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Bokor Bleile, E. Cortinovis, (2026).","ieee":"Y. Bokor Bleile and E. Cortinovis, “Quadrix.” Institute of Science and Technology Austria, 2026.","mla":"Bokor Bleile, Yossi, and Emanuele Cortinovis. Quadrix. Institute of Science and Technology Austria, 2026, doi:10.15479/AT-ISTA-21971.","apa":"Bokor Bleile, Y., & Cortinovis, E. (2026). Quadrix. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-21971","ista":"Bokor Bleile Y, Cortinovis E. 2026. Quadrix, Institute of Science and Technology Austria, 10.15479/AT-ISTA-21971.","ama":"Bokor Bleile Y, Cortinovis E. Quadrix. 2026. doi:10.15479/AT-ISTA-21971"},"keyword":["quadratics","mathematics","dendrites","geometry","topology"],"corr_author":"1","author":[{"last_name":"Bleile","full_name":"Bleile, Yossi","id":"920a7385-7995-11ef-9bfd-8c434cd8f3c2","first_name":"Yossi","orcid":"0000-0002-4861-9174"},{"full_name":"Cortinovis, Emanuele","first_name":"Emanuele","last_name":"Cortinovis"}],"project":[{"name":"Quantitative Unbiased Shape Analysis with Geometry & Topology","grant_number":"ESP 9584724","_id":"9106a876-16d5-11f0-9cad-bbf11c9952f9"}],"abstract":[{"text":"A Rust library for analyzing dendritic structures using quadric matrices. This project provides efficient tools for representing dendritic trees, computing quadric error metrics, and visualizing eigenvalue distributions on hexagonal plots.\r\n\r\nThis library implements quadric-based geometric analysis of dendritic structures, commonly found in neuroscience applications. Key features include:\r\n\r\nTree data structures: Hierarchical vertex and edge representations for dendritic trees\r\nQuadric matrices: Computation of quadric error metrics for edges and vertices\r\nVisualisation: Hexagonal plot generation using NormPolar transformations\r\nInteractive tools: Desktop application with plotting capabilities","lang":"eng"}]},{"ec_funded":1,"citation":{"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.","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","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.","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","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.","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."},"external_id":{"arxiv":["2601.18303"]},"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","volume":380,"project":[{"name":"Vigilant Algorithmic Monitoring of Software","grant_number":"101020093","_id":"62781420-2b32-11ec-9570-8d9b63373d4d","call_identifier":"H2020"}],"supplementarymaterial":"no","date_updated":"2026-08-03T07:03:28Z","publication_status":"published","department":[{"_id":"ToHe"}],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"date_created":"2026-08-03T07:02:30Z","creator":"dernst","file_size":919708,"access_level":"open_access","date_updated":"2026-08-03T07:02:30Z","relation":"main_file","checksum":"5d0ff4d267565188a8b4c7502e1bd243","file_id":"22625","file_name":"2026_LIPICSLICS_Brice.pdf","content_type":"application/pdf","success":1}],"language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2026-08-02T22:01:52Z","oa_version":"Published Version","arxiv":1,"intvolume":" 380","quality_controlled":"1","type":"conference","has_accepted_license":"1","researchdata_availability":"no","date_published":"2026-07-09T00:00:00Z","keyword":["Concurrent games","Shared randomness","Topology","Algebraic Geometry"],"OA_type":"gold","corr_author":"1","das_tickbox":"0","article_number":"23:1-23:26","author":[{"first_name":"Leonard J","full_name":"Brice, Leonard J","id":"ce3b3409-db6c-11f0-aa64-ad678f7fd937","last_name":"Brice"},{"orcid":"0000-0002-2985-7724","first_name":"Thomas A","full_name":"Henzinger, Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger"},{"last_name":"Thejaswini","full_name":"Thejaswini, K. S.","first_name":"K. S."}],"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."}],"publication_identifier":{"isbn":["9783959774345"],"issn":["1868-8969"]},"day":"09","fulldoi":"https://doi.org/10.4230/LIPIcs.LICS.2026.23","ddc":["000"],"file_date_updated":"2026-08-03T07:02:30Z","doi":"10.4230/LIPIcs.LICS.2026.23","OA_place":"publisher","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","article_processing_charge":"No","oa":1,"scopus_import":"1","title":"Dicey games: Shared sources of randomness in distributed systems","alternative_title":["LIPIcs"],"publication":"41st Annual Symposium on Logic in Computer Science","conference":{"location":"Lisbon, Portugal","end_date":"2026-07-23","name":"LICS: Logic in Computer Science","start_date":"2026-07-20"},"status":"public","_id":"22617","month":"07","year":"2026"},{"researchdata_availability":"no","date_published":"2026-05-27T00:00:00Z","type":"conference","has_accepted_license":"1","arxiv":1,"intvolume":" 367","quality_controlled":"1","language":[{"iso":"eng"}],"date_created":"2026-07-13T09:56:38Z","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"file_id":"22329","checksum":"9dfb96ee66985c724b499b0e5888dc8e","relation":"main_file","date_updated":"2026-07-14T06:08:05Z","success":1,"content_type":"application/pdf","file_name":"2026_LIPIcSSoCG_Edelsbrunner.pdf","file_size":2902144,"creator":"dernst","date_created":"2026-07-14T06:08:05Z","access_level":"open_access"}],"publication_status":"published","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"supplementarymaterial":"no","date_updated":"2026-08-12T09:02:56Z","project":[{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"},{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"}],"volume":367,"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","citation":{"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.","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.","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.","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","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.","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."},"external_id":{"arxiv":["2511.21961"]},"ec_funded":1,"status":"public","_id":"22299","month":"05","year":"2026","publication":"42nd International Symposium on Computational Geometry","alternative_title":["LIPIcs"],"conference":{"location":"New Brunswick, NJ, United States","end_date":"2026-06-05","name":"SoCG: Symposium on Computational Geometry","start_date":"2026-06-02"},"scopus_import":"1","title":"The depth poset under transpositions in the filter","article_processing_charge":"Yes","oa":1,"file_date_updated":"2026-07-14T06:08:05Z","doi":"10.4230/LIPICS.SOCG.2026.41","OA_place":"publisher","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","fulldoi":"https://doi.org/10.4230/LIPICS.SOCG.2026.41","ddc":["500"],"day":"27","publication_identifier":{"isbn":["9783959774185"],"eissn":["1868-8969"]},"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"}],"author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"first_name":"Michał","orcid":"0000-0001-9789-9750","full_name":"Lipiński, Michał","id":"dfffb474-4317-11ee-8f5c-fe3fc95a425e","last_name":"Lipiński"},{"full_name":"Mrozek, Marian","first_name":"Marian","orcid":"0000-0002-0619-6417","last_name":"Mrozek"},{"last_name":"Soriano Trigueros","full_name":"Soriano Trigueros, Manuel","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","first_name":"Manuel","orcid":"0000-0003-2449-1433"},{"first_name":"Fedor","full_name":"Zimin, Fedor","id":"afd27eda-91c1-11f0-aad8-c6edbec24c04","last_name":"Zimin"}],"das_tickbox":"0","corr_author":"1","article_number":"41:1-41:18","OA_type":"gold","keyword":["Algebraic topology","Lefschetz complexes","persistent homology","vines and vineyards","birth-death pairs","shallow pairs","relations","partial orders","transpositions","Theory of computation → Computational geometry"]},{"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).","volume":43,"project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"citation":{"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).","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.","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","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.","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","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."},"external_id":{"isi":["001289270900045"]},"issue":"4","type":"journal_article","has_accepted_license":"1","researchdata_availability":"no","date_published":"2024-07-01T00:00:00Z","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2024-07-05T12:08:57Z","oa_version":"Published Version","quality_controlled":"1","intvolume":" 43","file":[{"relation":"main_file","checksum":"0dc9f5a6422b8a49a79026900f349ee5","file_id":"17204","date_updated":"2024-07-05T12:05:17Z","success":1,"file_name":"sif-final.pdf","content_type":"application/pdf","creator":"chafner","file_size":7225150,"date_created":"2024-07-05T12:05:17Z","access_level":"open_access"},{"access_level":"open_access","date_created":"2024-07-05T12:06:03Z","creator":"chafner","file_size":397262,"file_name":"sif-supp-final.pdf","content_type":"application/pdf","date_updated":"2024-07-05T12:06:03Z","relation":"supplementary_material","checksum":"cde433c6a40688d5f1187fb5721f6f94","file_id":"17205"},{"access_level":"open_access","date_created":"2024-07-17T09:29:13Z","creator":"chafner","file_size":170001305,"title":"Submission Video","file_name":"sif-video-final.mp4","content_type":"video/mp4","date_updated":"2024-07-17T09:29:13Z","relation":"supplementary_material","checksum":"c0457a09c2ab9a1c2935c995dcc84907","file_id":"17276"}],"article_type":"original","supplementarymaterial":"yes","date_updated":"2026-10-01T09:30:01Z","department":[{"_id":"ChWo"}],"publication_status":"published","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"}],"author":[{"last_name":"Hafner","first_name":"Christian","id":"400429CC-F248-11E8-B48F-1D18A9856A87","full_name":"Hafner, Christian"},{"last_name":"Ly","full_name":"Ly, Mickaël","id":"6340d7f0-b48d-11eb-b10d-b7487e71d9f1","first_name":"Mickaël"},{"last_name":"Wojtan","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","full_name":"Wojtan, Christopher J","first_name":"Christopher J","orcid":"0000-0001-6646-5546"}],"keyword":["Topology Optimization","Mass Moments","Computational Geometry"],"corr_author":"1","das_tickbox":"0","isi":1,"article_number":"78","publication":"Transactions on Graphics","conference":{"start_date":"2024-07-28","end_date":"2024-08-01","location":"Denver, Colorado"},"status":"public","_id":"17203","month":"07","year":"2024","article_processing_charge":"Yes (via OA deal)","oa":1,"scopus_import":"1","title":"Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments","ddc":["516"],"fulldoi":"https://doi.org/10.1145/3658194","file_date_updated":"2024-07-17T09:29:13Z","doi":"10.1145/3658194","publisher":"Association for Computing Machinery","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"day":"01"},{"keyword":["surface tracking","topology change","non- manifold meshes","multi-material flows","solid modeling"],"OA_type":"hybrid","das_tickbox":"0","isi":1,"corr_author":"1","article_number":"54","abstract":[{"lang":"eng","text":"We introduce a multi-material non-manifold mesh-based surface tracking algorithm that converts self-intersections into topological changes. Our algorithm generalizes prior work on manifold surface tracking with topological changes: it preserves surface features like mesh-based methods, and it robustly handles topological changes like level set methods. Our method also offers improved efficiency and robustness over the state of the art. We demonstrate the effectiveness of the approach on a range of examples, including complex soap film simulations with thousands of interacting bubbles, and boolean unions of non-manifold meshes consisting of millions of triangles."}],"related_material":{"record":[{"status":"public","id":"19630","relation":"dissertation_contains"},{"relation":"dissertation_contains","id":"18301","status":"public"}]},"author":[{"last_name":"Synak","first_name":"Peter","full_name":"Synak, Peter","id":"331776E2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Aleksei","orcid":"0000-0003-2189-3904","id":"44b7120e-eb97-11eb-a6c2-e1557aa81d02","full_name":"Kalinov, Aleksei","last_name":"Kalinov"},{"id":"2afc607f-f128-11eb-9611-8f2a0dfcf074","full_name":"Strugaru, Irina-Malina","first_name":"Irina-Malina","last_name":"Strugaru"},{"first_name":"Arian","id":"36cea3aa-f38e-11ec-8ae0-c65ae6f6098f","full_name":"Etemadihaghighi, Arian","last_name":"Etemadihaghighi"},{"last_name":"Yang","full_name":"Yang, Huidong","first_name":"Huidong"},{"first_name":"Christopher J","orcid":"0000-0001-6646-5546","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","last_name":"Wojtan"}],"ddc":["004"],"fulldoi":"https://doi.org/10.1145/3658223","file_date_updated":"2025-11-11T09:50:52Z","doi":"10.1145/3658223","OA_place":"publisher","publisher":"Association for Computing Machinery","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"day":"01","publication":"ACM Transactions on Graphics","_id":"17219","status":"public","month":"07","year":"2024","article_processing_charge":"Yes (via OA deal)","oa":1,"scopus_import":"1","title":"Multi-material mesh-based surface tracking with implicit topology changes","citation":{"apa":"Synak, P., Kalinov, A., Strugaru, I.-M., Etemadi, A., Yang, H., & Wojtan, C. 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Wojtan, “Multi-material mesh-based surface tracking with implicit topology changes,” ACM Transactions on Graphics, vol. 43, no. 4. Association for Computing Machinery, 2024.","chicago":"Synak, Peter, Aleksei Kalinov, Irina-Malina Strugaru, Arian Etemadi, Huidong Yang, and Chris Wojtan. “Multi-Material Mesh-Based Surface Tracking with Implicit Topology Changes.” ACM Transactions on Graphics. Association for Computing Machinery, 2024. https://doi.org/10.1145/3658223."},"external_id":{"isi":["001289270900021"]},"issue":"4","acknowledgement":"Peter Heiss-Synak helped conceive the project, helped formulate the algorithm structure, contributed ideas and code to Sections 6 & 8, the mesh data structure, algorithm robustness and benchmarks, helped write the paper, and provided supervision and conceptual solutions throughout the project. Aleksei Kalinov contributed ideas and code to Sections 7, 8.5, and 5, the sparse grid data structure, algorithm robustness and benchmarks, optimized the performance, produced all results, most figures, and the supplementary video, helped write the text, and provided conceptual solutions throughout the project. Malina Strugaru helped implement the mesh data structure and designed re-meshing operations for non-manifold triangle meshes. Arian Etemadi developed early prototypes for ideas in Sections 8.1 and 8.3 and helped write the paper. Huidong Yang developed early prototypes for isosurface extraction and visualization. Chris Wojtan helped conceive the project, helped write the paper, and provided supervision, prototype grid data structure code, and conceptual solutions throughout the project. We thank the anonymous reviewers for their helpful comments, the members of the Visual Computing Group at ISTA for their feedback, Christopher Batty for discussions about LosTopos, and SideFX for the Houdini Education software licenses. This research was funded in part by the European Union (ERC-2021-COG 101045083 CoDiNA).","volume":43,"project":[{"name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088"}],"tmp":{"image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)"},"file":[{"success":1,"content_type":"application/pdf","file_name":"2024_ACMToG_HeissSynak.pdf","file_id":"17317","checksum":"1917067d4b52d7729019b03560004e43","relation":"main_file","date_updated":"2024-07-23T06:35:15Z","access_level":"open_access","file_size":48763368,"creator":"dernst","date_created":"2024-07-23T06:35:15Z"},{"date_updated":"2024-07-10T12:23:44Z","relation":"main_file","checksum":"a4f0e293184bfa034c0c585848806b17","file_id":"17221","file_name":"sdtopofixer_final.mp4","content_type":"video/mp4","success":1,"date_created":"2024-07-10T12:23:44Z","creator":"akalinov","file_size":48021463,"access_level":"open_access"},{"file_name":"SuperDuperTopoFixer.pdf","content_type":"application/pdf","date_updated":"2025-11-11T09:50:52Z","relation":"preprint","checksum":"18fc310a78ec91651148c45a8b89fa44","file_id":"20633","access_level":"open_access","date_created":"2025-11-11T09:50:52Z","creator":"akalinov","file_size":48639581,"title":"Authors' version of the text"}],"article_type":"original","supplementarymaterial":"no","date_updated":"2026-10-02T11:19:25Z","publication_status":"published","department":[{"_id":"GradSch"},{"_id":"ChWo"}],"type":"journal_article","has_accepted_license":"1","date_published":"2024-07-01T00:00:00Z","researchdata_availability":"no","language":[{"iso":"eng"}],"date_created":"2024-07-10T12:24:00Z","oa_version":"Published Version","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","quality_controlled":"1","intvolume":" 43"},{"publisher":"Institute of Science and Technology Austria","doi":"10.15479/at:ista:18301","file_date_updated":"2024-10-24T14:34:54Z","OA_place":"publisher","fulldoi":"https://doi.org/10.15479/at:ista:18301","ddc":["000"],"day":"15","publication_identifier":{"issn":["2791-4585"]},"year":"2024","month":"10","_id":"18301","status":"public","alternative_title":["ISTA Master's Thesis"],"title":"Filling the holes of non-manifold self-intersecting meshes for implicit topology changes in surface tracking","oa":1,"article_processing_charge":"No","das_tickbox":"0","corr_author":"1","keyword":["surface tracking","non-manifold","hole-filling","topology change","multi-material","solid-modeling"],"related_material":{"record":[{"status":"public","id":"17219","relation":"part_of_dissertation"}]},"abstract":[{"text":"Physics simulation in computer graphics can bring triangle meshes into topologically invalid states. The method in this thesis contributed to Heiss-Synak* and Kalinov* et al. [2024] who devised a non-manifold hybrid surface tracker—a surface tracker that repairs explicit non-manifold triangle meshes with the help of the implicit domain. Specifically, this thesis provides an algorithm for filling the holes that are left after removing problematic parts of the mesh.","lang":"eng"}],"doi_confirm":"1","author":[{"last_name":"Etemadihaghighi","first_name":"Arian","id":"36cea3aa-f38e-11ec-8ae0-c65ae6f6098f","full_name":"Etemadihaghighi, Arian"}],"degree_awarded":"MS","file":[{"access_level":"open_access","creator":"aetemadi","file_size":8914218,"date_created":"2024-10-24T14:34:42Z","success":1,"file_name":"thesis-arian-etemadi.pdf","content_type":"application/pdf","checksum":"80fb7923e229ad9d39253d7c8a8083d0","relation":"main_file","file_id":"18469","date_updated":"2024-10-24T14:34:42Z"},{"date_created":"2024-10-24T14:34:54Z","file_size":9802650,"creator":"aetemadi","access_level":"closed","date_updated":"2024-10-24T14:34:54Z","file_id":"18470","checksum":"1c02586ed7d441d5ec441867650568d1","relation":"source_file","content_type":"application/x-zip-compressed","file_name":"thesis-arian-etemadi-latex-source.zip"}],"tmp":{"image":"/images/cc_by_sa.png","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","short":"CC BY-SA (4.0)"},"publication_status":"published","department":[{"_id":"GradSch"},{"_id":"ChWo"}],"date_updated":"2026-10-02T11:19:26Z","supplementarymaterial":"no","date_published":"2024-10-15T00:00:00Z","researchdata_availability":"no","has_accepted_license":"1","type":"dissertation","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2024-10-11T19:52:20Z","oa_version":"Published Version","language":[{"iso":"eng"}],"citation":{"apa":"Etemadi, A. (2024). Filling the holes of non-manifold self-intersecting meshes for implicit topology changes in surface tracking. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18301","mla":"Etemadi, Arian. Filling the Holes of Non-Manifold Self-Intersecting Meshes for Implicit Topology Changes in Surface Tracking. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18301.","ista":"Etemadi A. 2024. Filling the holes of non-manifold self-intersecting meshes for implicit topology changes in surface tracking. Institute of Science and Technology Austria.","ama":"Etemadi A. Filling the holes of non-manifold self-intersecting meshes for implicit topology changes in surface tracking. 2024. doi:10.15479/at:ista:18301","short":"A. Etemadi, Filling the Holes of Non-Manifold Self-Intersecting Meshes for Implicit Topology Changes in Surface Tracking, Institute of Science and Technology Austria, 2024.","ieee":"A. Etemadi, “Filling the holes of non-manifold self-intersecting meshes for implicit topology changes in surface tracking,” Institute of Science and Technology Austria, 2024.","chicago":"Etemadi, Arian. “Filling the Holes of Non-Manifold Self-Intersecting Meshes for Implicit Topology Changes in Surface Tracking.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18301."},"page":"39","supervisor":[{"last_name":"Wojtan","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","first_name":"Christopher J","orcid":"0000-0001-6646-5546"}]},{"has_accepted_license":"1","type":"journal_article","date_published":"2023-01-01T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2023-01-16T10:04:06Z","oa_version":"Published Version","language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":" 69","file":[{"date_created":"2023-02-02T11:01:10Z","creator":"dernst","file_size":582850,"access_level":"open_access","date_updated":"2023-02-02T11:01:10Z","relation":"main_file","checksum":"46352e0ee71e460848f88685ca852681","file_id":"12488","file_name":"2023_DiscreteCompGeometry_Boissonnat.pdf","content_type":"application/pdf","success":1}],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","date_updated":"2025-04-14T07:44:00Z","department":[{"_id":"HeEd"}],"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).","volume":69,"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"grant_number":"M03073","name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"external_id":{"isi":["000862193600001"]},"page":"156-191","citation":{"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.","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.","short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, M. Wintraecken, Discrete & Computational Geometry 69 (2023) 156–191.","ista":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. 2023. Local criteria for triangulating general manifolds. Discrete & Computational Geometry. 69, 156–191.","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","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."},"ec_funded":1,"publication":"Discrete & Computational Geometry","year":"2023","status":"public","_id":"12287","month":"01","oa":1,"article_processing_charge":"No","title":"Local criteria for triangulating general manifolds","scopus_import":"1","fulldoi":"https://doi.org/10.1007/s00454-022-00431-7","ddc":["510"],"publisher":"Springer Nature","file_date_updated":"2023-02-02T11:01:10Z","doi":"10.1007/s00454-022-00431-7","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"day":"01","abstract":[{"lang":"eng","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."}],"author":[{"full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel","last_name":"Boissonnat"},{"last_name":"Dyer","first_name":"Ramsay","full_name":"Dyer, Ramsay"},{"full_name":"Ghosh, Arijit","first_name":"Arijit","last_name":"Ghosh"},{"full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken"}],"keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"isi":1,"corr_author":"1"},{"author":[{"last_name":"Lampart","first_name":"Jonas","full_name":"Lampart, Jonas"},{"last_name":"Mitrouskas","full_name":"Mitrouskas, David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","first_name":"David Johannes"},{"last_name":"Mysliwy","id":"316457FC-F248-11E8-B48F-1D18A9856A87","full_name":"Mysliwy, Krzysztof","first_name":"Krzysztof"}],"abstract":[{"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.","lang":"eng"}],"isi":1,"corr_author":"1","article_number":"17","keyword":["Geometry and Topology","Mathematical Physics"],"scopus_import":"1","title":"On the global minimum of the energy–momentum relation for the polaron","article_processing_charge":"Yes (via OA deal)","oa":1,"_id":"14192","status":"public","month":"07","year":"2023","publication":"Mathematical Physics, Analysis and Geometry","day":"26","publication_identifier":{"issn":["1385-0172"],"eissn":["1572-9656"]},"doi":"10.1007/s11040-023-09460-x","file_date_updated":"2023-08-23T10:59:15Z","publisher":"Springer Nature","fulldoi":"https://doi.org/10.1007/s11040-023-09460-x","ddc":["510"],"volume":26,"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.","issue":"3","citation":{"short":"J. Lampart, D.J. Mitrouskas, K. Mysliwy, Mathematical Physics, Analysis and Geometry 26 (2023).","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.","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","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.","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.","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."},"external_id":{"isi":["001032992600001"],"arxiv":["2206.14708"]},"intvolume":" 26","arxiv":1,"quality_controlled":"1","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","date_created":"2023-08-22T14:09:47Z","date_published":"2023-07-26T00:00:00Z","type":"journal_article","has_accepted_license":"1","publication_status":"published","department":[{"_id":"RoSe"}],"date_updated":"2024-10-09T21:06:41Z","article_type":"original","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"date_updated":"2023-08-23T10:59:15Z","file_id":"14225","relation":"main_file","checksum":"f0941cc66cb3ed06a12ca4b7e356cfd6","content_type":"application/pdf","file_name":"2023_MathPhysics_Lampart.pdf","success":1,"date_created":"2023-08-23T10:59:15Z","file_size":317026,"creator":"dernst","access_level":"open_access"}]},{"author":[{"last_name":"Kwan","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan"},{"last_name":"Sah","first_name":"Ashwin","full_name":"Sah, Ashwin"},{"first_name":"Lisa","full_name":"Sauermann, Lisa","last_name":"Sauermann"},{"first_name":"Mehtaab","full_name":"Sawhney, Mehtaab","last_name":"Sawhney"}],"abstract":[{"lang":"eng","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."}],"corr_author":"1","isi":1,"article_number":"e21","keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Analysis"],"scopus_import":"1","title":"Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture","article_processing_charge":"Yes","oa":1,"_id":"14499","status":"public","month":"08","year":"2023","publication":"Forum of Mathematics, Pi","day":"24","publication_identifier":{"issn":["2050-5086"]},"doi":"10.1017/fmp.2023.17","file_date_updated":"2023-11-07T09:16:23Z","publisher":"Cambridge University Press","fulldoi":"https://doi.org/10.1017/fmp.2023.17","ddc":["510"],"project":[{"name":"Randomness and structure in combinatorics","grant_number":"101076777","_id":"bd95085b-d553-11ed-ba76-e55d3349be45"}],"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.","volume":11,"citation":{"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).","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","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","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."},"external_id":{"arxiv":["2208.02874"],"isi":["001123866200001"]},"intvolume":" 11","arxiv":1,"quality_controlled":"1","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa_version":"Published Version","date_created":"2023-11-07T09:02:48Z","date_published":"2023-08-24T00:00:00Z","type":"journal_article","has_accepted_license":"1","department":[{"_id":"MaKw"}],"publication_status":"published","date_updated":"2025-09-09T13:16:15Z","article_type":"original","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"success":1,"file_name":"2023_ForumMathematics_Kwan.pdf","content_type":"application/pdf","relation":"main_file","checksum":"54b824098d59073cc87a308d458b0a3e","file_id":"14500","date_updated":"2023-11-07T09:16:23Z","access_level":"open_access","creator":"dernst","file_size":1218719,"date_created":"2023-11-07T09:16:23Z"}]},{"keyword":["Geometry and Topology","Mathematical Physics"],"isi":1,"corr_author":"1","das_tickbox":"1","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"}],"author":[{"first_name":"Nils","full_name":"Carqueville, Nils","last_name":"Carqueville"},{"id":"7943226E-220E-11EA-94C7-D59F3DDC885E","full_name":"Szegedy, Lorant","first_name":"Lorant","orcid":"0000-0003-2834-5054","last_name":"Szegedy"}],"ddc":["530"],"fulldoi":"https://doi.org/10.4171/qt/193","publisher":"EMS Press","file_date_updated":"2024-01-09T09:25:34Z","doi":"10.4171/qt/193","publication_identifier":{"issn":["1663-487X"]},"day":"16","publication":"Quantum Topology","year":"2023","status":"public","_id":"14756","month":"10","oa":1,"article_processing_charge":"Yes","title":"Fully extended r-spin TQFTs","scopus_import":"1","external_id":{"isi":["001104620800003"]},"citation":{"ista":"Carqueville N, Szegedy L. 2023. Fully extended r-spin TQFTs. Quantum Topology. 14(3), 467–532.","ama":"Carqueville N, Szegedy L. Fully extended r-spin TQFTs. Quantum Topology. 2023;14(3):467-532. doi:10.4171/qt/193","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.","ieee":"N. Carqueville and L. Szegedy, “Fully extended r-spin TQFTs,” Quantum Topology, vol. 14, no. 3. EMS Press, pp. 467–532, 2023.","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."},"page":"467-532","issue":"3","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.","volume":14,"file":[{"file_size":707344,"creator":"dernst","date_created":"2024-01-09T09:25:34Z","access_level":"open_access","file_id":"14764","checksum":"b0590aff6e7ec89cc149ba94d459d3a3","relation":"main_file","date_updated":"2024-01-09T09:25:34Z","success":1,"content_type":"application/pdf","file_name":"2023_QuantumTopol_Carqueville.pdf"}],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","date_updated":"2026-07-06T11:52:15Z","publication_status":"published","department":[{"_id":"MiLe"}],"has_accepted_license":"1","type":"journal_article","date_published":"2023-10-16T00:00:00Z","date_created":"2024-01-08T13:14:48Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","language":[{"iso":"eng"}],"intvolume":" 14","quality_controlled":"1"},{"volume":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","external_id":{"isi":["000883222200003"]},"citation":{"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.","short":"U. Wagner, E. Welzl, Discrete & Computational Geometry 68 (2022) 1227–1284.","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.","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","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.","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","ista":"Wagner U, Welzl E. 2022. Connectivity of triangulation flip graphs in the plane. Discrete & Computational Geometry. 68(4), 1227–1284."},"page":"1227-1284","issue":"4","date_published":"2022-11-14T00:00:00Z","has_accepted_license":"1","type":"journal_article","quality_controlled":"1","intvolume":" 68","oa_version":"Published Version","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2023-01-12T12:02:28Z","language":[{"iso":"eng"}],"article_type":"original","file":[{"access_level":"open_access","file_size":1747581,"creator":"dernst","date_created":"2023-01-23T11:10:03Z","success":1,"content_type":"application/pdf","file_name":"2022_DiscreteCompGeometry_Wagner.pdf","file_id":"12345","checksum":"307e879d09e52eddf5b225d0aaa9213a","relation":"main_file","date_updated":"2023-01-23T11:10:03Z"}],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"department":[{"_id":"UlWa"}],"publication_status":"published","date_updated":"2025-07-10T11:54:56Z","related_material":{"record":[{"status":"public","id":"7807","relation":"earlier_version"},{"status":"public","relation":"earlier_version","id":"7990"}]},"abstract":[{"lang":"eng","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."}],"author":[{"last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Welzl, Emo","first_name":"Emo","last_name":"Welzl"}],"isi":1,"corr_author":"1","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"year":"2022","month":"11","_id":"12129","status":"public","publication":"Discrete & Computational Geometry","title":"Connectivity of triangulation flip graphs in the plane","scopus_import":"1","oa":1,"article_processing_charge":"No","publisher":"Springer Nature","file_date_updated":"2023-01-23T11:10:03Z","doi":"10.1007/s00454-022-00436-2","ddc":["510"],"fulldoi":"https://doi.org/10.1007/s00454-022-00436-2","day":"14","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]}},{"keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"article_number":"e96","corr_author":"1","isi":1,"author":[{"last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"abstract":[{"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.","lang":"eng"}],"publication_identifier":{"issn":["2050-5094"]},"day":"27","fulldoi":"https://doi.org/10.1017/fms.2022.86","ddc":["510"],"publisher":"Cambridge University Press","doi":"10.1017/fms.2022.86","file_date_updated":"2023-01-24T10:02:40Z","oa":1,"article_processing_charge":"No","title":"Rank-uniform local law for Wigner matrices","scopus_import":"1","publication":"Forum of Mathematics, Sigma","year":"2022","status":"public","_id":"12148","month":"10","ec_funded":1,"external_id":{"isi":["000873719200001"]},"citation":{"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.","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","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.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.","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","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022."},"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.","volume":10,"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020"}],"date_updated":"2025-04-14T07:57:18Z","publication_status":"published","department":[{"_id":"LaEr"}],"file":[{"file_size":817089,"creator":"dernst","date_created":"2023-01-24T10:02:40Z","access_level":"open_access","file_id":"12356","relation":"main_file","checksum":"94a049aeb1eea5497aa097712a73c400","date_updated":"2023-01-24T10:02:40Z","success":1,"content_type":"application/pdf","file_name":"2022_ForumMath_Cipolloni.pdf"}],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","date_created":"2023-01-12T12:07:30Z","language":[{"iso":"eng"}],"intvolume":" 10","quality_controlled":"1","has_accepted_license":"1","type":"journal_article","date_published":"2022-10-27T00:00:00Z"},{"keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Numerical Analysis","Algebra and Number Theory"],"isi":1,"corr_author":"1","author":[{"full_name":"Carlen, Eric A.","first_name":"Eric A.","last_name":"Carlen"},{"last_name":"Zhang","first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan"}],"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_identifier":{"issn":["0024-3795"]},"day":"01","ddc":["510"],"fulldoi":"https://doi.org/10.1016/j.laa.2022.09.001","doi":"10.1016/j.laa.2022.09.001","file_date_updated":"2023-01-27T08:08:39Z","publisher":"Elsevier","article_processing_charge":"Yes (via OA deal)","oa":1,"scopus_import":"1","title":"Monotonicity versions of Epstein's concavity theorem and related inequalities","publication":"Linear Algebra and its Applications","_id":"12216","status":"public","month":"12","year":"2022","citation":{"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.","short":"E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310.","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","ista":"Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and its Applications. 654, 289–310.","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","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."},"page":"289-310","external_id":{"isi":["000860689600014"]},"acknowledgement":"Work partially supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.","volume":654,"project":[{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","grant_number":"M03337","name":"Curvature-dimension in noncommutative analysis"}],"date_updated":"2025-04-14T13:05:27Z","publication_status":"published","department":[{"_id":"JaMa"}],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"file_id":"12415","relation":"main_file","checksum":"cf3cb7e7e34baa967849f01d8f0c1ae4","date_updated":"2023-01-27T08:08:39Z","success":1,"content_type":"application/pdf","file_name":"2022_LinearAlgebra_Carlen.pdf","file_size":441184,"creator":"dernst","date_created":"2023-01-27T08:08:39Z","access_level":"open_access"}],"article_type":"original","language":[{"iso":"eng"}],"date_created":"2023-01-16T09:46:38Z","oa_version":"Published Version","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 654","quality_controlled":"1","type":"journal_article","has_accepted_license":"1","date_published":"2022-12-01T00:00:00Z"},{"type":"journal_article","date_published":"2022-01-07T00:00:00Z","language":[{"iso":"eng"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_created":"2026-03-30T12:22:47Z","oa_version":"Preprint","quality_controlled":"1","intvolume":" 9","arxiv":1,"article_type":"letter_note","date_updated":"2026-04-27T09:14:46Z","publication_status":"published","extern":"1","volume":9,"citation":{"chicago":"Roques-Carmes, Charles, Zin Lin, Rasmus E. Christiansen, Yannick Salamin, Steven E. Kooi, John D. Joannopoulos, Steven G. Johnson, and Marin Soljačić. “Toward 3D-Printed Inverse-Designed Metaoptics.” ACS Photonics. American Chemical Society, 2022. https://doi.org/10.1021/acsphotonics.1c01442.","ama":"Roques-Carmes C, Lin Z, Christiansen RE, et al. Toward 3D-printed inverse-designed metaoptics. ACS Photonics. 2022;9(1):43-51. doi:10.1021/acsphotonics.1c01442","ista":"Roques-Carmes C, Lin Z, Christiansen RE, Salamin Y, Kooi SE, Joannopoulos JD, Johnson SG, Soljačić M. 2022. Toward 3D-printed inverse-designed metaoptics. ACS Photonics. 9(1), 43–51.","apa":"Roques-Carmes, C., Lin, Z., Christiansen, R. E., Salamin, Y., Kooi, S. E., Joannopoulos, J. D., … Soljačić, M. (2022). Toward 3D-printed inverse-designed metaoptics. ACS Photonics. American Chemical Society. https://doi.org/10.1021/acsphotonics.1c01442","mla":"Roques-Carmes, Charles, et al. “Toward 3D-Printed Inverse-Designed Metaoptics.” ACS Photonics, vol. 9, no. 1, American Chemical Society, 2022, pp. 43–51, doi:10.1021/acsphotonics.1c01442.","ieee":"C. Roques-Carmes et al., “Toward 3D-printed inverse-designed metaoptics,” ACS Photonics, vol. 9, no. 1. American Chemical Society, pp. 43–51, 2022.","short":"C. Roques-Carmes, Z. Lin, R.E. Christiansen, Y. Salamin, S.E. Kooi, J.D. Joannopoulos, S.G. Johnson, M. Soljačić, ACS Photonics 9 (2022) 43–51."},"page":"43-51","external_id":{"arxiv":["2105.11326"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.11326","open_access":"1"}],"issue":"1","publication":"ACS Photonics","_id":"21527","month":"01","status":"public","year":"2022","article_processing_charge":"No","oa":1,"scopus_import":"1","title":"Toward 3D-printed inverse-designed metaoptics","ddc":["530"],"fulldoi":"https://doi.org/10.1021/acsphotonics.1c01442","OA_place":"repository","doi":"10.1021/acsphotonics.1c01442","publisher":"American Chemical Society","publication_identifier":{"eissn":["2330-4022"]},"day":"07","abstract":[{"text":"Optical metasurfaces have been heralded as the platform to integrate multiple functionalities in a compact form-factor, with the potential to replace bulky optical components. A central stepping stone toward realizing this promise is the demonstration of multifunctionality under several constraints (e.g., at multiple incident wavelengths and/or angles) in a single device, an achievement being hampered by design limitations inherent to single-layer planar geometries. Here, we propose a framework for the inverse design of multilayer metaoptics via topology optimization, showing that even few-wavelength thick devices can achieve high-efficiency multifunctionality, such as multiangle light concentration and plan-achromaticity. We embody our framework in multiple closely spaced patterned layers of a low-index polymer, with fabrication constraints specific to this platform enforced in the optimization process. We experimentally demonstrate our approach with an inverse-designed 3D-printed light concentrator working at five different nonparaxial angles of incidence. Our framework paves the way toward realizing multifunctional ultracompact 3D nanophotonic devices.","lang":"eng"}],"author":[{"first_name":"Charles","full_name":"Roques-Carmes, Charles","id":"e2e68fc9-6505-11ef-a541-eb4e72cc3e82","last_name":"Roques-Carmes"},{"last_name":"Lin","full_name":"Lin, Zin","first_name":"Zin"},{"full_name":"Christiansen, Rasmus E.","first_name":"Rasmus E.","last_name":"Christiansen"},{"last_name":"Salamin","full_name":"Salamin, Yannick","first_name":"Yannick"},{"full_name":"Kooi, Steven E.","first_name":"Steven E.","last_name":"Kooi"},{"last_name":"Joannopoulos","first_name":"John D.","full_name":"Joannopoulos, John D."},{"last_name":"Johnson","first_name":"Steven G.","full_name":"Johnson, Steven G."},{"last_name":"Soljačić","first_name":"Marin","full_name":"Soljačić, Marin"}],"keyword":["metasurfaces","inverse design","multilayered metaoptics","3D printing","topology optimization"],"OA_type":"green"},{"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020"}],"volume":10,"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.","citation":{"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.","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","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.","short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).","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."},"external_id":{"isi":["000743615000001"],"arxiv":["2012.15239"]},"ec_funded":1,"date_published":"2022-01-18T00:00:00Z","type":"journal_article","has_accepted_license":"1","quality_controlled":"1","arxiv":1,"intvolume":" 10","language":[{"iso":"eng"}],"oa_version":"Published Version","date_created":"2022-01-18T16:18:51Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_type":"original","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"content_type":"application/pdf","file_name":"2022_ForumMathSigma_Henheik.pdf","success":1,"date_updated":"2022-01-19T09:27:43Z","file_id":"10646","checksum":"87592a755adcef22ea590a99dc728dd3","relation":"main_file","access_level":"open_access","date_created":"2022-01-19T09:27:43Z","file_size":705323,"creator":"cchlebak"}],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"publication_status":"published","date_updated":"2025-04-14T07:57:17Z","abstract":[{"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","lang":"eng"}],"author":[{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha"},{"first_name":"Stefan","full_name":"Teufel, Stefan","last_name":"Teufel"}],"corr_author":"1","isi":1,"article_number":"e4","keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"month":"01","_id":"10643","status":"public","year":"2022","publication":"Forum of Mathematics, Sigma","scopus_import":"1","title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","article_processing_charge":"Yes","oa":1,"doi":"10.1017/fms.2021.80","file_date_updated":"2022-01-19T09:27:43Z","publisher":"Cambridge University Press","ddc":["510"],"fulldoi":"https://doi.org/10.1017/fms.2021.80","day":"18","publication_identifier":{"eissn":["2050-5094"]}},{"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"date_updated":"2022-01-14T07:27:45Z","file_id":"10624","relation":"main_file","checksum":"d44f8123a52592a75b2c3b8ee2cd2435","content_type":"application/pdf","file_name":"2022_MathPhyAnalGeo_Henheik.pdf","success":1,"date_created":"2022-01-14T07:27:45Z","file_size":505804,"creator":"cchlebak","access_level":"open_access"}],"article_type":"original","date_updated":"2026-07-29T13:18:16Z","publication_status":"published","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"type":"journal_article","has_accepted_license":"1","date_published":"2022-01-11T00:00:00Z","language":[{"iso":"eng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","date_created":"2022-01-13T15:40:53Z","quality_controlled":"1","arxiv":1,"intvolume":" 25","citation":{"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.","ieee":"S. J. Henheik, “The BCS critical temperature at high density,” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1. Springer Nature, 2022.","short":"S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022).","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","ista":"Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 25(1), 3.","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","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."},"external_id":{"isi":["000741387600001"],"arxiv":["2106.02015"]},"issue":"1","ec_funded":1,"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.","volume":25,"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"fulldoi":"https://doi.org/10.1007/s11040-021-09415-0","ddc":["514"],"file_date_updated":"2022-01-14T07:27:45Z","doi":"10.1007/s11040-021-09415-0","publisher":"Springer Nature","publication_identifier":{"issn":["1385-0172"],"eissn":["1572-9656"]},"day":"11","publication":"Mathematical Physics, Analysis and Geometry","month":"01","_id":"10623","status":"public","year":"2022","article_processing_charge":"Yes (via OA deal)","oa":1,"scopus_import":"1","title":"The BCS critical temperature at high density","keyword":["geometry and topology","mathematical physics"],"isi":1,"corr_author":"1","article_number":"3","abstract":[{"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.","lang":"eng"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"19540"}]},"author":[{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","last_name":"Henheik"}]},{"file_date_updated":"2023-01-30T11:45:13Z","doi":"10.37236/10794","publisher":"Electronic Journal of Combinatorics","ddc":["510"],"fulldoi":"https://doi.org/10.37236/10794","day":"21","publication_identifier":{"eissn":["1077-8926"]},"_id":"12286","month":"10","status":"public","year":"2022","publication":"The Electronic Journal of Combinatorics","scopus_import":"1","title":"Loose cores and cycles in random hypergraphs","article_processing_charge":"No","oa":1,"isi":1,"article_number":"P4.13","keyword":["Computational Theory and Mathematics","Geometry and Topology","Theoretical Computer Science","Applied Mathematics","Discrete Mathematics and Combinatorics"],"abstract":[{"text":"Inspired by the study of loose cycles in hypergraphs, we define the loose core in hypergraphs as a structurewhich mirrors the close relationship between cycles and $2$-cores in graphs. We prove that in the $r$-uniform binomial random hypergraph $H^r(n,p)$, the order of the loose core undergoes a phase transition at a certain critical threshold and determine this order, as well as the number of edges, asymptotically in the subcritical and supercritical regimes.
\r\nOur main tool is an algorithm called CoreConstruct, which enables us to analyse a peeling process for the loose core. By analysing this algorithm we determine the asymptotic degree distribution of vertices in the loose core and in particular how many vertices and edges the loose core contains. As a corollary we obtain an improved upper bound on the length of the longest loose cycle in $H^r(n,p)$.","lang":"eng"}],"author":[{"last_name":"Cooley","first_name":"Oliver","id":"43f4ddd0-a46b-11ec-8df6-ef3703bd721d","full_name":"Cooley, Oliver"},{"first_name":"Mihyun","full_name":"Kang, Mihyun","last_name":"Kang"},{"first_name":"Julian","full_name":"Zalla, Julian","last_name":"Zalla"}],"article_type":"original","tmp":{"image":"/image/cc_by_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","short":"CC BY-ND (4.0)"},"file":[{"date_updated":"2023-01-30T11:45:13Z","relation":"main_file","checksum":"00122b2459f09b5ae43073bfba565e94","file_id":"12462","file_name":"2022_ElecJournCombinatorics_Cooley_Kang_Zalla.pdf","content_type":"application/pdf","success":1,"date_created":"2023-01-30T11:45:13Z","creator":"dernst","file_size":626953,"access_level":"open_access"}],"department":[{"_id":"MaKw"}],"publication_status":"published","date_updated":"2026-08-04T09:29:03Z","date_published":"2022-10-21T00:00:00Z","type":"journal_article","has_accepted_license":"1","quality_controlled":"1","intvolume":" 29","language":[{"iso":"eng"}],"date_created":"2023-01-16T10:03:57Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","citation":{"chicago":"Cooley, Oliver, Mihyun Kang, and Julian Zalla. “Loose Cores and Cycles in Random Hypergraphs.” The Electronic Journal of Combinatorics. Electronic Journal of Combinatorics, 2022. https://doi.org/10.37236/10794.","short":"O. Cooley, M. Kang, J. Zalla, The Electronic Journal of Combinatorics 29 (2022).","ieee":"O. Cooley, M. Kang, and J. Zalla, “Loose cores and cycles in random hypergraphs,” The Electronic Journal of Combinatorics, vol. 29, no. 4. Electronic Journal of Combinatorics, 2022.","mla":"Cooley, Oliver, et al. “Loose Cores and Cycles in Random Hypergraphs.” The Electronic Journal of Combinatorics, vol. 29, no. 4, P4.13, Electronic Journal of Combinatorics, 2022, doi:10.37236/10794.","apa":"Cooley, O., Kang, M., & Zalla, J. (2022). Loose cores and cycles in random hypergraphs. The Electronic Journal of Combinatorics. Electronic Journal of Combinatorics. https://doi.org/10.37236/10794","ista":"Cooley O, Kang M, Zalla J. 2022. Loose cores and cycles in random hypergraphs. The Electronic Journal of Combinatorics. 29(4), P4.13.","ama":"Cooley O, Kang M, Zalla J. Loose cores and cycles in random hypergraphs. The Electronic Journal of Combinatorics. 2022;29(4). doi:10.37236/10794"},"external_id":{"isi":["000876763300001"]},"issue":"4","acknowledgement":"Supported by Austrian Science Fund (FWF): I3747, W1230.","volume":29},{"department":[{"_id":"UlWa"}],"publication_status":"published","date_updated":"2023-08-17T07:07:58Z","article_type":"original","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"success":1,"file_name":"2021_AnalysisMetricSpaces_Ivanov.pdf","content_type":"application/pdf","relation":"main_file","checksum":"7e615ac8489f5eae580b6517debfdc53","file_id":"10857","date_updated":"2022-03-18T09:31:59Z","access_level":"open_access","creator":"dernst","file_size":789801,"date_created":"2022-03-18T09:31:59Z"}],"quality_controlled":"1","arxiv":1,"intvolume":" 9","language":[{"iso":"eng"}],"oa_version":"Published Version","date_created":"2022-03-18T09:25:14Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2021-01-29T00:00:00Z","type":"journal_article","has_accepted_license":"1","issue":"1","citation":{"chicago":"Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.” Analysis and Geometry in Metric Spaces. De Gruyter, 2021. https://doi.org/10.1515/agms-2020-0103.","short":"G. Ivanov, I. Tsiutsiurupa, Analysis and Geometry in Metric Spaces 9 (2021) 1–18.","ieee":"G. Ivanov and I. Tsiutsiurupa, “On the volume of sections of the cube,” Analysis and Geometry in Metric Spaces, vol. 9, no. 1. De Gruyter, pp. 1–18, 2021.","mla":"Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.” Analysis and Geometry in Metric Spaces, vol. 9, no. 1, De Gruyter, 2021, pp. 1–18, doi:10.1515/agms-2020-0103.","apa":"Ivanov, G., & Tsiutsiurupa, I. (2021). On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. De Gruyter. https://doi.org/10.1515/agms-2020-0103","ista":"Ivanov G, Tsiutsiurupa I. 2021. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 9(1), 1–18.","ama":"Ivanov G, Tsiutsiurupa I. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 2021;9(1):1-18. doi:10.1515/agms-2020-0103"},"page":"1-18","external_id":{"isi":["000734286800001"],"arxiv":["2004.02674"]},"volume":9,"acknowledgement":"The authors acknowledge the support of the grant of the Russian Government N 075-15-\r\n2019-1926. G.I.was supported also by the SwissNational Science Foundation grant 200021-179133. The authors are very grateful to the anonymous reviewer for valuable remarks.","day":"29","publication_identifier":{"issn":["2299-3274"]},"file_date_updated":"2022-03-18T09:31:59Z","doi":"10.1515/agms-2020-0103","publisher":"De Gruyter","ddc":["510"],"fulldoi":"https://doi.org/10.1515/agms-2020-0103","scopus_import":"1","title":"On the volume of sections of the cube","article_processing_charge":"No","oa":1,"month":"01","_id":"10856","status":"public","year":"2021","publication":"Analysis and Geometry in Metric Spaces","isi":1,"keyword":["Applied Mathematics","Geometry and Topology","Analysis"],"author":[{"full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","first_name":"Grigory","last_name":"Ivanov"},{"full_name":"Tsiutsiurupa, Igor","first_name":"Igor","last_name":"Tsiutsiurupa"}],"abstract":[{"text":"We study the properties of the maximal volume k-dimensional sections of the n-dimensional cube [−1, 1]n. We obtain a first order necessary condition for a k-dimensional subspace to be a local maximizer of the volume of such sections, which we formulate in a geometric way. We estimate the length of the projection of a vector of the standard basis of Rn onto a k-dimensional subspace that maximizes the volume of the intersection. We \u001cnd the optimal upper bound on the volume of a planar section of the cube [−1, 1]n , n ≥ 2.","lang":"eng"}]},{"extern":"1","publication_status":"published","date_updated":"2025-04-14T09:10:06Z","article_type":"original","quality_controlled":"1","intvolume":" 66","arxiv":1,"language":[{"iso":"eng"}],"oa_version":"Preprint","date_created":"2022-06-17T08:45:15Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2021-10-01T00:00:00Z","type":"journal_article","issue":"3","page":"1202-1216","citation":{"apa":"Avvakumov, S., & Kudrya, S. (2021). Vanishing of all equivariant obstructions and the mapping degree. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-021-00299-z","mla":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” Discrete & Computational Geometry, vol. 66, no. 3, Springer Nature, 2021, pp. 1202–16, doi:10.1007/s00454-021-00299-z.","ama":"Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. Discrete & Computational Geometry. 2021;66(3):1202-1216. doi:10.1007/s00454-021-00299-z","ista":"Avvakumov S, Kudrya S. 2021. Vanishing of all equivariant obstructions and the mapping degree. Discrete & Computational Geometry. 66(3), 1202–1216.","short":"S. Avvakumov, S. Kudrya, Discrete & Computational Geometry 66 (2021) 1202–1216.","ieee":"S. Avvakumov and S. Kudrya, “Vanishing of all equivariant obstructions and the mapping degree,” Discrete & Computational Geometry, vol. 66, no. 3. Springer Nature, pp. 1202–1216, 2021.","chicago":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” Discrete & Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-021-00299-z."},"external_id":{"arxiv":["1910.12628"]},"acknowledgement":"S. Avvakumov has received funding from the European Research Council under the European Union’s Seventh Framework Programme ERC Grant agreement ERC StG 716424–CASe. S. Kudrya was supported by the Austrian Academic Exchange Service (OeAD), ICM-2019-13577.","volume":66,"day":"01","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"doi":"10.1007/s00454-021-00299-z","publisher":"Springer Nature","fulldoi":"https://doi.org/10.1007/s00454-021-00299-z","scopus_import":"1","title":"Vanishing of all equivariant obstructions and the mapping degree","article_processing_charge":"No","status":"public","_id":"11446","month":"10","year":"2021","publication":"Discrete & Computational Geometry","corr_author":"1","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"author":[{"last_name":"Avvakumov","first_name":"Sergey","orcid":"0000-0002-7840-5062","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","full_name":"Avvakumov, Sergey"},{"last_name":"Kudrya","full_name":"Kudrya, Sergey","id":"ecf01965-d252-11ea-95a5-8ada5f6c6a67","first_name":"Sergey"}],"related_material":{"record":[{"relation":"earlier_version","id":"8182","status":"public"}]},"abstract":[{"text":"Suppose that n is not a prime power and not twice a prime power. We prove that for any Hausdorff compactum X with a free action of the symmetric group Sn, there exists an Sn-equivariant map X→Rn whose image avoids the diagonal {(x,x,…,x)∈Rn∣x∈R}. Previously, the special cases of this statement for certain X were usually proved using the equivartiant obstruction theory. Such calculations are difficult and may become infeasible past the first (primary) obstruction. We take a different approach which allows us to prove the vanishing of all obstructions simultaneously. The essential step in the proof is classifying the possible degrees of Sn-equivariant maps from the boundary ∂Δn−1 of (n−1)-simplex to itself. Existence of equivariant maps between spaces is important for many questions arising from discrete mathematics and geometry, such as Kneser’s conjecture, the Square Peg conjecture, the Splitting Necklace problem, and the Topological Tverberg conjecture, etc. We demonstrate the utility of our result applying it to one such question, a specific instance of envy-free division problem.","lang":"eng"}]},{"publication_status":"published","department":[{"_id":"HeEd"}],"date_updated":"2025-04-14T07:43:50Z","article_type":"original","file":[{"file_id":"9795","checksum":"c848986091e56699dc12de85adb1e39c","relation":"main_file","date_updated":"2021-08-06T09:52:29Z","success":1,"content_type":"application/pdf","file_name":"2021_DescreteCompGeopmetry_Boissonnat.pdf","file_size":983307,"creator":"kschuh","date_created":"2021-08-06T09:52:29Z","access_level":"open_access"}],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"intvolume":" 66","quality_controlled":"1","oa_version":"Published Version","date_created":"2020-12-12T11:07:02Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","language":[{"iso":"eng"}],"date_published":"2021-07-01T00:00:00Z","has_accepted_license":"1","type":"journal_article","ec_funded":1,"issue":"1","external_id":{"isi":["000597770300001"]},"citation":{"short":"J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, Discrete & Computational Geometry 66 (2021) 386–434.","ieee":"J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Triangulating submanifolds: An elementary and quantified version of Whitney’s method,” Discrete & Computational Geometry, vol. 66, no. 1. Springer Nature, pp. 386–434, 2021.","mla":"Boissonnat, Jean-Daniel, et al. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry, vol. 66, no. 1, Springer Nature, 2021, pp. 386–434, doi:10.1007/s00454-020-00250-8.","apa":"Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00250-8","ama":"Boissonnat J-D, Kachanovich S, Wintraecken M. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 2021;66(1):386-434. doi:10.1007/s00454-020-00250-8","ista":"Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 66(1), 386–434.","chicago":"Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00250-8."},"page":"386-434","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"volume":66,"acknowledgement":"This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement Number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). The third author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. Open access funding provided by the Institute of Science and Technology (IST Austria).","day":"01","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"publisher":"Springer Nature","file_date_updated":"2021-08-06T09:52:29Z","doi":"10.1007/s00454-020-00250-8","ddc":["516"],"fulldoi":"https://doi.org/10.1007/s00454-020-00250-8","title":"Triangulating submanifolds: An elementary and quantified version of Whitney’s method","scopus_import":"1","oa":1,"article_processing_charge":"Yes (via OA deal)","year":"2021","status":"public","_id":"8940","month":"07","publication":"Discrete & Computational Geometry","isi":1,"corr_author":"1","keyword":["Theoretical Computer Science","Computational Theory and Mathematics","Geometry and Topology","Discrete Mathematics and Combinatorics"],"author":[{"first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat"},{"last_name":"Kachanovich","full_name":"Kachanovich, Siargey","first_name":"Siargey"},{"orcid":"0000-0002-7472-2220","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken"}],"abstract":[{"lang":"eng","text":"We quantise Whitney’s construction to prove the existence of a triangulation for any C^2 manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric."}]}]