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S.","full_name":"Thejaswini, K. S."}],"researchdata_availability":"no","date_published":"2026-07-09T00:00:00Z","external_id":{"arxiv":["2601.18303"]},"article_number":"23:1-23:26","alternative_title":["LIPIcs"],"quality_controlled":"1","keyword":["Concurrent games","Shared randomness","Topology","Algebraic Geometry"],"das_tickbox":"0","_id":"22617","article_processing_charge":"No","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication":"41st Annual Symposium on Logic in Computer Science","volume":380,"acknowledgement":"This work was supported in part by the ERC-2020-AdG 101020093 (VAMOS).\r\nLéonard Brice: Part of this work was realised when this author was an FNRS aspirant at Université libre de Bruxelles.\r\nK. S. Thejaswini: Part of this work was realised when this author was a post-doctoral researcher at IST Austria.\r\nAcknowledgements We thank all our colleagues who took the time to hear our puzzle and wasted several hours of their research time in pursuit of the optimal bounds for the 3-player matching.\r\npennies problem.\r\n","status":"public","intvolume":" 380","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Consider a 4-player version of Matching Pennies where a team of three players competes against the Devil. Each player simultaneously says \"Heads\" or \"Tails\". The team wins if all four choices match; otherwise the Devil wins. If all team players randomise independently, they win with probability 1/8; if all players share a common source of randomness, they win with probability 1/2. What happens when each pair of team players shares a source of randomness? Can the team do better than win with probability 1/4? The surprising (and nontrivial) answer is yes!\r\nWe introduce Dicey Games, a formal framework motivated by the study of distributed systems with shared sources of randomness (of which the above example is a specific instance). We characterise the existence, representation and computational complexity of optimal strategies in Dicey Games, and we study the problem of allocating limited sources of randomness optimally within a team."}],"month":"07","conference":{"name":"LICS: Logic in Computer Science","start_date":"2026-07-20","location":"Lisbon, Portugal","end_date":"2026-07-23"},"arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","ddc":["000"],"oa_version":"Published Version","doi":"10.4230/LIPIcs.LICS.2026.23","date_created":"2026-08-02T22:01:52Z","date_updated":"2026-08-03T07:03:28Z","department":[{"_id":"ToHe"}],"ec_funded":1,"supplementarymaterial":"no","type":"conference","project":[{"_id":"62781420-2b32-11ec-9570-8d9b63373d4d","call_identifier":"H2020","grant_number":"101020093","name":"Vigilant Algorithmic Monitoring of Software"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"fulldoi":"https://doi.org/10.4230/LIPIcs.LICS.2026.23","citation":{"ieee":"L. J. Brice, T. A. Henzinger, and K. S. Thejaswini, “Dicey games: Shared sources of randomness in distributed systems,” in 41st Annual Symposium on Logic in Computer Science, Lisbon, Portugal, 2026, vol. 380.","apa":"Brice, L. J., Henzinger, T. A., & Thejaswini, K. S. (2026). Dicey games: Shared sources of randomness in distributed systems. In 41st Annual Symposium on Logic in Computer Science (Vol. 380). Lisbon, Portugal: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.LICS.2026.23","mla":"Brice, Leonard J., et al. “Dicey Games: Shared Sources of Randomness in Distributed Systems.” 41st Annual Symposium on Logic in Computer Science, vol. 380, 23:1-23:26, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:10.4230/LIPIcs.LICS.2026.23.","ama":"Brice LJ, Henzinger TA, Thejaswini KS. Dicey games: Shared sources of randomness in distributed systems. In: 41st Annual Symposium on Logic in Computer Science. Vol 380. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:10.4230/LIPIcs.LICS.2026.23","chicago":"Brice, Leonard J, Thomas A Henzinger, and K. S. Thejaswini. “Dicey Games: Shared Sources of Randomness in Distributed Systems.” In 41st Annual Symposium on Logic in Computer Science, Vol. 380. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. https://doi.org/10.4230/LIPIcs.LICS.2026.23.","ista":"Brice LJ, Henzinger TA, Thejaswini KS. 2026. Dicey games: Shared sources of randomness in distributed systems. 41st Annual Symposium on Logic in Computer Science. LICS: Logic in Computer Science, LIPIcs, vol. 380, 23:1-23:26.","short":"L.J. Brice, T.A. Henzinger, K.S. Thejaswini, in:, 41st Annual Symposium on Logic in Computer Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026."},"publication_identifier":{"issn":["1868-8969"],"isbn":["9783959774345"]},"oa":1,"scopus_import":"1","OA_place":"publisher","OA_type":"gold","day":"09","file":[{"file_id":"22625","file_name":"2026_LIPICSLICS_Brice.pdf","file_size":919708,"relation":"main_file","date_updated":"2026-08-03T07:02:30Z","date_created":"2026-08-03T07:02:30Z","creator":"dernst","content_type":"application/pdf","checksum":"5d0ff4d267565188a8b4c7502e1bd243","success":1,"access_level":"open_access"}],"file_date_updated":"2026-08-03T07:02:30Z"},{"publication_status":"published","year":"2026","has_accepted_license":"1","date_published":"2026-07-01T00:00:00Z","title":"Charting the landscape of diameter computation on geometric intersection graphs in the plane","author":[{"full_name":"Chan, Timothy M.","last_name":"Chan","orcid":"0000-0002-8093-0675","first_name":"Timothy M."},{"orcid":"0000-0001-6714-7988","first_name":"Hsien-Chih","last_name":"Chang","full_name":"Chang, Hsien-Chih"},{"orcid":"0000-0001-5083-6082","first_name":"Jie","last_name":"Gao","full_name":"Gao, Jie"},{"last_name":"Kisfaludi-Bak","first_name":"Sándor","orcid":"0000-0002-6856-2902","full_name":"Kisfaludi-Bak, Sándor"},{"last_name":"Le","orcid":"0000-0001-8223-9944","first_name":"Hung","full_name":"Le, Hung"},{"last_name":"Zheng","first_name":"Da Wei","id":"af77956b-e859-11ef-8dc9-d301b898e32f","full_name":"Zheng, Da Wei"}],"researchdata_availability":"no","_id":"22405","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","article_processing_charge":"No","external_id":{"arxiv":["2605.10692"]},"article_number":"54:1-54:22","das_tickbox":"0","quality_controlled":"1","keyword":["String graphs","Fine-grained complexity","Theory of computation → Computational geometry"],"status":"public","acknowledgement":"Timothy M. Chan: Supported by NSF grant CCF-2224271.\r\nHsien-Chih Chang: Supported by NSF CAREER award CCF-2443017.\r\nJie Gao: Supported by NSF DMS-2220271, DMS-2311064, IIS-2229876, CCF-2118953, CNS-2515159.\r\nSándor Kisfaludi-Bak: Supported by the Research Council of Finland, Grant 363444.\r\nHung Le: Supported by an NSF grant CCF-2517033 and an NSF CAREER Award CCF-2237288.\r\nDa Wei Zheng: This project has received funding from the Austrian Science Fund (FWF) grant\r\nDOI 10.55776/I5982. For open access purposes, the author has applied a CC BY public copyright\r\nlicense to any author-accepted manuscript version arising from this submission.\r\n","intvolume":" 374","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in 2D, the problem is solvable in truly subquadratic time [Chan et al., 2025], while for other objects, including unit segments and equilateral triangles in 2D or unit balls and axis-parallel unit cubes in 3D, there is no truly subquadratic time algorithm under the Orthogonal Vector (OV) hypothesis [Bringmann et al., 2022]. \r\nWe undertake a comprehensive study of computing the diameter of geometric intersection graphs for various types of objects. We discover many new irregularities, showing that the landscape is extremely nuanced: the source of hardness is a combination of the object type, the true diameter value, and how the objects intersect with each other. Our highlighted results for the 2D case include: \r\n1) The diameter of non-degenerate, axis-aligned line segments can be computed in truly subquadratic time. Previous hardness result [Bringmann et al., 2022] for line segments applies only to degenerate instances. On the other hand, for the degenerate case, we show that a truly subquadratic time algorithm exists when the true diameter is constant. \r\n2) An almost-linear-time algorithm for unit-square graphs of constant diameter. Previous algorithms [Duraj et al., 2024; Chan et al., 2025] rely on succinct representation assuming bounded VC-dimension; for such a strategy Ω(n^{7/4}) time is an inherent barrier. \r\n3) An Õ(n^{4/3})-time algorithm to decide if the diameter of a unit-disk graph is at most 2. This improves upon the recent algorithm with running time Õ(n^{2-1/9}) [Chan et al., 2025]. \r\n4) Deciding if the diameter of intersection graphs of fat triangles or line segments is at most 2 is truly subquadratic-hard under fine-grained complexity assumptions. Previous lower bounds [Bringmann et al., 2022] only hold when deciding if diameter is at most 3. Our findings are presented in a pair of papers. This paper focuses solely on the 2D case, while the companion paper is devoted to higher-dimensional cases."}],"publication":"53rd International Colloquium on Automata, Languages, and Programming","volume":374,"date_created":"2026-07-27T05:53:08Z","date_updated":"2026-08-12T09:03:26Z","doi":"10.4230/LIPICS.ICALP.2026.54","month":"07","conference":{"start_date":"2026-07-07","name":"ICALP: Automata, Languages and Programming","end_date":"2026-07-10","location":"Egham, United Kingdom"},"arxiv":1,"corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["000"],"oa_version":"Published Version","project":[{"grant_number":"I05982","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","name":"Static and Dynamic Hierarchical Graph Decompositions"}],"department":[{"_id":"MoHe"}],"supplementarymaterial":"no","type":"conference","oa":1,"scopus_import":"1","OA_place":"publisher","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"fulldoi":"https://doi.org/10.4230/LIPICS.ICALP.2026.54","publication_identifier":{"eissn":["1868-8969","9783959774284"]},"citation":{"chicago":"Chan, Timothy M., Hsien-Chih Chang, Jie Gao, Sándor Kisfaludi-Bak, Hung Le, and Da Wei Zheng. “Charting the Landscape of Diameter Computation on Geometric Intersection Graphs in the Plane.” In 53rd International Colloquium on Automata, Languages, and Programming, Vol. 374. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. https://doi.org/10.4230/LIPICS.ICALP.2026.54.","ista":"Chan TM, Chang H-C, Gao J, Kisfaludi-Bak S, Le H, Zheng DW. 2026. Charting the landscape of diameter computation on geometric intersection graphs in the plane. 53rd International Colloquium on Automata, Languages, and Programming. ICALP: Automata, Languages and Programming vol. 374, 54:1-54:22.","short":"T.M. Chan, H.-C. Chang, J. Gao, S. Kisfaludi-Bak, H. Le, D.W. Zheng, in:, 53rd International Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.","apa":"Chan, T. M., Chang, H.-C., Gao, J., Kisfaludi-Bak, S., Le, H., & Zheng, D. W. (2026). Charting the landscape of diameter computation on geometric intersection graphs in the plane. In 53rd International Colloquium on Automata, Languages, and Programming (Vol. 374). Egham, United Kingdom: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.ICALP.2026.54","ieee":"T. M. Chan, H.-C. Chang, J. Gao, S. Kisfaludi-Bak, H. Le, and D. W. Zheng, “Charting the landscape of diameter computation on geometric intersection graphs in the plane,” in 53rd International Colloquium on Automata, Languages, and Programming, Egham, United Kingdom, 2026, vol. 374.","mla":"Chan, Timothy M., et al. “Charting the Landscape of Diameter Computation on Geometric Intersection Graphs in the Plane.” 53rd International Colloquium on Automata, Languages, and Programming, vol. 374, 54:1-54:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:10.4230/LIPICS.ICALP.2026.54.","ama":"Chan TM, Chang H-C, Gao J, Kisfaludi-Bak S, Le H, Zheng DW. Charting the landscape of diameter computation on geometric intersection graphs in the plane. In: 53rd International Colloquium on Automata, Languages, and Programming. Vol 374. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:10.4230/LIPICS.ICALP.2026.54"},"file":[{"date_created":"2026-07-27T06:20:41Z","relation":"main_file","date_updated":"2026-07-27T06:20:41Z","file_size":1440497,"file_name":"2026_LIPIcSICALP_Chan.pdf","file_id":"22407","checksum":"1e66eba4cfe4e74ab28108b1ca0bb956","content_type":"application/pdf","creator":"dernst","success":1,"access_level":"open_access"}],"file_date_updated":"2026-07-27T06:20:41Z","OA_type":"gold","day":"01"},{"project":[{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"},{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413"}],"department":[{"_id":"HeEd"},{"_id":"GradSch"}],"ec_funded":1,"type":"conference","supplementarymaterial":"no","doi":"10.4230/LIPICS.SOCG.2026.41","date_updated":"2026-08-12T09:02:56Z","date_created":"2026-07-13T09:56:38Z","month":"05","conference":{"location":"New Brunswick, NJ, United States","end_date":"2026-06-05","name":"SoCG: Symposium on Computational Geometry","start_date":"2026-06-02"},"arxiv":1,"corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","ddc":["500"],"file":[{"date_created":"2026-07-14T06:08:05Z","relation":"main_file","date_updated":"2026-07-14T06:08:05Z","file_id":"22329","file_name":"2026_LIPIcSSoCG_Edelsbrunner.pdf","file_size":2902144,"checksum":"9dfb96ee66985c724b499b0e5888dc8e","creator":"dernst","content_type":"application/pdf","success":1,"access_level":"open_access"}],"file_date_updated":"2026-07-14T06:08:05Z","OA_type":"gold","day":"27","oa":1,"scopus_import":"1","OA_place":"publisher","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"fulldoi":"https://doi.org/10.4230/LIPICS.SOCG.2026.41","citation":{"short":"H. Edelsbrunner, M. Lipiński, M. Mrozek, M. Soriano Trigueros, F. Zimin, in:, 42nd International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.","chicago":"Edelsbrunner, Herbert, Michał Lipiński, Marian Mrozek, Manuel Soriano Trigueros, and Fedor Zimin. “The Depth Poset under Transpositions in the Filter.” In 42nd International Symposium on Computational Geometry, Vol. 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. https://doi.org/10.4230/LIPICS.SOCG.2026.41.","ista":"Edelsbrunner H, Lipiński M, Mrozek M, Soriano Trigueros M, Zimin F. 2026. The depth poset under transpositions in the filter. 42nd International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 367, 41:1-41:18.","ieee":"H. Edelsbrunner, M. Lipiński, M. Mrozek, M. Soriano Trigueros, and F. Zimin, “The depth poset under transpositions in the filter,” in 42nd International Symposium on Computational Geometry, New Brunswick, NJ, United States, 2026, vol. 367.","apa":"Edelsbrunner, H., Lipiński, M., Mrozek, M., Soriano Trigueros, M., & Zimin, F. (2026). The depth poset under transpositions in the filter. In 42nd International Symposium on Computational Geometry (Vol. 367). New Brunswick, NJ, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2026.41","mla":"Edelsbrunner, Herbert, et al. “The Depth Poset under Transpositions in the Filter.” 42nd International Symposium on Computational Geometry, vol. 367, 41:1-41:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:10.4230/LIPICS.SOCG.2026.41.","ama":"Edelsbrunner H, Lipiński M, Mrozek M, Soriano Trigueros M, Zimin F. The depth poset under transpositions in the filter. In: 42nd International Symposium on Computational Geometry. Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:10.4230/LIPICS.SOCG.2026.41"},"publication_identifier":{"isbn":["9783959774185"],"eissn":["1868-8969"]},"date_published":"2026-05-27T00:00:00Z","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Lipiński, Michał","id":"dfffb474-4317-11ee-8f5c-fe3fc95a425e","first_name":"Michał","orcid":"0000-0001-9789-9750","last_name":"Lipiński"},{"orcid":"0000-0002-0619-6417","first_name":"Marian","last_name":"Mrozek","full_name":"Mrozek, Marian"},{"full_name":"Soriano Trigueros, Manuel","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","orcid":"0000-0003-2449-1433","first_name":"Manuel","last_name":"Soriano Trigueros"},{"full_name":"Zimin, Fedor","id":"afd27eda-91c1-11f0-aad8-c6edbec24c04","last_name":"Zimin","first_name":"Fedor"}],"title":"The depth poset under transpositions in the filter","researchdata_availability":"no","publication_status":"published","year":"2026","has_accepted_license":"1","language":[{"iso":"eng"}],"intvolume":" 367","status":"public","acknowledgement":"The authors thank Jakub Leśkiewicz and Bartosz Furmanek for discussions\r\nthat helped improve the paper. Herbert Edelsbrunner: DFG Collaborative Research Center TRR 109, Austrian Science\r\nFund (FWF), grant no. I 02979-N35\r\nMichał Lipiński: European Union’s Horizon 2020 research and innovation programme under the\r\nMarie Skłodowska-Curie Grant Agreement No. 101034413\r\nMarian Mrozek: Polish National Science Center under Opus Grant 2019/35/B/ST1/00874 and Opus\r\nGrant 2025/57/B/ST1/00550","abstract":[{"text":"The depth poset of a filtered Lefschetz complex reflects the dependencies between the cancellations of different shallow birth-death pairs. Using the fast algorithms for computing the depth poset in [Edelsbrunner et al., 2026] and for updating the persistence diagram under transpositions in [Cohen-Steiner et al., 2006], we give a complete case analysis of how transpositions of cells in the filter affect the depth poset. In addition, we present statistics on the depth poset for random point data and its sensitivity to the transpositions that occur in random straight-line homotopies.","lang":"eng"}],"publication":"42nd International Symposium on Computational Geometry","volume":367,"_id":"22299","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","article_processing_charge":"Yes","external_id":{"arxiv":["2511.21961"]},"article_number":"41:1-41:18","alternative_title":["LIPIcs"],"keyword":["Algebraic topology","Lefschetz complexes","persistent homology","vines and vineyards","birth-death pairs","shallow pairs","relations","partial orders","transpositions","Theory of computation → Computational geometry"],"quality_controlled":"1","das_tickbox":"0"},{"external_id":{"arxiv":["2109.04233"]},"keyword":["Mean curvature flow","gradient flows","varifolds","weak solutions","weak-strong uniqueness","calibrated geometry","gradient-flow calibrations"],"das_tickbox":"1","quality_controlled":"1","_id":"10011","article_processing_charge":"No","publisher":"International Press of Boston","volume":130,"publication":"Journal of Differential Geometry","abstract":[{"lang":"eng","text":"We propose a new weak solution concept for (two-phase) mean curvature flow which enjoys both (unconditional) existence and (weak-strong) uniqueness properties. These solutions are evolving varifolds, just as in Brakke's formulation, but are coupled to the phase volumes by a simple transport equation. First, we show that, in the exact same setup as in Ilmanen's proof [J. Differential Geom. 38, 417-461, (1993)], any limit point of solutions to the Allen-Cahn equation is a varifold solution in our sense. Second, we prove that any calibrated flow in the sense of Fischer et al. [arXiv:2003.05478] - and hence any classical solution to mean curvature flow-is unique in the class of our new varifold solutions. This is in sharp contrast to the case of Brakke flows, which a priori may disappear at any given time and are therefore fatally non-unique. Finally, we propose an extension of the solution concept to the multi-phase case which is at least guaranteed to satisfy a weak-strong uniqueness principle."}],"language":[{"iso":"eng"}],"acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819), and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813. The content of this paper was developed and parts of it were written during a visit of the first author to the Hausdorff Center of Mathematics (HCM), University of Bonn. The hospitality and the support of HCM are gratefully acknowledged.","status":"public","intvolume":" 130","publication_status":"published","year":"2025","title":"A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness","author":[{"full_name":"Hensel, Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","last_name":"Hensel","orcid":"0000-0001-7252-8072","first_name":"Sebastian"},{"last_name":"Laux","first_name":"Tim","full_name":"Laux, Tim"}],"date_published":"2025-05-01T00:00:00Z","citation":{"ama":"Hensel S, Laux T. A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness. Journal of Differential Geometry. 2025;130:209-268. doi:10.4310/jdg/1747065796","ieee":"S. Hensel and T. Laux, “A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness,” Journal of Differential Geometry, vol. 130. International Press of Boston, pp. 209–268, 2025.","apa":"Hensel, S., & Laux, T. (2025). A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness. Journal of Differential Geometry. International Press of Boston. https://doi.org/10.4310/jdg/1747065796","mla":"Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for Mean Curvature Flow: Convergence of the Allen-Cahn Equation and Weak-Strong Uniqueness.” Journal of Differential Geometry, vol. 130, International Press of Boston, 2025, pp. 209–68, doi:10.4310/jdg/1747065796.","ista":"Hensel S, Laux T. 2025. A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness. Journal of Differential Geometry. 130, 209–268.","chicago":"Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for Mean Curvature Flow: Convergence of the Allen-Cahn Equation and Weak-Strong Uniqueness.” Journal of Differential Geometry. International Press of Boston, 2025. https://doi.org/10.4310/jdg/1747065796.","short":"S. Hensel, T. Laux, Journal of Differential Geometry 130 (2025) 209–268."},"fulldoi":"https://doi.org/10.4310/jdg/1747065796","publication_identifier":{"issn":["0022-040X"],"eissn":["1945-743X"]},"main_file_link":[{"url":"https://arxiv.org/abs/2109.04233","open_access":"1"}],"scopus_import":"1","oa":1,"OA_place":"repository","OA_type":"green","article_type":"original","day":"01","month":"05","oa_version":"Preprint","arxiv":1,"corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-07-06T13:37:21Z","doi":"10.4310/jdg/1747065796","date_created":"2021-09-13T12:17:10Z","ec_funded":1,"department":[{"_id":"JuFi"}],"type":"journal_article","page":"209-268","project":[{"call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819","name":"Bridging Scales in Random Materials"}]},{"abstract":[{"lang":"eng","text":"We show that Laplace isospectral deformations within a conformal class of generic Liouville metrics on the two-dimensional torus that are linear in the deformation parameter are necessarily trivial. Two of the main ingredients in our proof are a noncancellation result for the wave trace and an analysis of the second order variational formula for the energy functional associated to closed geodesics. Noncancellation allows us to detect parts of the length spectrum from the Laplace spectrum and conclude rational integrability for the deformed geodesic flow (Liouville metrics are folklorically conjectured to be the only Riemannian metrics with integrable geodesic flow on the torus). We then use the second variational formula to show how the preservation of a single rational torus is sufficient to conclude triviality of the deformation, assuming linearity. We also present some evidence that our hypothesis of linearity may indeed be necessary."}],"language":[{"iso":"eng"}],"status":"public","publication":"arXiv","article_processing_charge":"No","_id":"22340","keyword":["Differential Geometry (math.DG)","Mathematical Physics (math-ph)","Dynamical Systems (math.DS)","Spectral Theory (math.SP)","FOS: Mathematics","FOS: Mathematics","FOS: Physical sciences","FOS: Physical sciences","58J42","37J35","37J35","35P20","58J40","58J50","37D40"],"external_id":{"arxiv":["2511.10398"]},"date_published":"2025-11-13T00:00:00Z","author":[{"last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim","orcid":"0000-0002-6051-2628"},{"last_name":"Li","first_name":"Yunzhe","full_name":"Li, Yunzhe","id":"41cb05d3-f128-11eb-9611-e4e2b3cfba31"},{"full_name":"Vig, Amir","id":"49d58dd5-45f5-11ec-9f86-8ce1276989b9","first_name":"Amir","last_name":"Vig"}],"title":"Spectral rigidity of Liouville tori","year":"2025","publication_status":"draft","day":"13","OA_type":"green","OA_place":"repository","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2511.10398"}],"oa":1,"fulldoi":"https://doi.org/10.48550/ARXIV.2511.10398","citation":{"ista":"Henheik SJ, Kaloshin V, Li Y, Vig A. Spectral rigidity of Liouville tori. arXiv, 10.48550/ARXIV.2511.10398.","chicago":"Henheik, Sven Joscha, Vadim Kaloshin, Yunzhe Li, and Amir Vig. “Spectral Rigidity of Liouville Tori.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2511.10398.","short":"S.J. Henheik, V. Kaloshin, Y. Li, A. Vig, ArXiv (n.d.).","ama":"Henheik SJ, Kaloshin V, Li Y, Vig A. Spectral rigidity of Liouville tori. arXiv. doi:10.48550/ARXIV.2511.10398","apa":"Henheik, S. J., Kaloshin, V., Li, Y., & Vig, A. (n.d.). Spectral rigidity of Liouville tori. arXiv. https://doi.org/10.48550/ARXIV.2511.10398","ieee":"S. J. Henheik, V. Kaloshin, Y. Li, and A. Vig, “Spectral rigidity of Liouville tori,” arXiv. .","mla":"Henheik, Sven Joscha, et al. “Spectral Rigidity of Liouville Tori.” ArXiv, doi:10.48550/ARXIV.2511.10398."},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"related_material":{"record":[{"id":"22255","relation":"dissertation_contains","status":"public"}]},"type":"preprint","department":[{"_id":"VaKa"},{"_id":"LaEr"}],"doi":"10.48550/ARXIV.2511.10398","date_updated":"2026-07-20T14:58:23Z","date_created":"2026-07-14T12:51:50Z","oa_version":"Preprint","arxiv":1,"corr_author":"1","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","month":"11"},{"file_date_updated":"2024-07-17T09:29:13Z","file":[{"date_created":"2024-07-05T12:05:17Z","date_updated":"2024-07-05T12:05:17Z","relation":"main_file","file_id":"17204","file_name":"sif-final.pdf","file_size":7225150,"checksum":"0dc9f5a6422b8a49a79026900f349ee5","creator":"chafner","content_type":"application/pdf","success":1,"access_level":"open_access"},{"relation":"supplementary_material","date_updated":"2024-07-05T12:06:03Z","date_created":"2024-07-05T12:06:03Z","file_size":397262,"file_name":"sif-supp-final.pdf","file_id":"17205","checksum":"cde433c6a40688d5f1187fb5721f6f94","content_type":"application/pdf","creator":"chafner","access_level":"open_access"},{"creator":"chafner","content_type":"video/mp4","checksum":"c0457a09c2ab9a1c2935c995dcc84907","file_id":"17276","file_name":"sif-video-final.mp4","file_size":170001305,"date_created":"2024-07-17T09:29:13Z","date_updated":"2024-07-17T09:29:13Z","relation":"supplementary_material","access_level":"open_access","title":"Submission Video"}],"day":"01","article_type":"original","oa":1,"scopus_import":"1","fulldoi":"https://doi.org/10.1145/3658194","publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"citation":{"ama":"Hafner C, Ly M, Wojtan C. Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments. Transactions on Graphics. 2024;43(4). doi:10.1145/3658194","ieee":"C. Hafner, M. Ly, and C. Wojtan, “Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments,” Transactions on Graphics, vol. 43, no. 4. Association for Computing Machinery, 2024.","mla":"Hafner, Christian, et al. “Spin-It Faster: Quadrics Solve All Topology Optimization Problems That Depend Only on Mass Moments.” Transactions on Graphics, vol. 43, no. 4, 78, Association for Computing Machinery, 2024, doi:10.1145/3658194.","apa":"Hafner, C., Ly, M., & Wojtan, C. (2024). Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments. Transactions on Graphics. Denver, Colorado: Association for Computing Machinery. https://doi.org/10.1145/3658194","ista":"Hafner C, Ly M, Wojtan C. 2024. Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments. Transactions on Graphics. 43(4), 78.","chicago":"Hafner, Christian, Mickaël Ly, and Chris Wojtan. “Spin-It Faster: Quadrics Solve All Topology Optimization Problems That Depend Only on Mass Moments.” Transactions on Graphics. Association for Computing Machinery, 2024. https://doi.org/10.1145/3658194.","short":"C. Hafner, M. Ly, C. Wojtan, Transactions on Graphics 43 (2024)."},"project":[{"grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"type":"journal_article","department":[{"_id":"ChWo"}],"doi":"10.1145/3658194","date_updated":"2025-09-08T08:29:09Z","date_created":"2024-07-05T12:08:57Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1","conference":{"start_date":"2024-07-28","location":"Denver, Colorado","end_date":"2024-08-01"},"ddc":["516"],"oa_version":"Published Version","month":"07","intvolume":" 43","language":[{"iso":"eng"}],"status":"public","acknowledgement":"We thank Gianmarco Cherchi for his help in tailoring the Mesh Booleans code for this project, Stefan Jeschke for his help with the photographs, Malina Strugaru and Aleksei Kalinov for their help with the samples, and the anonymous reviewers as well as the members of the ISTA Visual Computing Group for their feedback. This project was funded in part by the European Research Council (ERC Consolidator Grant 101045083 CoDiNA).","abstract":[{"text":"The behavior of a rigid body primarily depends on its mass moments, which consist of the mass, center of mass, and moments of inertia. It is possible to manipulate these quantities without altering the geometric appearance of an object by introducing cavities in its interior. Algorithms that find cavities of suitable shapes and sizes have enabled the computational design of spinning tops, yo-yos, wheels, buoys, and statically balanced objects. Previous work is based, for example, on topology optimization on voxel grids, which introduces a large number of optimization variables and box constraints, or offset surface computation, which cannot guarantee that solutions to a feasible problem will always be found.\r\n\r\nIn this work, we provide a mathematical analysis of constrained topology optimization problems that depend only on mass moments. This class of problems covers, among others, all applications mentioned above. Our main result is to show that no matter the outer shape of the rigid body to be optimized or the optimization objective and constraints considered, the optimal solution always features a quadric-shaped interface between material and cavities. This proves that optimal interfaces are always ellipsoids, hyperboloids, paraboloids, or one of a few degenerate cases, such as planes.\r\n\r\nThis insight lets us replace a difficult topology optimization problem with a provably equivalent non-linear equation system in a small number (<10) of variables, which represent the coefficients of the quadric. This system can be solved in a few seconds for most examples, provides insights into the geometric structure of many specific applications, and lets us describe their solution properties. Finally, our method integrates seamlessly into modern fabrication workflows because our solutions are analytical surfaces that are native to the CAD domain.","lang":"eng"}],"publication":"Transactions on Graphics","volume":43,"publisher":"Association for Computing Machinery","article_processing_charge":"Yes (via OA deal)","_id":"17203","quality_controlled":"1","keyword":["Topology Optimization","Mass Moments","Computational Geometry"],"external_id":{"isi":["001289270900045"]},"article_number":"78","issue":"4","date_published":"2024-07-01T00:00:00Z","author":[{"last_name":"Hafner","first_name":"Christian","full_name":"Hafner, Christian","id":"400429CC-F248-11E8-B48F-1D18A9856A87"},{"id":"6340d7f0-b48d-11eb-b10d-b7487e71d9f1","full_name":"Ly, Mickaël","last_name":"Ly","first_name":"Mickaël"},{"last_name":"Wojtan","first_name":"Christopher J","orcid":"0000-0001-6646-5546","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87"}],"title":"Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments","isi":1,"year":"2024","has_accepted_license":"1","publication_status":"published"},{"month":"10","ddc":["516"],"oa_version":"Published Version","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","corr_author":"1","date_created":"2024-10-19T12:00:37Z","date_updated":"2026-04-07T12:42:44Z","doi":"10.15479/at:ista:18443","department":[{"_id":"GradSch"},{"_id":"TaHa"}],"type":"dissertation","page":"178","project":[{"name":"Branes on hyperkähler manifolds","grant_number":"26069","_id":"6286e8c4-2b32-11ec-9570-f5297902f67f"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"supervisor":[{"last_name":"Hausel","first_name":"Tamás","orcid":"0000-0002-9582-2634","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Hausel, Tamás"}],"fulldoi":"https://doi.org/10.15479/at:ista:18443","citation":{"short":"M.A. Sisak, T-Dual Branes on Hyperkähler Manifolds, Institute of Science and Technology Austria, 2024.","chicago":"Sisak, Maria A. “T-Dual Branes on Hyperkähler Manifolds.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18443.","ista":"Sisak MA. 2024. T-dual branes on hyperkähler manifolds. Institute of Science and Technology Austria.","apa":"Sisak, M. A. (2024). T-dual branes on hyperkähler manifolds. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18443","ieee":"M. A. Sisak, “T-dual branes on hyperkähler manifolds,” Institute of Science and Technology Austria, 2024.","mla":"Sisak, Maria A. T-Dual Branes on Hyperkähler Manifolds. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18443.","ama":"Sisak MA. T-dual branes on hyperkähler manifolds. 2024. doi:10.15479/at:ista:18443"},"publication_identifier":{"issn":["2663-337X"]},"oa":1,"OA_place":"publisher","OA_type":"free access","day":"24","file":[{"content_type":"application/pdf","creator":"msisak","checksum":"8c4893e726aaa4b3efb82758da9b6851","file_name":"MASisak_dissertation.pdf","file_size":1672547,"file_id":"18467","date_created":"2024-10-23T14:42:45Z","date_updated":"2024-10-23T14:42:45Z","relation":"main_file","access_level":"open_access","success":1},{"date_created":"2024-10-23T14:43:56Z","relation":"source_file","date_updated":"2024-10-24T08:09:13Z","file_id":"18468","file_size":617913,"file_name":"MASisak_source.zip","checksum":"1831b072e861a1e5481024ca9d02b036","creator":"msisak","content_type":"application/x-zip-compressed","access_level":"closed"}],"file_date_updated":"2024-10-24T08:09:13Z","publication_status":"published","has_accepted_license":"1","year":"2024","author":[{"full_name":"Sisak, Maria A","id":"44A03D04-AEA4-11E9-B225-EA2DE6697425","last_name":"Sisak","first_name":"Maria A"}],"title":"T-dual branes on hyperkähler manifolds","date_published":"2024-10-24T00:00:00Z","degree_awarded":"PhD","alternative_title":["ISTA Thesis"],"keyword":["hyperkaehler geometry","branes","mirror symmetry","T-duality"],"_id":"18443","publisher":"Institute of Science and Technology Austria","article_processing_charge":"No","abstract":[{"lang":"eng","text":"In [KW06] Kapustin and Witten conjectured that there is a mirror symmetry relation between\r\nthe hyperkähler structures on certain Higgs bundle moduli spaces. As a consequence, they\r\nconjecture an equivalence between categories of BBB and BAA-branes. At the classical\r\nlevel, this mirror symmetry is given by T-duality between semi-flat hyperkähler structures on\r\nalgebraic integrable systems.\r\nIn this thesis, we investigate the T-duality relation between hyperkähler structures and the\r\ncorresponding branes on affine torus bundles. We use the techniques of generalized geometry\r\nto show that semi-flat hyperkähler structures are T-dual on algebraic integrable systems.\r\nWe also describe T-duality for generalized branes. Motivated by Fourier-Mukai transform\r\nwe upgrade the T-duality between generalized branes to T-duality of submanifolds endowed\r\nwith U(1)-bundles and connections. This T-duality in the appropriate context specializes to\r\nT-duality between BBB and BAA-branes.\r\n"}],"language":[{"iso":"eng"}],"status":"public"},{"date_published":"2023-01-01T00:00:00Z","author":[{"first_name":"Jean-Daniel","last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel"},{"last_name":"Dyer","first_name":"Ramsay","full_name":"Dyer, Ramsay"},{"full_name":"Ghosh, Arijit","last_name":"Ghosh","first_name":"Arijit"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs","first_name":"Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken"}],"title":"Local criteria for triangulating general manifolds","isi":1,"year":"2023","has_accepted_license":"1","publication_status":"published","acknowledgement":"This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). Arijit Ghosh is supported by Ramanujan Fellowship (No. SB/S2/RJN-064/2015). Part of this work was done when Arijit Ghosh was a Researcher at Max-Planck-Institute for Informatics, Germany, supported by the IndoGerman Max Planck Center for Computer Science (IMPECS). Mathijs Wintraecken also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Austrian Science Fund (FWF): M-3073. A part of the results described in this paper were presented at SoCG 2018 and in [3]. \r\nOpen access funding provided by the Austrian Science Fund (FWF).","language":[{"iso":"eng"}],"intvolume":" 69","status":"public","abstract":[{"text":"We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use.","lang":"eng"}],"publication":"Discrete & Computational Geometry","volume":69,"publisher":"Springer Nature","article_processing_charge":"No","_id":"12287","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"quality_controlled":"1","external_id":{"isi":["000862193600001"]},"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","grant_number":"M03073","name":"Learning and triangulating manifolds via collapses"}],"page":"156-191","type":"journal_article","department":[{"_id":"HeEd"}],"ec_funded":1,"doi":"10.1007/s00454-022-00431-7","date_created":"2023-01-16T10:04:06Z","date_updated":"2025-04-14T07:44:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","corr_author":"1","oa_version":"Published Version","ddc":["510"],"month":"01","file_date_updated":"2023-02-02T11:01:10Z","file":[{"success":1,"access_level":"open_access","file_id":"12488","file_size":582850,"file_name":"2023_DiscreteCompGeometry_Boissonnat.pdf","relation":"main_file","date_created":"2023-02-02T11:01:10Z","date_updated":"2023-02-02T11:01:10Z","creator":"dernst","content_type":"application/pdf","checksum":"46352e0ee71e460848f88685ca852681"}],"day":"01","article_type":"original","scopus_import":"1","oa":1,"fulldoi":"https://doi.org/10.1007/s00454-022-00431-7","citation":{"apa":"Boissonnat, J.-D., Dyer, R., Ghosh, A., & Wintraecken, M. (2023). Local criteria for triangulating general manifolds. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00431-7","mla":"Boissonnat, Jean-Daniel, et al. “Local Criteria for Triangulating General Manifolds.” Discrete & Computational Geometry, vol. 69, Springer Nature, 2023, pp. 156–91, doi:10.1007/s00454-022-00431-7.","ieee":"J.-D. Boissonnat, R. Dyer, A. Ghosh, and M. Wintraecken, “Local criteria for triangulating general manifolds,” Discrete & Computational Geometry, vol. 69. Springer Nature, pp. 156–191, 2023.","ama":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. Local criteria for triangulating general manifolds. Discrete & Computational Geometry. 2023;69:156-191. doi:10.1007/s00454-022-00431-7","short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, M. Wintraecken, Discrete & Computational Geometry 69 (2023) 156–191.","chicago":"Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, and Mathijs Wintraecken. “Local Criteria for Triangulating General Manifolds.” Discrete & Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-022-00431-7.","ista":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. 2023. Local criteria for triangulating general manifolds. Discrete & Computational Geometry. 69, 156–191."},"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"}},{"date_published":"2023-07-26T00:00:00Z","title":"On the global minimum of the energy–momentum relation for the polaron","author":[{"last_name":"Lampart","first_name":"Jonas","full_name":"Lampart, Jonas"},{"first_name":"David Johannes","last_name":"Mitrouskas","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","full_name":"Mitrouskas, David Johannes"},{"full_name":"Mysliwy, Krzysztof","id":"316457FC-F248-11E8-B48F-1D18A9856A87","last_name":"Mysliwy","first_name":"Krzysztof"}],"isi":1,"year":"2023","has_accepted_license":"1","publication_status":"published","intvolume":" 26","status":"public","acknowledgement":"D.M. and K.M. thank Robert Seiringer for helpful discussions. Open access funding provided by Institute of Science and Technology (IST Austria). Financial support from the Agence Nationale de la Recherche (ANR) through the projects ANR-17-CE40-0016, ANR-17-CE40-0007-01, ANR-17-EURE-0002 (J.L.) and from the European Union’s Horizon 2020 research and innovation programme under the Maria Skłodowska-Curie grant agreement No. 665386 (K.M.) is gratefully acknowledged.","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the translation invariant Fröhlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling."}],"publication":"Mathematical Physics, Analysis and Geometry","volume":26,"article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","_id":"14192","quality_controlled":"1","keyword":["Geometry and Topology","Mathematical Physics"],"external_id":{"arxiv":["2206.14708"],"isi":["001032992600001"]},"article_number":"17","issue":"3","type":"journal_article","department":[{"_id":"RoSe"}],"date_updated":"2024-10-09T21:06:41Z","date_created":"2023-08-22T14:09:47Z","doi":"10.1007/s11040-023-09460-x","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","arxiv":1,"ddc":["510"],"oa_version":"Published Version","month":"07","file_date_updated":"2023-08-23T10:59:15Z","file":[{"success":1,"access_level":"open_access","relation":"main_file","date_created":"2023-08-23T10:59:15Z","date_updated":"2023-08-23T10:59:15Z","file_size":317026,"file_name":"2023_MathPhysics_Lampart.pdf","file_id":"14225","checksum":"f0941cc66cb3ed06a12ca4b7e356cfd6","content_type":"application/pdf","creator":"dernst"}],"day":"26","article_type":"original","scopus_import":"1","oa":1,"fulldoi":"https://doi.org/10.1007/s11040-023-09460-x","citation":{"ieee":"J. Lampart, D. J. Mitrouskas, and K. Mysliwy, “On the global minimum of the energy–momentum relation for the polaron,” Mathematical Physics, Analysis and Geometry, vol. 26, no. 3. Springer Nature, 2023.","mla":"Lampart, Jonas, et al. “On the Global Minimum of the Energy–Momentum Relation for the Polaron.” Mathematical Physics, Analysis and Geometry, vol. 26, no. 3, 17, Springer Nature, 2023, doi:10.1007/s11040-023-09460-x.","apa":"Lampart, J., Mitrouskas, D. J., & Mysliwy, K. (2023). On the global minimum of the energy–momentum relation for the polaron. Mathematical Physics, Analysis and Geometry. Springer Nature. https://doi.org/10.1007/s11040-023-09460-x","ama":"Lampart J, Mitrouskas DJ, Mysliwy K. On the global minimum of the energy–momentum relation for the polaron. Mathematical Physics, Analysis and Geometry. 2023;26(3). doi:10.1007/s11040-023-09460-x","chicago":"Lampart, Jonas, David Johannes Mitrouskas, and Krzysztof Mysliwy. “On the Global Minimum of the Energy–Momentum Relation for the Polaron.” Mathematical Physics, Analysis and Geometry. Springer Nature, 2023. https://doi.org/10.1007/s11040-023-09460-x.","ista":"Lampart J, Mitrouskas DJ, Mysliwy K. 2023. On the global minimum of the energy–momentum relation for the polaron. Mathematical Physics, Analysis and Geometry. 26(3), 17.","short":"J. Lampart, D.J. Mitrouskas, K. Mysliwy, Mathematical Physics, Analysis and Geometry 26 (2023)."},"publication_identifier":{"eissn":["1572-9656"],"issn":["1385-0172"]},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"}},{"date_updated":"2025-09-09T13:16:15Z","doi":"10.1017/fmp.2023.17","date_created":"2023-11-07T09:02:48Z","month":"08","ddc":["510"],"oa_version":"Published Version","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1","arxiv":1,"project":[{"_id":"bd95085b-d553-11ed-ba76-e55d3349be45","grant_number":"101076777","name":"Randomness and structure in combinatorics"}],"department":[{"_id":"MaKw"}],"type":"journal_article","oa":1,"scopus_import":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"ama":"Kwan MA, Sah A, Sauermann L, Sawhney M. Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. Forum of Mathematics, Pi. 2023;11. doi:10.1017/fmp.2023.17","ieee":"M. A. Kwan, A. Sah, L. Sauermann, and M. Sawhney, “Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture,” Forum of Mathematics, Pi, vol. 11. Cambridge University Press, 2023.","mla":"Kwan, Matthew Alan, et al. “Anticoncentration in Ramsey Graphs and a Proof of the Erdős–McKay Conjecture.” Forum of Mathematics, Pi, vol. 11, e21, Cambridge University Press, 2023, doi:10.1017/fmp.2023.17.","apa":"Kwan, M. A., Sah, A., Sauermann, L., & Sawhney, M. (2023). Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. Forum of Mathematics, Pi. Cambridge University Press. https://doi.org/10.1017/fmp.2023.17","ista":"Kwan MA, Sah A, Sauermann L, Sawhney M. 2023. Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. Forum of Mathematics, Pi. 11, e21.","chicago":"Kwan, Matthew Alan, Ashwin Sah, Lisa Sauermann, and Mehtaab Sawhney. “Anticoncentration in Ramsey Graphs and a Proof of the Erdős–McKay Conjecture.” Forum of Mathematics, Pi. Cambridge University Press, 2023. https://doi.org/10.1017/fmp.2023.17.","short":"M.A. Kwan, A. Sah, L. Sauermann, M. Sawhney, Forum of Mathematics, Pi 11 (2023)."},"fulldoi":"https://doi.org/10.1017/fmp.2023.17","publication_identifier":{"issn":["2050-5086"]},"file":[{"file_name":"2023_ForumMathematics_Kwan.pdf","file_size":1218719,"file_id":"14500","date_created":"2023-11-07T09:16:23Z","relation":"main_file","date_updated":"2023-11-07T09:16:23Z","content_type":"application/pdf","creator":"dernst","checksum":"54b824098d59073cc87a308d458b0a3e","success":1,"access_level":"open_access"}],"file_date_updated":"2023-11-07T09:16:23Z","article_type":"original","day":"24","isi":1,"publication_status":"published","has_accepted_license":"1","year":"2023","date_published":"2023-08-24T00:00:00Z","author":[{"orcid":"0000-0002-4003-7567","first_name":"Matthew Alan","last_name":"Kwan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan"},{"full_name":"Sah, Ashwin","first_name":"Ashwin","last_name":"Sah"},{"first_name":"Lisa","last_name":"Sauermann","full_name":"Sauermann, Lisa"},{"first_name":"Mehtaab","last_name":"Sawhney","full_name":"Sawhney, Mehtaab"}],"title":"Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture","_id":"14499","publisher":"Cambridge University Press","article_processing_charge":"Yes","article_number":"e21","external_id":{"isi":["001123866200001"],"arxiv":["2208.02874"]},"keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Analysis"],"quality_controlled":"1","abstract":[{"text":"An n-vertex graph is called C-Ramsey if it has no clique or independent set of size Clog2n (i.e., if it has near-optimal Ramsey behavior). In this paper, we study edge statistics in Ramsey graphs, in particular obtaining very precise control of the distribution of the number of edges in a random vertex subset of a C-Ramsey graph. This brings together two ongoing lines of research: the study of ‘random-like’ properties of Ramsey graphs and the study of small-ball probability for low-degree polynomials of independent random variables.\r\n\r\nThe proof proceeds via an ‘additive structure’ dichotomy on the degree sequence and involves a wide range of different tools from Fourier analysis, random matrix theory, the theory of Boolean functions, probabilistic combinatorics and low-rank approximation. In particular, a key ingredient is a new sharpened version of the quadratic Carbery–Wright theorem on small-ball probability for polynomials of Gaussians, which we believe is of independent interest. One of the consequences of our result is the resolution of an old conjecture of Erdős and McKay, for which Erdős reiterated in several of his open problem collections and for which he offered one of his notorious monetary prizes.","lang":"eng"}],"intvolume":" 11","acknowledgement":"Kwan was supported for part of this work by ERC Starting Grant ‘RANDSTRUCT’ No. 101076777. Sah and Sawhney were supported by NSF Graduate Research Fellowship Program DGE-2141064. Sah was supported by the PD Soros Fellowship. Sauermann was supported by NSF Award DMS-2100157, and for part of this work by a Sloan Research Fellowship.","status":"public","language":[{"iso":"eng"}],"volume":11,"publication":"Forum of Mathematics, Pi"},{"publication_status":"published","year":"2023","has_accepted_license":"1","isi":1,"title":"Fully extended r-spin TQFTs","author":[{"full_name":"Carqueville, Nils","first_name":"Nils","last_name":"Carqueville"},{"id":"7943226E-220E-11EA-94C7-D59F3DDC885E","full_name":"Szegedy, Lorant","last_name":"Szegedy","orcid":"0000-0003-2834-5054","first_name":"Lorant"}],"date_published":"2023-10-16T00:00:00Z","external_id":{"isi":["001104620800003"]},"issue":"3","das_tickbox":"1","keyword":["Geometry and Topology","Mathematical Physics"],"quality_controlled":"1","_id":"14756","publisher":"EMS Press","article_processing_charge":"Yes","publication":"Quantum Topology","volume":14,"acknowledgement":"N.C. is supported by the DFG Heisenberg Programme.\r\nWe are grateful to Tobias Dyckerhoff, Lukas Müller, Ingo Runkel, and Christopher Schommer-Pries for helpful discussions.","status":"public","intvolume":" 14","language":[{"iso":"eng"}],"abstract":[{"text":"We prove the r-spin cobordism hypothesis in the setting of (weak) 2-categories for every positive integer r: the 2-groupoid of 2-dimensional fully extended r-spin TQFTs with given target is equivalent to the homotopy fixed points of an induced Spin 2r -action. In particular, such TQFTs are classified by fully dualisable objects together with a trivialisation of the rth power of their Serre automorphisms. For r=1, we recover the oriented case (on which our proof builds), while ordinary spin structures correspond to r=2.\r\nTo construct examples, we explicitly describe Spin 2r-homotopy fixed points in the equivariant completion of any symmetric monoidal 2-category. We also show that every object in a 2-category of Landau–Ginzburg models gives rise to fully extended spin TQFTs and that half of these do not factor through the oriented bordism 2-category.","lang":"eng"}],"month":"10","corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["530"],"oa_version":"Published Version","date_updated":"2026-07-06T11:52:15Z","date_created":"2024-01-08T13:14:48Z","doi":"10.4171/qt/193","department":[{"_id":"MiLe"}],"type":"journal_article","page":"467-532","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"ieee":"N. Carqueville and L. Szegedy, “Fully extended r-spin TQFTs,” Quantum Topology, vol. 14, no. 3. EMS Press, pp. 467–532, 2023.","apa":"Carqueville, N., & Szegedy, L. (2023). Fully extended r-spin TQFTs. Quantum Topology. EMS Press. https://doi.org/10.4171/qt/193","mla":"Carqueville, Nils, and Lorant Szegedy. “Fully Extended R-Spin TQFTs.” Quantum Topology, vol. 14, no. 3, EMS Press, 2023, pp. 467–532, doi:10.4171/qt/193.","ama":"Carqueville N, Szegedy L. Fully extended r-spin TQFTs. Quantum Topology. 2023;14(3):467-532. doi:10.4171/qt/193","short":"N. Carqueville, L. Szegedy, Quantum Topology 14 (2023) 467–532.","chicago":"Carqueville, Nils, and Lorant Szegedy. “Fully Extended R-Spin TQFTs.” Quantum Topology. EMS Press, 2023. https://doi.org/10.4171/qt/193.","ista":"Carqueville N, Szegedy L. 2023. Fully extended r-spin TQFTs. Quantum Topology. 14(3), 467–532."},"fulldoi":"https://doi.org/10.4171/qt/193","publication_identifier":{"issn":["1663-487X"]},"scopus_import":"1","oa":1,"article_type":"original","day":"16","file":[{"access_level":"open_access","success":1,"content_type":"application/pdf","creator":"dernst","checksum":"b0590aff6e7ec89cc149ba94d459d3a3","file_name":"2023_QuantumTopol_Carqueville.pdf","file_size":707344,"file_id":"14764","date_created":"2024-01-09T09:25:34Z","date_updated":"2024-01-09T09:25:34Z","relation":"main_file"}],"file_date_updated":"2024-01-09T09:25:34Z"},{"status":"public","language":[{"iso":"eng"}],"acknowledgement":"We thank the reviewers for the valuable feedback. We also thank the Miba Machine Shop at ISTA, PCBWay, and PragoBoard for helping us with fabrication and assembly. This project was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 715767 – MATERIALIZABLE).","intvolume":" 42","abstract":[{"text":"We propose a computational design approach for covering a surface with individually addressable RGB LEDs, effectively forming a low-resolution surface screen. To achieve a low-cost and scalable approach, we propose creating designs from flat PCB panels bent in-place along the surface of a 3D printed core. Working with standard rigid PCBs enables the use of\r\nestablished PCB manufacturing services, allowing the fabrication of designs with several hundred LEDs. \r\nOur approach optimizes the PCB geometry for folding, and then jointly optimizes the LED packing, circuit and routing, solving a challenging layout problem under strict manufacturing requirements. Unlike paper, PCBs cannot bend beyond a certain point without breaking. Therefore, we introduce parametric cut patterns acting as hinges, designed to allow bending while remaining compact. To tackle the joint optimization of placement, circuit and routing, we propose a specialized algorithm that splits the global problem into one sub-problem per triangle, which is then individually solved.\r\nOur technique generates PCB blueprints in a completely automated way. After being fabricated by a PCB manufacturing service, the boards are bent and glued by the user onto the 3D printed support. We demonstrate our technique on a range of physical models and virtual examples, creating intricate surface light patterns from hundreds of LEDs.","lang":"eng"}],"publication":"Transactions on Graphics","volume":42,"publisher":"Association for Computing Machinery","article_processing_charge":"No","_id":"13049","keyword":["PCB design and layout","Mesh geometry models"],"quality_controlled":"1","external_id":{"isi":["001044671300108"]},"issue":"4","article_number":"142","date_published":"2023-07-26T00:00:00Z","title":"PCBend: Light up your 3D shapes with foldable circuit boards","author":[{"last_name":"Freire","first_name":"Marco","full_name":"Freire, Marco"},{"id":"FF8FA64C-AA6A-11E9-99AD-50D4E5697425","full_name":"Bhargava, Manas","last_name":"Bhargava","first_name":"Manas","orcid":"0009-0007-6138-6890"},{"last_name":"Schreck","first_name":"Camille","full_name":"Schreck, Camille","id":"2B14B676-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Pierre-Alexandre","last_name":"Hugron","full_name":"Hugron, Pierre-Alexandre"},{"last_name":"Bickel","first_name":"Bernd","orcid":"0000-0001-6511-9385","id":"49876194-F248-11E8-B48F-1D18A9856A87","full_name":"Bickel, Bernd"},{"last_name":"Lefebvre","first_name":"Sylvain","full_name":"Lefebvre, Sylvain"}],"isi":1,"year":"2023","has_accepted_license":"1","publication_status":"published","file_date_updated":"2023-06-20T12:20:51Z","file":[{"checksum":"a0b0ba3b36f43a94388e8824613d812a","content_type":"application/pdf","creator":"dernst","relation":"main_file","date_created":"2023-06-19T11:02:23Z","date_updated":"2023-06-19T11:02:23Z","file_size":78940724,"file_name":"2023_ACMToG_Freire.pdf","file_id":"13156","access_level":"open_access","success":1},{"success":1,"access_level":"open_access","file_id":"13157","file_size":34345905,"file_name":"2023_ACMToG_SuppMaterial_Freire.pdf","relation":"main_file","date_updated":"2023-06-20T12:20:51Z","date_created":"2023-06-20T12:20:51Z","creator":"dernst","content_type":"application/pdf","checksum":"b9206bbb67af82df49b7e7cdbde3410c"}],"day":"26","article_type":"original","oa":1,"scopus_import":"1","fulldoi":"https://doi.org/10.1145/3592411","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"citation":{"short":"M. Freire, M. Bhargava, C. Schreck, P.-A. Hugron, B. Bickel, S. Lefebvre, Transactions on Graphics 42 (2023).","ista":"Freire M, Bhargava M, Schreck C, Hugron P-A, Bickel B, Lefebvre S. 2023. PCBend: Light up your 3D shapes with foldable circuit boards. Transactions on Graphics. 42(4), 142.","chicago":"Freire, Marco, Manas Bhargava, Camille Schreck, Pierre-Alexandre Hugron, Bernd Bickel, and Sylvain Lefebvre. “PCBend: Light up Your 3D Shapes with Foldable Circuit Boards.” Transactions on Graphics. Association for Computing Machinery, 2023. https://doi.org/10.1145/3592411.","ama":"Freire M, Bhargava M, Schreck C, Hugron P-A, Bickel B, Lefebvre S. PCBend: Light up your 3D shapes with foldable circuit boards. Transactions on Graphics. 2023;42(4). doi:10.1145/3592411","apa":"Freire, M., Bhargava, M., Schreck, C., Hugron, P.-A., Bickel, B., & Lefebvre, S. (2023). PCBend: Light up your 3D shapes with foldable circuit boards. Transactions on Graphics. Los Angeles, CA, United States: Association for Computing Machinery. https://doi.org/10.1145/3592411","ieee":"M. Freire, M. Bhargava, C. Schreck, P.-A. Hugron, B. Bickel, and S. Lefebvre, “PCBend: Light up your 3D shapes with foldable circuit boards,” Transactions on Graphics, vol. 42, no. 4. Association for Computing Machinery, 2023.","mla":"Freire, Marco, et al. “PCBend: Light up Your 3D Shapes with Foldable Circuit Boards.” Transactions on Graphics, vol. 42, no. 4, 142, Association for Computing Machinery, 2023, doi:10.1145/3592411."},"acknowledged_ssus":[{"_id":"M-Shop"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"name":"MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and Modeling","_id":"24F9549A-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"715767"}],"related_material":{"record":[{"id":"20276","status":"public","relation":"dissertation_contains"}]},"type":"journal_article","department":[{"_id":"GradSch"},{"_id":"BeBi"}],"ec_funded":1,"date_created":"2023-05-22T08:37:04Z","date_updated":"2026-07-29T13:03:30Z","doi":"10.1145/3592411","conference":{"location":"Los Angeles, CA, United States","end_date":"2023-08-10","name":"SIGGRAPH: Computer Graphics and Interactive Techniques Conference","start_date":"2023-08-06"},"corr_author":"1","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa_version":"Submitted Version","ddc":["006"],"month":"07"},{"project":[{"name":"MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and Modeling","_id":"24F9549A-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"715767"}],"related_material":{"record":[{"id":"12897","status":"public","relation":"part_of_dissertation"}]},"type":"journal_article","ec_funded":1,"department":[{"_id":"BeBi"}],"date_updated":"2026-09-12T22:30:07Z","date_created":"2023-07-04T07:41:30Z","doi":"10.1145/3606033","ddc":["516"],"oa_version":"Submitted Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","month":"09","file_date_updated":"2023-07-04T08:11:28Z","file":[{"access_level":"open_access","success":1,"creator":"chafner","content_type":"application/pdf","checksum":"4954c1cfa487725bc156dcfec872478a","file_id":"13194","file_name":"kirchhoff-rods.pdf","file_size":19635168,"date_updated":"2023-07-04T08:11:28Z","relation":"main_file","date_created":"2023-07-04T08:11:28Z"},{"title":"Supplemental Material with Proofs","access_level":"open_access","file_name":"supp-main.pdf","file_size":420909,"file_id":"13190","date_updated":"2023-07-04T07:46:28Z","relation":"supplementary_material","date_created":"2023-07-04T07:46:28Z","content_type":"application/pdf","creator":"chafner","checksum":"79c9975fbc82ff71f1767331d2204cca"},{"creator":"chafner","content_type":"application/pdf","checksum":"4ab647e4f03c711e1e6a5fc1eb8684db","file_id":"13191","file_name":"supp-cheat.pdf","file_size":430086,"date_updated":"2023-07-04T07:46:30Z","relation":"supplementary_material","date_created":"2023-07-04T07:46:30Z","access_level":"open_access","title":"Cheat Sheet for Notation"},{"content_type":"video/mp4","creator":"chafner","checksum":"c0fd9a57d012046de90c185ffa904b76","file_size":268088064,"file_name":"kirchhoff-video-final.mp4","file_id":"13192","date_created":"2023-07-04T07:46:39Z","relation":"supplementary_material","date_updated":"2023-07-04T07:46:39Z","title":"Supplemental Video","access_level":"open_access"},{"access_level":"open_access","title":"Matlab Source Code with Example","file_id":"13193","file_name":"matlab-submission.zip","file_size":25790,"relation":"supplementary_material","date_created":"2023-07-04T07:47:10Z","date_updated":"2023-07-04T07:47:10Z","creator":"chafner","content_type":"application/x-zip-compressed","checksum":"71b00712b489ada2cd9815910ee180a9"}],"day":"20","article_type":"original","oa":1,"scopus_import":"1","fulldoi":"https://doi.org/10.1145/3606033","acknowledged_ssus":[{"_id":"M-Shop"}],"citation":{"ista":"Hafner C, Bickel B. 2023. The design space of Kirchhoff rods. ACM Transactions on Graphics. 42(5), 171.","chicago":"Hafner, Christian, and Bernd Bickel. “The Design Space of Kirchhoff Rods.” ACM Transactions on Graphics. Association for Computing Machinery, 2023. https://doi.org/10.1145/3606033.","short":"C. Hafner, B. Bickel, ACM Transactions on Graphics 42 (2023).","ama":"Hafner C, Bickel B. The design space of Kirchhoff rods. ACM Transactions on Graphics. 2023;42(5). doi:10.1145/3606033","mla":"Hafner, Christian, and Bernd Bickel. “The Design Space of Kirchhoff Rods.” ACM Transactions on Graphics, vol. 42, no. 5, 171, Association for Computing Machinery, 2023, doi:10.1145/3606033.","apa":"Hafner, C., & Bickel, B. (2023). The design space of Kirchhoff rods. ACM Transactions on Graphics. Association for Computing Machinery. https://doi.org/10.1145/3606033","ieee":"C. Hafner and B. Bickel, “The design space of Kirchhoff rods,” ACM Transactions on Graphics, vol. 42, no. 5. Association for Computing Machinery, 2023."},"publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"date_published":"2023-09-20T00:00:00Z","author":[{"full_name":"Hafner, Christian","id":"400429CC-F248-11E8-B48F-1D18A9856A87","first_name":"Christian","last_name":"Hafner"},{"full_name":"Bickel, Bernd","id":"49876194-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6511-9385","first_name":"Bernd","last_name":"Bickel"}],"title":"The design space of Kirchhoff rods","isi":1,"has_accepted_license":"1","year":"2023","publication_status":"published","abstract":[{"text":"The Kirchhoff rod model describes the bending and twisting of slender elastic rods in three dimensions, and has been widely studied to enable the prediction of how a rod will deform, given its geometry and boundary conditions. In this work, we study a number of inverse problems with the goal of computing the geometry of a straight rod that will automatically deform to match a curved target shape after attaching its endpoints to a support structure. Our solution lets us finely control the static equilibrium state of a rod by varying the cross-sectional profiles along its length.\r\nWe also show that the set of physically realizable equilibrium states admits a concise geometric description in terms of linear line complexes, which leads to very efficient computational design algorithms. Implemented in an interactive software tool, they allow us to convert three-dimensional hand-drawn spline curves to elastic rods, and give feedback about the feasibility and practicality of a design in real time. We demonstrate the efficacy of our method by designing and manufacturing several physical prototypes with applications to interior design and soft robotics.","lang":"eng"}],"status":"public","language":[{"iso":"eng"}],"acknowledgement":"We thank the anonymous reviewers for their generous feedback, and Julian Fischer for his help in proving Proposition 1. 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. 715767).","intvolume":" 42","volume":42,"publication":"ACM Transactions on Graphics","publisher":"Association for Computing Machinery","article_processing_charge":"No","_id":"13188","quality_controlled":"1","keyword":["Computer Graphics","Computational Design","Computational Geometry","Shape Modeling"],"issue":"5","article_number":"171","external_id":{"isi":["001086833300010"]}},{"title":"Connectivity of triangulation flip graphs in the plane","author":[{"full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","orcid":"0000-0002-1494-0568","last_name":"Wagner"},{"last_name":"Welzl","first_name":"Emo","full_name":"Welzl, Emo"}],"date_published":"2022-11-14T00:00:00Z","publication_status":"published","year":"2022","has_accepted_license":"1","isi":1,"publication":"Discrete & Computational Geometry","volume":68,"status":"public","intvolume":" 68","acknowledgement":"This is a full and revised version of [38] (on partial triangulations) in Proceedings of the 36th Annual International Symposium on Computational Geometry (SoCG‘20) and of some of the results in [37] (on full triangulations) in Proceedings of the 31st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA‘20).\r\nThis research started at the 11th Gremo’s Workshop on Open Problems (GWOP), Alp Sellamatt, Switzerland, June 24–28, 2013, motivated by a question posed by Filip Mori´c on full triangulations. Research was supported by the Swiss National Science Foundation within the collaborative DACH project Arrangements and Drawings as SNSF Project 200021E-171681, and by IST Austria and Berlin Free University during a sabbatical stay of the second author. We thank Michael Joswig, Jesús De Loera, and Francisco Santos for helpful discussions on the topics of this paper, and Daniel Bertschinger and Valentin Stoppiello for carefully reading earlier versions and for many helpful comments.\r\nOpen access funding provided by the Swiss Federal Institute of Technology Zürich","language":[{"iso":"eng"}],"abstract":[{"text":"Given a finite point set P in general position in the plane, a full triangulation of P is a maximal straight-line embedded plane graph on P. A partial triangulation of P is a full triangulation of some subset P′ of P containing all extreme points in P. A bistellar flip on a partial triangulation either flips an edge (called edge flip), removes a non-extreme point of degree 3, or adds a point in P∖P′ as vertex of degree 3. The bistellar flip graph has all partial triangulations as vertices, and a pair of partial triangulations is adjacent if they can be obtained from one another by a bistellar flip. The edge flip graph is defined with full triangulations as vertices, and edge flips determining the adjacencies. Lawson showed in the early seventies that these graphs are connected. The goal of this paper is to investigate the structure of these graphs, with emphasis on their vertex connectivity. For sets P of n points in the plane in general position, we show that the edge flip graph is ⌈n/2−2⌉-vertex connected, and the bistellar flip graph is (n−3)-vertex connected; both results are tight. The latter bound matches the situation for the subfamily of regular triangulations (i.e., partial triangulations obtained by lifting the points to 3-space and projecting back the lower convex hull), where (n−3)-vertex connectivity has been known since the late eighties through the secondary polytope due to Gelfand, Kapranov, & Zelevinsky and Balinski’s Theorem. For the edge flip-graph, we additionally show that the vertex connectivity is at least as large as (and hence equal to) the minimum degree (i.e., the minimum number of flippable edges in any full triangulation), provided that n is large enough. Our methods also yield several other results: (i) The edge flip graph can be covered by graphs of polytopes of dimension ⌈n/2−2⌉ (products of associahedra) and the bistellar flip graph can be covered by graphs of polytopes of dimension n−3 (products of secondary polytopes). (ii) A partial triangulation is regular, if it has distance n−3 in the Hasse diagram of the partial order of partial subdivisions from the trivial subdivision. (iii) All partial triangulations of a point set are regular iff the partial order of partial subdivisions has height n−3. (iv) There are arbitrarily large sets P with non-regular partial triangulations and such that every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular triangulations.","lang":"eng"}],"external_id":{"isi":["000883222200003"]},"issue":"4","quality_controlled":"1","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"_id":"12129","article_processing_charge":"No","publisher":"Springer Nature","department":[{"_id":"UlWa"}],"type":"journal_article","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"7807"},{"relation":"earlier_version","status":"public","id":"7990"}]},"page":"1227-1284","month":"11","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","corr_author":"1","oa_version":"Published Version","ddc":["510"],"doi":"10.1007/s00454-022-00436-2","date_created":"2023-01-12T12:02:28Z","date_updated":"2025-07-10T11:54:56Z","article_type":"original","day":"14","file":[{"access_level":"open_access","success":1,"content_type":"application/pdf","creator":"dernst","checksum":"307e879d09e52eddf5b225d0aaa9213a","file_size":1747581,"file_name":"2022_DiscreteCompGeometry_Wagner.pdf","file_id":"12345","date_updated":"2023-01-23T11:10:03Z","relation":"main_file","date_created":"2023-01-23T11:10:03Z"}],"file_date_updated":"2023-01-23T11:10:03Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"fulldoi":"https://doi.org/10.1007/s00454-022-00436-2","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"citation":{"ieee":"U. Wagner and E. Welzl, “Connectivity of triangulation flip graphs in the plane,” Discrete & Computational Geometry, vol. 68, no. 4. Springer Nature, pp. 1227–1284, 2022.","mla":"Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane.” Discrete & Computational Geometry, vol. 68, no. 4, Springer Nature, 2022, pp. 1227–84, doi:10.1007/s00454-022-00436-2.","apa":"Wagner, U., & Welzl, E. (2022). Connectivity of triangulation flip graphs in the plane. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00436-2","ama":"Wagner U, Welzl E. Connectivity of triangulation flip graphs in the plane. Discrete & Computational Geometry. 2022;68(4):1227-1284. doi:10.1007/s00454-022-00436-2","chicago":"Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane.” Discrete & Computational Geometry. Springer Nature, 2022. https://doi.org/10.1007/s00454-022-00436-2.","ista":"Wagner U, Welzl E. 2022. Connectivity of triangulation flip graphs in the plane. Discrete & Computational Geometry. 68(4), 1227–1284.","short":"U. Wagner, E. Welzl, Discrete & Computational Geometry 68 (2022) 1227–1284."},"oa":1,"scopus_import":"1"},{"_id":"12148","article_processing_charge":"No","publisher":"Cambridge University Press","external_id":{"isi":["000873719200001"]},"article_number":"e96","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"quality_controlled":"1","status":"public","intvolume":" 10","language":[{"iso":"eng"}],"acknowledgement":"L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331. D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","abstract":[{"lang":"eng","text":"We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables."}],"publication":"Forum of Mathematics, Sigma","volume":10,"isi":1,"publication_status":"published","year":"2022","has_accepted_license":"1","date_published":"2022-10-27T00:00:00Z","title":"Rank-uniform local law for Wigner matrices","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603"},{"last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"scopus_import":"1","oa":1,"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"fulldoi":"https://doi.org/10.1017/fms.2022.86","publication_identifier":{"issn":["2050-5094"]},"citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2022.86.","ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2022.86","mla":"Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 10, e96, Cambridge University Press, 2022, doi:10.1017/fms.2022.86.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2022.86","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022."},"file":[{"access_level":"open_access","success":1,"checksum":"94a049aeb1eea5497aa097712a73c400","content_type":"application/pdf","creator":"dernst","date_updated":"2023-01-24T10:02:40Z","date_created":"2023-01-24T10:02:40Z","relation":"main_file","file_name":"2022_ForumMath_Cipolloni.pdf","file_size":817089,"file_id":"12356"}],"file_date_updated":"2023-01-24T10:02:40Z","article_type":"original","day":"27","doi":"10.1017/fms.2022.86","date_updated":"2025-04-14T07:57:18Z","date_created":"2023-01-12T12:07:30Z","month":"10","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","corr_author":"1","oa_version":"Published Version","ddc":["510"],"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331"}],"department":[{"_id":"LaEr"}],"ec_funded":1,"type":"journal_article"},{"isi":1,"publication_status":"published","year":"2022","has_accepted_license":"1","date_published":"2022-12-01T00:00:00Z","title":"Monotonicity versions of Epstein's concavity theorem and related inequalities","author":[{"last_name":"Carlen","first_name":"Eric A.","full_name":"Carlen, Eric A."},{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan","first_name":"Haonan","last_name":"Zhang"}],"_id":"12216","publisher":"Elsevier","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000860689600014"]},"quality_controlled":"1","keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Numerical Analysis","Algebra and Number Theory"],"acknowledgement":"Work partially supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.","language":[{"iso":"eng"}],"intvolume":" 654","status":"public","abstract":[{"text":"Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The latter says that quantum operations can never increase the relative entropy. The monotonicity versions often have many advantages, and often have direct physical application, as in the example just mentioned. Moreover, the monotonicity results are often valid for a larger class of maps than, say, quantum operations (which are completely positive). In this paper we prove several new monotonicity results, the first of which is a monotonicity theorem that has as a simple corollary a celebrated concavity theorem of Epstein. Our starting points are the monotonicity versions of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs of these in their general forms using interpolation. We then prove our new monotonicity theorems by several duality arguments.","lang":"eng"}],"publication":"Linear Algebra and its Applications","volume":654,"date_updated":"2025-04-14T13:05:27Z","date_created":"2023-01-16T09:46:38Z","doi":"10.1016/j.laa.2022.09.001","month":"12","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","corr_author":"1","ddc":["510"],"oa_version":"Published Version","project":[{"grant_number":"M03337","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","name":"Curvature-dimension in noncommutative analysis"}],"page":"289-310","department":[{"_id":"JaMa"}],"type":"journal_article","oa":1,"scopus_import":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"fulldoi":"https://doi.org/10.1016/j.laa.2022.09.001","citation":{"short":"E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310.","ista":"Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and its Applications. 654, 289–310.","chicago":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” Linear Algebra and Its Applications. Elsevier, 2022. https://doi.org/10.1016/j.laa.2022.09.001.","ama":"Carlen EA, Zhang H. Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and its Applications. 2022;654:289-310. doi:10.1016/j.laa.2022.09.001","ieee":"E. A. Carlen and H. Zhang, “Monotonicity versions of Epstein’s concavity theorem and related inequalities,” Linear Algebra and its Applications, vol. 654. Elsevier, pp. 289–310, 2022.","mla":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” Linear Algebra and Its Applications, vol. 654, Elsevier, 2022, pp. 289–310, doi:10.1016/j.laa.2022.09.001.","apa":"Carlen, E. A., & Zhang, H. (2022). Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2022.09.001"},"publication_identifier":{"issn":["0024-3795"]},"file":[{"success":1,"access_level":"open_access","file_size":441184,"file_name":"2022_LinearAlgebra_Carlen.pdf","file_id":"12415","date_created":"2023-01-27T08:08:39Z","relation":"main_file","date_updated":"2023-01-27T08:08:39Z","content_type":"application/pdf","creator":"dernst","checksum":"cf3cb7e7e34baa967849f01d8f0c1ae4"}],"file_date_updated":"2023-01-27T08:08:39Z","article_type":"original","day":"01"},{"file_date_updated":"2022-01-03T11:08:31Z","file":[{"checksum":"2593abbf195e38efa93b6006b1e90eb1","content_type":"application/pdf","creator":"alisjak","date_updated":"2022-01-03T11:08:31Z","relation":"main_file","date_created":"2022-01-03T11:08:31Z","file_name":"2021_MathAnn_DelloSchiavo.pdf","file_size":410090,"file_id":"10596","access_level":"open_access","success":1}],"day":"01","article_type":"original","oa":1,"scopus_import":"1","fulldoi":"https://doi.org/10.1007/s00208-021-02331-2","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"citation":{"mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” Mathematische Annalen, vol. 384, Springer Nature, 2022, pp. 1815–32, doi:10.1007/s00208-021-02331-2.","apa":"Dello Schiavo, L., & Suzuki, K. (2022). Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-021-02331-2","ieee":"L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces and applications,” Mathematische Annalen, vol. 384. Springer Nature, pp. 1815–1832, 2022.","ama":"Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 2022;384:1815-1832. doi:10.1007/s00208-021-02331-2","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” Mathematische Annalen. Springer Nature, 2022. https://doi.org/10.1007/s00208-021-02331-2.","ista":"Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 384, 1815–1832.","short":"L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832."},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"page":"1815-1832","type":"journal_article","department":[{"_id":"JaMa"}],"ec_funded":1,"date_created":"2022-01-02T23:01:35Z","date_updated":"2025-04-14T07:27:46Z","doi":"10.1007/s00208-021-02331-2","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","arxiv":1,"corr_author":"1","oa_version":"Published Version","ddc":["510"],"month":"12","language":[{"iso":"eng"}],"acknowledgement":"The authors are grateful to Dr. Bang-Xian Han for helpful discussions on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino Antonelli for reading a preliminary version of this work and for their valuable comments and suggestions. Finally, they wish to express their gratitude to two anonymous Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S. gratefully acknowledges funding of his position by the Austrian Science Fund (FWF) grant F65, and by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number 17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium.","intvolume":" 384","status":"public","abstract":[{"text":"We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds.","lang":"eng"}],"publication":"Mathematische Annalen","volume":384,"publisher":"Springer Nature","article_processing_charge":"Yes (via OA deal)","_id":"10588","keyword":["quasi curvature-dimension condition","sub-riemannian geometry","Sobolev-to-Lipschitz property","Varadhan short-time asymptotics"],"quality_controlled":"1","external_id":{"arxiv":["2110.05137"],"isi":["000734150200001"]},"date_published":"2022-12-01T00:00:00Z","author":[{"last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo"},{"full_name":"Suzuki, Kohei","first_name":"Kohei","last_name":"Suzuki"}],"title":"Sobolev-to-Lipschitz property on QCD- spaces and applications","isi":1,"year":"2022","has_accepted_license":"1","publication_status":"published"},{"article_number":"e4","external_id":{"isi":["000743615000001"],"arxiv":["2012.15239"]},"quality_controlled":"1","keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"_id":"10643","publisher":"Cambridge University Press","article_processing_charge":"Yes","volume":10,"publication":"Forum of Mathematics, Sigma","abstract":[{"lang":"eng","text":"We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n"}],"language":[{"iso":"eng"}],"acknowledgement":"J.H. acknowledges partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen is gratefully acknowledged.","intvolume":" 10","status":"public","publication_status":"published","has_accepted_license":"1","year":"2022","isi":1,"author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X"},{"first_name":"Stefan","last_name":"Teufel","full_name":"Teufel, Stefan"}],"title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","date_published":"2022-01-18T00:00:00Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"fulldoi":"https://doi.org/10.1017/fms.2021.80","citation":{"short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2021.80.","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022.","apa":"Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.80","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma, vol. 10, e4, Cambridge University Press, 2022, doi:10.1017/fms.2021.80.","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2021.80"},"publication_identifier":{"eissn":["2050-5094"]},"oa":1,"scopus_import":"1","article_type":"original","day":"18","file":[{"file_id":"10646","file_name":"2022_ForumMathSigma_Henheik.pdf","file_size":705323,"relation":"main_file","date_updated":"2022-01-19T09:27:43Z","date_created":"2022-01-19T09:27:43Z","creator":"cchlebak","content_type":"application/pdf","checksum":"87592a755adcef22ea590a99dc728dd3","success":1,"access_level":"open_access"}],"file_date_updated":"2022-01-19T09:27:43Z","month":"01","ddc":["510"],"oa_version":"Published Version","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","arxiv":1,"corr_author":"1","date_updated":"2025-04-14T07:57:17Z","date_created":"2022-01-18T16:18:51Z","doi":"10.1017/fms.2021.80","ec_funded":1,"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"type":"journal_article","project":[{"grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}]},{"publication":"Mathematical Physics, Analysis and Geometry","volume":25,"intvolume":" 25","acknowledgement":"I am very grateful to Robert Seiringer for his guidance during this project and for many valuable comments on an earlier version of the manuscript. Moreover, I would like to thank Asbjørn Bækgaard Lauritsen for many helpful discussions and comments, pointing out the reference [22] and for his involvement in a closely related joint project [13]. Finally, I am grateful to Christian Hainzl for valuable comments on an earlier version of the manuscript and Andreas Deuchert for interesting discussions.","status":"public","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory."}],"keyword":["geometry and topology","mathematical physics"],"quality_controlled":"1","external_id":{"arxiv":["2106.02015"],"isi":["000741387600001"]},"issue":"1","article_number":"3","publisher":"Springer Nature","article_processing_charge":"Yes (via OA deal)","_id":"10623","title":"The BCS critical temperature at high density","author":[{"last_name":"Henheik","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"}],"date_published":"2022-01-11T00:00:00Z","year":"2022","has_accepted_license":"1","publication_status":"published","isi":1,"day":"11","article_type":"original","file_date_updated":"2022-01-14T07:27:45Z","file":[{"checksum":"d44f8123a52592a75b2c3b8ee2cd2435","content_type":"application/pdf","creator":"cchlebak","date_updated":"2022-01-14T07:27:45Z","relation":"main_file","date_created":"2022-01-14T07:27:45Z","file_size":505804,"file_name":"2022_MathPhyAnalGeo_Henheik.pdf","file_id":"10624","access_level":"open_access","success":1}],"publication_identifier":{"eissn":["1572-9656"],"issn":["1385-0172"]},"fulldoi":"https://doi.org/10.1007/s11040-021-09415-0","citation":{"apa":"Henheik, S. J. (2022). The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. Springer Nature. https://doi.org/10.1007/s11040-021-09415-0","ieee":"S. J. Henheik, “The BCS critical temperature at high density,” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1. Springer Nature, 2022.","mla":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1, 3, Springer Nature, 2022, doi:10.1007/s11040-021-09415-0.","ama":"Henheik SJ. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 2022;25(1). doi:10.1007/s11040-021-09415-0","short":"S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022).","chicago":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical Physics, Analysis and Geometry. Springer Nature, 2022. https://doi.org/10.1007/s11040-021-09415-0.","ista":"Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 25(1), 3."},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"scopus_import":"1","oa":1,"type":"journal_article","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"ec_funded":1,"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"}]},"arxiv":1,"corr_author":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","ddc":["514"],"month":"01","date_created":"2022-01-13T15:40:53Z","date_updated":"2026-07-29T13:18:16Z","doi":"10.1007/s11040-021-09415-0"}]