, G., &#38; Köse, S. (2023). Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. <i>Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.disc.2023.113363\">https://doi.org/10.1016/j.disc.2023.113363</a>","mla":"Ivanov, Grigory, and Seyda Köse. “Erdős-Ko-Rado and Hilton-Milner Theorems for Two-Forms.” <i>Discrete Mathematics</i>, vol. 346, no. 6, 113363, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.disc.2023.113363\">10.1016/j.disc.2023.113363</a>.","ista":"Ivanov G, Köse S. 2023. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. Discrete Mathematics. 346(6), 113363.","chicago":"Ivanov, Grigory, and Seyda Köse. “Erdős-Ko-Rado and Hilton-Milner Theorems for Two-Forms.” <i>Discrete Mathematics</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.disc.2023.113363\">https://doi.org/10.1016/j.disc.2023.113363</a>."},"issue":"6","month":"06","arxiv":1,"article_number":"113363","department":[{"_id":"UlWa"},{"_id":"GradSch"}],"intvolume":"       346","abstract":[{"text":"The celebrated Erdős–Ko–Rado theorem about the maximal size of an intersecting family of r-element subsets of  was extended to the setting of exterior algebra in [5, Theorem 2.3] and in [6, Theorem 1.4]. However, the equality case has not been settled yet. In this short note, we show that the extension of the Erdős–Ko–Rado theorem and the characterization of the equality case therein, as well as those of the Hilton–Milner theorem to the setting of exterior algebra in the simplest non-trivial case of two-forms follow from a folklore puzzle about possible arrangements of an intersecting family of lines.","lang":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0012-365X"]},"title":"Erdős-Ko-Rado and Hilton-Milner theorems for two-forms","oa_version":"Preprint","scopus_import":"1","day":"01","author":[{"last_name":"Ivanov","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory","first_name":"Grigory"},{"first_name":"Seyda","full_name":"Köse, Seyda","id":"8ba3170d-dc85-11ea-9058-c4251c96a6eb","last_name":"Köse"}],"date_created":"2023-02-26T23:01:00Z","article_type":"letter_note","volume":346},{"has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"intvolume":"        24","abstract":[{"text":"The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results: 1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan. 2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2. 3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved.","lang":"eng"}],"publication_identifier":{"eissn":["1365-8050"],"issn":["1462-7264"]},"publication_status":"published","file_date_updated":"2023-04-17T08:10:28Z","author":[{"first_name":"Ahmad","full_name":"Biniaz, Ahmad","last_name":"Biniaz"},{"last_name":"Jain","full_name":"Jain, Kshitij","first_name":"Kshitij"},{"first_name":"Anna","full_name":"Lubiw, Anna","last_name":"Lubiw"},{"last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","full_name":"Masárová, Zuzana","first_name":"Zuzana","orcid":"0000-0002-6660-1322"},{"first_name":"Tillmann","full_name":"Miltzow, Tillmann","last_name":"Miltzow"},{"last_name":"Mondal","full_name":"Mondal, Debajyoti","first_name":"Debajyoti"},{"first_name":"Anurag Murty","full_name":"Naredla, Anurag Murty","last_name":"Naredla"},{"last_name":"Tkadlec","full_name":"Tkadlec, Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","first_name":"Josef","orcid":"0000-0002-1097-9684"},{"first_name":"Alexi","last_name":"Turcotte","full_name":"Turcotte, Alexi"}],"day":"18","scopus_import":"1","title":"Token swapping on trees","oa_version":"Published Version","volume":24,"article_type":"original","date_created":"2023-04-16T22:01:08Z","oa":1,"language":[{"iso":"eng"}],"issue":"2","citation":{"chicago":"Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” <i>Discrete Mathematics and Theoretical Computer Science</i>. EPI Sciences, 2023. <a href=\"https://doi.org/10.46298/DMTCS.8383\">https://doi.org/10.46298/DMTCS.8383</a>.","ista":"Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. 2023. Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. 24(2), 9.","mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” <i>Discrete Mathematics and Theoretical Computer Science</i>, vol. 24, no. 2, 9, EPI Sciences, 2023, doi:<a href=\"https://doi.org/10.46298/DMTCS.8383\">10.46298/DMTCS.8383</a>.","apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (2023). Token swapping on trees. <i>Discrete Mathematics and Theoretical Computer Science</i>. EPI Sciences. <a href=\"https://doi.org/10.46298/DMTCS.8383\">https://doi.org/10.46298/DMTCS.8383</a>","ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. <i>Discrete Mathematics and Theoretical Computer Science</i>. 2023;24(2). doi:<a href=\"https://doi.org/10.46298/DMTCS.8383\">10.46298/DMTCS.8383</a>","short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, Discrete Mathematics and Theoretical Computer Science 24 (2023).","ieee":"A. Biniaz <i>et al.</i>, “Token swapping on trees,” <i>Discrete Mathematics and Theoretical Computer Science</i>, vol. 24, no. 2. EPI Sciences, 2023."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","arxiv":1,"month":"01","department":[{"_id":"KrCh"},{"_id":"HeEd"},{"_id":"UlWa"}],"file":[{"date_created":"2023-04-17T08:10:28Z","file_size":2072197,"creator":"dernst","date_updated":"2023-04-17T08:10:28Z","file_id":"12844","success":1,"file_name":"2022_DMTCS_Biniaz.pdf","access_level":"open_access","content_type":"application/pdf","relation":"main_file","checksum":"439102ea4f6e2aeefd7107dfb9ccf532"}],"article_number":"9","ddc":["000"],"quality_controlled":"1","doi":"10.46298/DMTCS.8383","article_processing_charge":"No","publisher":"EPI Sciences","date_updated":"2024-01-04T12:42:09Z","_id":"12833","type":"journal_article","status":"public","publication":"Discrete Mathematics and Theoretical Computer Science","acknowledgement":"This work was begun at the University of Waterloo and was partially supported by the Natural Sciences and Engineering Council of Canada (NSERC).\r\n","date_published":"2023-01-18T00:00:00Z","year":"2023","external_id":{"arxiv":["1903.06981"]},"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"7950"}]}},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2003.13536"}],"quality_controlled":"1","page":"1133-1154","date_updated":"2023-08-02T14:38:58Z","_id":"10776","type":"journal_article","doi":"10.1007/s00454-021-00364-7","article_processing_charge":"No","publisher":"Springer Nature","date_published":"2022-12-01T00:00:00Z","acknowledgement":"The work by Zuzana Patáková has been partially supported by Charles University Research Center Program No. UNCE/SCI/022, and part of it was done during her research stay at IST Austria. The work by Martin Tancer is supported by the GAČR Grant 19-04113Y and by the Charles University Projects PRIMUS/17/SCI/3 and UNCE/SCI/004.","publication":"Discrete and Computational Geometry","status":"public","isi":1,"year":"2022","external_id":{"isi":["000750681500001"],"arxiv":["2003.13536"]},"publication_status":"published","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"intvolume":"        68","abstract":[{"lang":"eng","text":"Let K be a convex body in Rn (i.e., a compact convex set with nonempty interior). Given a point p in the interior of K, a hyperplane h passing through p is called barycentric if p is the barycenter of K∩h. In 1961, Grünbaum raised the question whether, for every K, there exists an interior point p through which there are at least n+1 distinct barycentric hyperplanes. Two years later, this was seemingly resolved affirmatively by showing that this is the case if p=p0 is the point of maximal depth in K. However, while working on a related question, we noticed that one of the auxiliary claims in the proof is incorrect. Here, we provide a counterexample; this re-opens Grünbaum’s question. It follows from known results that for n≥2, there are always at least three distinct barycentric cuts through the point p0∈K of maximal depth. Using tools related to Morse theory we are able to improve this bound: four distinct barycentric cuts through p0 are guaranteed if n≥3."}],"volume":68,"article_type":"original","date_created":"2022-02-20T23:01:35Z","author":[{"full_name":"Patakova, Zuzana","id":"48B57058-F248-11E8-B48F-1D18A9856A87","last_name":"Patakova","orcid":"0000-0002-3975-1683","first_name":"Zuzana"},{"last_name":"Tancer","full_name":"Tancer, Martin","first_name":"Martin"},{"first_name":"Uli","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner"}],"day":"01","scopus_import":"1","title":"Barycentric cuts through a convex body","oa_version":"Preprint","citation":{"apa":"Patakova, Z., Tancer, M., &#38; Wagner, U. (2022). Barycentric cuts through a convex body. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-021-00364-7\">https://doi.org/10.1007/s00454-021-00364-7</a>","mla":"Patakova, Zuzana, et al. “Barycentric Cuts through a Convex Body.” <i>Discrete and Computational Geometry</i>, vol. 68, Springer Nature, 2022, pp. 1133–54, doi:<a href=\"https://doi.org/10.1007/s00454-021-00364-7\">10.1007/s00454-021-00364-7</a>.","chicago":"Patakova, Zuzana, Martin Tancer, and Uli Wagner. “Barycentric Cuts through a Convex Body.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00454-021-00364-7\">https://doi.org/10.1007/s00454-021-00364-7</a>.","ista":"Patakova Z, Tancer M, Wagner U. 2022. Barycentric cuts through a convex body. Discrete and Computational Geometry. 68, 1133–1154.","ieee":"Z. Patakova, M. Tancer, and U. Wagner, “Barycentric cuts through a convex body,” <i>Discrete and Computational Geometry</i>, vol. 68. Springer Nature, pp. 1133–1154, 2022.","short":"Z. Patakova, M. Tancer, U. Wagner, Discrete and Computational Geometry 68 (2022) 1133–1154.","ama":"Patakova Z, Tancer M, Wagner U. Barycentric cuts through a convex body. <i>Discrete and Computational Geometry</i>. 2022;68:1133-1154. doi:<a href=\"https://doi.org/10.1007/s00454-021-00364-7\">10.1007/s00454-021-00364-7</a>"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"UlWa"}],"arxiv":1,"month":"12"},{"has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"abstract":[{"text":"We introduce a new way of representing logarithmically concave functions on Rd. It allows us to extend the notion of the largest volume ellipsoid contained in a convex body to the setting of logarithmically concave functions as follows. For every s>0, we define a class of non-negative functions on Rd derived from ellipsoids in Rd+1. For any log-concave function f on Rd , and any fixed s>0, we consider functions belonging to this class, and find the one with the largest integral under the condition that it is pointwise less than or equal to f, and we call it the John s-function of f. After establishing existence and uniqueness, we give a characterization of this function similar to the one given by John in his fundamental theorem. We find that John s-functions converge to characteristic functions of ellipsoids as s tends to zero and to Gaussian densities as s tends to infinity.\r\nAs an application, we prove a quantitative Helly type result: the integral of the pointwise minimum of any family of log-concave functions is at least a constant cd multiple of the integral of the pointwise minimum of a properly chosen subfamily of size 3d+2, where cd depends only on d.","lang":"eng"}],"intvolume":"       282","publication_status":"published","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"file_date_updated":"2022-08-02T10:40:48Z","author":[{"last_name":"Ivanov","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory","first_name":"Grigory"},{"last_name":"Naszódi","full_name":"Naszódi, Márton","first_name":"Márton"}],"scopus_import":"1","day":"01","oa_version":"Published Version","title":"Functional John ellipsoids","volume":282,"article_type":"original","date_created":"2022-03-20T23:01:38Z","oa":1,"language":[{"iso":"eng"}],"issue":"11","citation":{"short":"G. Ivanov, M. Naszódi, Journal of Functional Analysis 282 (2022).","ieee":"G. Ivanov and M. Naszódi, “Functional John ellipsoids,” <i>Journal of Functional Analysis</i>, vol. 282, no. 11. Elsevier, 2022.","ama":"Ivanov G, Naszódi M. Functional John ellipsoids. <i>Journal of Functional Analysis</i>. 2022;282(11). doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109441\">10.1016/j.jfa.2022.109441</a>","mla":"Ivanov, Grigory, and Márton Naszódi. “Functional John Ellipsoids.” <i>Journal of Functional Analysis</i>, vol. 282, no. 11, 109441, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109441\">10.1016/j.jfa.2022.109441</a>.","apa":"Ivanov, G., &#38; Naszódi, M. (2022). Functional John ellipsoids. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2022.109441\">https://doi.org/10.1016/j.jfa.2022.109441</a>","ista":"Ivanov G, Naszódi M. 2022. Functional John ellipsoids. Journal of Functional Analysis. 282(11), 109441.","chicago":"Ivanov, Grigory, and Márton Naszódi. “Functional John Ellipsoids.” <i>Journal of Functional Analysis</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jfa.2022.109441\">https://doi.org/10.1016/j.jfa.2022.109441</a>."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","arxiv":1,"month":"06","department":[{"_id":"UlWa"}],"article_number":"109441","file":[{"content_type":"application/pdf","access_level":"open_access","file_name":"2022_JourFunctionalAnalysis_Ivanov.pdf","success":1,"checksum":"1cf185e264e04c87cb1ce67a00db88ab","relation":"main_file","date_updated":"2022-08-02T10:40:48Z","creator":"dernst","file_size":734482,"date_created":"2022-08-02T10:40:48Z","file_id":"11721"}],"ddc":["510"],"quality_controlled":"1","doi":"10.1016/j.jfa.2022.109441","article_processing_charge":"Yes (via OA deal)","publisher":"Elsevier","date_updated":"2023-08-02T14:51:11Z","_id":"10887","type":"journal_article","status":"public","publication":"Journal of Functional Analysis","acknowledgement":"G.I. was supported by the Ministry of Education and Science of the Russian Federation in the framework of MegaGrant no 075-15-2019-1926. M.N. was supported by the National Research, Development and Innovation Fund (NRDI) grants K119670 and KKP-133864 as well as the Bolyai Scholarship of the Hungarian Academy of Sciences and the New National Excellence Programme and the TKP2020-NKA-06 program provided by the NRDI. ","date_published":"2022-06-01T00:00:00Z","isi":1,"year":"2022","external_id":{"isi":["000781371300008"],"arxiv":["2006.09934"]}},{"oa":1,"language":[{"iso":"eng"}],"citation":{"mla":"Arroyo Guevara, Alan M., and Stefan Felsner. “Approximating the Bundled Crossing Number.” <i>WALCOM 2022: Algorithms and Computation</i>, vol. 13174, Springer Nature, 2022, pp. 383–95, doi:<a href=\"https://doi.org/10.1007/978-3-030-96731-4_31\">10.1007/978-3-030-96731-4_31</a>.","apa":"Arroyo Guevara, A. M., &#38; Felsner, S. (2022). Approximating the bundled crossing number. In <i>WALCOM 2022: Algorithms and Computation</i> (Vol. 13174, pp. 383–395). Jember, Indonesia: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-96731-4_31\">https://doi.org/10.1007/978-3-030-96731-4_31</a>","ista":"Arroyo Guevara AM, Felsner S. 2022. Approximating the bundled crossing number. WALCOM 2022: Algorithms and Computation. WALCOM: Algorithms and ComputationLNCS vol. 13174, 383–395.","chicago":"Arroyo Guevara, Alan M, and Stefan Felsner. “Approximating the Bundled Crossing Number.” In <i>WALCOM 2022: Algorithms and Computation</i>, 13174:383–95. LNCS. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/978-3-030-96731-4_31\">https://doi.org/10.1007/978-3-030-96731-4_31</a>.","short":"A.M. Arroyo Guevara, S. Felsner, in:, WALCOM 2022: Algorithms and Computation, Springer Nature, 2022, pp. 383–395.","ieee":"A. M. Arroyo Guevara and S. Felsner, “Approximating the bundled crossing number,” in <i>WALCOM 2022: Algorithms and Computation</i>, Jember, Indonesia, 2022, vol. 13174, pp. 383–395.","ama":"Arroyo Guevara AM, Felsner S. Approximating the bundled crossing number. In: <i>WALCOM 2022: Algorithms and Computation</i>. Vol 13174. LNCS. Springer Nature; 2022:383-395. doi:<a href=\"https://doi.org/10.1007/978-3-030-96731-4_31\">10.1007/978-3-030-96731-4_31</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"month":"03","department":[{"_id":"UlWa"}],"abstract":[{"text":"Bundling crossings is a strategy which can enhance the readability of graph drawings. In this paper we consider bundlings for families of pseudosegments, i.e., simple curves such that any two have share at most one point at which they cross. Our main result is that there is a polynomial-time algorithm to compute an 8-approximation of the bundled crossing number of such instances (up to adding a term depending on the facial structure). This 8-approximation also holds for bundlings of good drawings of graphs. In the special case of circular drawings the approximation factor is 8 (no extra term), this improves upon the 10-approximation of Fink et al. [6]. We also show how to compute a 92-approximation when the intersection graph of the pseudosegments is bipartite.","lang":"eng"}],"intvolume":"     13174","publication_identifier":{"isbn":["9783030967307"],"issn":["0302-9743"],"eissn":["1611-3349"]},"publication_status":"published","author":[{"orcid":"0000-0003-2401-8670","first_name":"Alan M","last_name":"Arroyo Guevara","full_name":"Arroyo Guevara, Alan M","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Felsner","full_name":"Felsner, Stefan","first_name":"Stefan"}],"day":"16","scopus_import":"1","oa_version":"Preprint","title":"Approximating the bundled crossing number","volume":13174,"date_created":"2022-04-17T22:01:47Z","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"status":"public","publication":"WALCOM 2022: Algorithms and Computation","ec_funded":1,"acknowledgement":"This work was initiated during the Workshop on Geometric Graphs in November 2019 in Strobl, Austria. We would like to thank Oswin Aichholzer, Fabian Klute, Man-Kwun Chiu, Martin Balko, Pavel Valtr for their avid discussions during the workshop. The first author has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska Curie grant agreement No 754411. The second author has been supported by the German Research Foundation DFG Project FE 340/12-1.","date_published":"2022-03-16T00:00:00Z","conference":{"name":"WALCOM: Algorithms and Computation","start_date":"2022-03-24","end_date":"2022-03-26","location":"Jember, Indonesia"},"year":"2022","external_id":{"arxiv":["2109.14892"]},"related_material":{"record":[{"relation":"later_version","status":"public","id":"13969"}]},"page":"383-395","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2109.14892"}],"quality_controlled":"1","doi":"10.1007/978-3-030-96731-4_31","article_processing_charge":"No","publisher":"Springer Nature","date_updated":"2023-09-25T10:56:10Z","_id":"11185","type":"conference","series_title":"LNCS"},{"oa":1,"language":[{"iso":"eng"}],"issue":"2","citation":{"apa":"Ivanov, G., &#38; Naszodi, M. (2022). A quantitative Helly-type theorem: Containment in a homothet. <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21M1403308\">https://doi.org/10.1137/21M1403308</a>","mla":"Ivanov, Grigory, and Marton Naszodi. “A Quantitative Helly-Type Theorem: Containment in a Homothet.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 36, no. 2, Society for Industrial and Applied Mathematics, 2022, pp. 951–57, doi:<a href=\"https://doi.org/10.1137/21M1403308\">10.1137/21M1403308</a>.","ista":"Ivanov G, Naszodi M. 2022. A quantitative Helly-type theorem: Containment in a homothet. SIAM Journal on Discrete Mathematics. 36(2), 951–957.","chicago":"Ivanov, Grigory, and Marton Naszodi. “A Quantitative Helly-Type Theorem: Containment in a Homothet.” <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21M1403308\">https://doi.org/10.1137/21M1403308</a>.","ieee":"G. Ivanov and M. Naszodi, “A quantitative Helly-type theorem: Containment in a homothet,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 36, no. 2. Society for Industrial and Applied Mathematics, pp. 951–957, 2022.","short":"G. Ivanov, M. Naszodi, SIAM Journal on Discrete Mathematics 36 (2022) 951–957.","ama":"Ivanov G, Naszodi M. A quantitative Helly-type theorem: Containment in a homothet. <i>SIAM Journal on Discrete Mathematics</i>. 2022;36(2):951-957. doi:<a href=\"https://doi.org/10.1137/21M1403308\">10.1137/21M1403308</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"04","arxiv":1,"department":[{"_id":"UlWa"}],"abstract":[{"lang":"eng","text":"We introduce a new variant of quantitative Helly-type theorems: the minimal homothetic distance of the intersection of a family of convex sets to the intersection of a subfamily of a fixed size. As an application, we establish the following quantitative Helly-type result for the diameter. If $K$ is the intersection of finitely many convex bodies in $\\mathbb{R}^d$, then one can select $2d$ of these bodies whose intersection is of diameter at most $(2d)^3{diam}(K)$. The best previously known estimate, due to Brazitikos [Bull. Hellenic Math. Soc., 62 (2018), pp. 19--25], is $c d^{11/2}$. Moreover, we confirm that the multiplicative factor $c d^{1/2}$ conjectured by Bárány, Katchalski, and Pach [Proc. Amer. Math. Soc., 86 (1982), pp. 109--114] cannot be improved. The bounds above follow from our key result that concerns sparse approximation of a convex polytope by the convex hull of a well-chosen subset of its vertices: Assume that $Q \\subset {\\mathbb R}^d$ is a polytope whose centroid is the origin. Then there exist at most 2d vertices of $Q$ whose convex hull $Q^{\\prime \\prime}$ satisfies $Q \\subset - 8d^3 Q^{\\prime \\prime}.$"}],"intvolume":"        36","publication_identifier":{"issn":["0895-4801"]},"publication_status":"published","author":[{"first_name":"Grigory","last_name":"Ivanov","full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E"},{"last_name":"Naszodi","full_name":"Naszodi, Marton","first_name":"Marton"}],"scopus_import":"1","day":"11","title":"A quantitative Helly-type theorem: Containment in a homothet","oa_version":"Preprint","volume":36,"article_type":"original","date_created":"2022-06-05T22:01:50Z","status":"public","publication":"SIAM Journal on Discrete Mathematics","acknowledgement":"G.I. acknowledges the financial support from the Ministry of Educational and Science of the Russian Federation in the framework of MegaGrant no 075-15-2019-1926. M.N. was supported by the National Research, Development and Innovation Fund (NRDI) grants K119670 and\r\nKKP-133864 as well as the Bolyai Scholarship of the Hungarian Academy of Sciences and the New National Excellence Programme and the TKP2020-NKA-06 program provided by the NRDI.","date_published":"2022-04-11T00:00:00Z","isi":1,"year":"2022","external_id":{"arxiv":["2103.04122"],"isi":["000793158200002"]},"page":"951-957","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2103.04122"}],"quality_controlled":"1","doi":"10.1137/21M1403308","article_processing_charge":"No","publisher":"Society for Industrial and Applied Mathematics","date_updated":"2023-10-18T06:58:03Z","_id":"11435","type":"journal_article"},{"project":[{"grant_number":"M02281","name":"Eliminating intersections in drawings of graphs","call_identifier":"FWF","_id":"261FA626-B435-11E9-9278-68D0E5697425"}],"publication":"Discrete and Computational Geometry","status":"public","date_published":"2022-09-01T00:00:00Z","acknowledgement":"We thank Zdeněk Dvořák, Xavier Goaoc, and Pavel Paták for helpful discussions. We also thank Bojan Mohar, Paul Seymour, Gelasio Salazar, Jim Geelen, and John Maharry for information about their unpublished results related to Conjecture 3.1. Finally we thank the reviewers for corrections and suggestions for improving the presentation.\r\nSupported by Austrian Science Fund (FWF): M2281-N35. Supported by project 19-04113Y of the Czech Science Foundation (GAČR), by the Czech-French collaboration project EMBEDS II (CZ: 7AMB17FR029, FR: 38087RM), and by Charles University project UNCE/SCI/004.","isi":1,"year":"2022","external_id":{"arxiv":["1803.05085"],"isi":["000825014500001"]},"related_material":{"record":[{"id":"186","relation":"earlier_version","status":"public"}]},"page":"425-447","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1803.05085"}],"quality_controlled":"1","doi":"10.1007/s00454-022-00412-w","article_processing_charge":"No","publisher":"Springer Nature","date_updated":"2023-08-14T12:43:52Z","_id":"11593","type":"journal_article","oa":1,"language":[{"iso":"eng"}],"citation":{"ama":"Fulek R, Kynčl J. The Z2-Genus of Kuratowski minors. <i>Discrete and Computational Geometry</i>. 2022;68:425-447. doi:<a href=\"https://doi.org/10.1007/s00454-022-00412-w\">10.1007/s00454-022-00412-w</a>","ieee":"R. Fulek and J. Kynčl, “The Z2-Genus of Kuratowski minors,” <i>Discrete and Computational Geometry</i>, vol. 68. Springer Nature, pp. 425–447, 2022.","short":"R. Fulek, J. Kynčl, Discrete and Computational Geometry 68 (2022) 425–447.","ista":"Fulek R, Kynčl J. 2022. The Z2-Genus of Kuratowski minors. Discrete and Computational Geometry. 68, 425–447.","chicago":"Fulek, Radoslav, and Jan Kynčl. “The Z2-Genus of Kuratowski Minors.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00454-022-00412-w\">https://doi.org/10.1007/s00454-022-00412-w</a>.","apa":"Fulek, R., &#38; Kynčl, J. (2022). The Z2-Genus of Kuratowski minors. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-022-00412-w\">https://doi.org/10.1007/s00454-022-00412-w</a>","mla":"Fulek, Radoslav, and Jan Kynčl. “The Z2-Genus of Kuratowski Minors.” <i>Discrete and Computational Geometry</i>, vol. 68, Springer Nature, 2022, pp. 425–47, doi:<a href=\"https://doi.org/10.1007/s00454-022-00412-w\">10.1007/s00454-022-00412-w</a>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"month":"09","department":[{"_id":"UlWa"}],"intvolume":"        68","abstract":[{"lang":"eng","text":"A drawing of a graph on a surface is independently even if every pair of nonadjacent edges in the drawing crosses an even number of times. The Z2 -genus of a graph G is the minimum g such that G has an independently even drawing on the orientable surface of genus g. An unpublished result by Robertson and Seymour implies that for every t, every graph of sufficiently large genus contains as a minor a projective t×t grid or one of the following so-called t -Kuratowski graphs: K3,t, or t copies of K5 or K3,3 sharing at most two common vertices. We show that the Z2-genus of graphs in these families is unbounded in t; in fact, equal to their genus. Together, this implies that the genus of a graph is bounded from above by a function of its Z2-genus, solving a problem posed by Schaefer and Štefankovič, and giving an approximate version of the Hanani–Tutte theorem on orientable surfaces. We also obtain an analogous result for Euler genus and Euler Z2-genus of graphs."}],"publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"author":[{"first_name":"Radoslav","orcid":"0000-0001-8485-1774","last_name":"Fulek","full_name":"Fulek, Radoslav","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Kynčl, Jan","last_name":"Kynčl","first_name":"Jan"}],"scopus_import":"1","day":"01","oa_version":"Preprint","title":"The Z2-Genus of Kuratowski minors","volume":68,"article_type":"original","date_created":"2022-07-17T22:01:56Z"},{"department":[{"_id":"GradSch"},{"_id":"UlWa"}],"file":[{"file_id":"11780","date_updated":"2022-08-10T15:34:04Z","creator":"pwild","file_size":16828,"date_created":"2022-08-10T15:34:04Z","description":"Code for computer-assisted proofs in Section 8.4.7 in Thesis","checksum":"f5f3af1fb7c8a24b71ddc88ad7f7c5b4","relation":"supplementary_material","content_type":"text/x-python","access_level":"open_access","file_name":"flags.py"},{"date_updated":"2022-08-10T15:34:10Z","creator":"pwild","date_created":"2022-08-10T15:34:10Z","file_size":12226,"file_id":"11781","access_level":"open_access","content_type":"text/x-c++src","file_name":"lowerbound.cpp","checksum":"1f7c12dfe3bdaa9b147e4fbc3d34e3d5","description":"Code for proof of Lemma 8.20 in Thesis","relation":"supplementary_material"},{"relation":"supplementary_material","checksum":"4cf81455c49e5dec3b9b2e3980137eeb","description":"Code for proof of Proposition 7.9 in Thesis","file_name":"upperbound.py","access_level":"open_access","content_type":"text/x-python","file_id":"11782","file_size":3240,"date_created":"2022-08-10T15:34:17Z","date_updated":"2022-08-10T15:34:17Z","creator":"pwild"},{"access_level":"open_access","content_type":"application/pdf","file_name":"finalthesisPascalWildPDFA.pdf","checksum":"4e96575b10cbe4e0d0db2045b2847774","relation":"main_file","creator":"pwild","date_updated":"2022-08-11T16:08:33Z","file_size":5086282,"date_created":"2022-08-11T16:08:33Z","file_id":"11809","title":"High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes"},{"file_id":"11810","file_size":18150068,"date_created":"2022-08-11T16:09:19Z","date_updated":"2022-08-11T16:09:19Z","creator":"pwild","relation":"source_file","checksum":"92d94842a1fb6dca5808448137573b2e","file_name":"ThesisSubmission.zip","access_level":"closed","content_type":"application/zip"}],"supervisor":[{"last_name":"Wagner","full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","orcid":"0000-0002-1494-0568"}],"month":"08","citation":{"apa":"Wild, P. (2022). <i>High-dimensional expansion and crossing numbers of simplicial complexes</i>. Institute of Science and Technology. <a href=\"https://doi.org/10.15479/at:ista:11777\">https://doi.org/10.15479/at:ista:11777</a>","mla":"Wild, Pascal. <i>High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes</i>. Institute of Science and Technology, 2022, doi:<a href=\"https://doi.org/10.15479/at:ista:11777\">10.15479/at:ista:11777</a>.","chicago":"Wild, Pascal. “High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes.” Institute of Science and Technology, 2022. <a href=\"https://doi.org/10.15479/at:ista:11777\">https://doi.org/10.15479/at:ista:11777</a>.","ista":"Wild P. 2022. High-dimensional expansion and crossing numbers of simplicial complexes. Institute of Science and Technology.","ieee":"P. Wild, “High-dimensional expansion and crossing numbers of simplicial complexes,” Institute of Science and Technology, 2022.","short":"P. Wild, High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes, Institute of Science and Technology, 2022.","ama":"Wild P. High-dimensional expansion and crossing numbers of simplicial complexes. 2022. doi:<a href=\"https://doi.org/10.15479/at:ista:11777\">10.15479/at:ista:11777</a>"},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa":1,"language":[{"iso":"eng"}],"date_created":"2022-08-10T15:51:19Z","author":[{"last_name":"Wild","id":"4C20D868-F248-11E8-B48F-1D18A9856A87","full_name":"Wild, Pascal","first_name":"Pascal"}],"day":"11","title":"High-dimensional expansion and crossing numbers of simplicial complexes","oa_version":"Published Version","publication_status":"published","publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-021-3"]},"file_date_updated":"2022-08-11T16:09:19Z","has_accepted_license":"1","abstract":[{"text":"In this dissertation we study coboundary expansion of simplicial complex with a view of giving geometric applications.\r\nOur main novel tool is an equivariant version of Gromov's celebrated Topological Overlap Theorem. The equivariant topological overlap theorem leads to various geometric applications including a quantitative non-embeddability result for sufficiently thick buildings (which partially resolves a conjecture of Tancer and Vorwerk) and an improved lower bound on the pair-crossing number of (bounded degree) expander graphs. Additionally, we will give new proofs for several known lower bounds for geometric problems such as the number of Tverberg partitions or the crossing number of complete bipartite graphs.\r\nFor the aforementioned applications one is naturally lead to study expansion properties of joins of simplicial complexes. In the presence of a special certificate for expansion (as it is the case, e.g., for spherical buildings), the join of two expanders is an expander. On the flip-side, we report quite some evidence that coboundary expansion exhibits very non-product-like behaviour under taking joins. For instance, we exhibit infinite families of graphs $(G_n)_{n\\in \\mathbb{N}}$ and $(H_n)_{n\\in\\mathbb{N}}$ whose join $G_n*H_n$ has expansion of lower order than the product of the expansion constant of the graphs. Moreover, we show an upper bound of $(d+1)/2^d$ on the normalized coboundary expansion constants for the complete multipartite complex $[n]^{*(d+1)}$ (under a mild divisibility condition on $n$).\r\nVia the probabilistic method the latter result extends to an upper bound of $(d+1)/2^d+\\varepsilon$ on the coboundary expansion constant of the spherical building associated with $\\mathrm{PGL}_{d+2}(\\mathbb{F}_q)$ for any $\\varepsilon>0$ and sufficiently large $q=q(\\varepsilon)$. This disproves a conjecture of Lubotzky, Meshulam and Mozes -- in a rather strong sense.\r\nBy improving on existing lower bounds we make further progress towards closing the gap between the known lower and upper bounds on the coboundary expansion constants of $[n]^{*(d+1)}$. The best improvements we achieve using computer-aided proofs and flag algebras. The exact value even for the complete $3$-partite $2$-dimensional complex $[n]^{*3}$ remains unknown but we are happy to conjecture a precise value for every $n$. %Moreover, we show that a previously shown lower bound on the expansion constant of the spherical building associated with $\\mathrm{PGL}_{2}(\\mathbb{F}_q)$ is not tight.\r\nIn a loosely structured, last chapter of this thesis we collect further smaller observations related to expansion. We point out a link between discrete Morse theory and a technique for showing coboundary expansion, elaborate a bit on the hardness of computing coboundary expansion constants, propose a new criterion for coboundary expansion (in a very dense setting) and give one way of making the folklore result that expansion of links is a necessary condition for a simplicial complex to be an expander precise.","lang":"eng"}],"year":"2022","ec_funded":1,"date_published":"2022-08-11T00:00:00Z","degree_awarded":"PhD","project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","grant_number":"665385","call_identifier":"H2020"}],"status":"public","date_updated":"2023-06-22T09:56:36Z","_id":"11777","type":"dissertation","doi":"10.15479/at:ista:11777","alternative_title":["ISTA Thesis"],"article_processing_charge":"No","publisher":"Institute of Science and Technology","page":"170","ddc":["500","516","514"]}]