[{"department":[{"_id":"HeEd"}],"date_updated":"2021-12-03T07:31:26Z","status":"public","type":"journal_article","article_type":"letter_note","_id":"10071","volume":68,"issue":"9","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["1088-9477"],"issn":["0002-9920"]},"intvolume":" 68","month":"10","main_file_link":[{"open_access":"1","url":"http://www.ams.org/notices/"}],"scopus_import":"1","alternative_title":["Early Career"],"oa_version":"Published Version","title":"How to tutorial-a-thon","article_processing_charge":"No","author":[{"first_name":"Henry","last_name":"Adams","full_name":"Adams, Henry"},{"id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","first_name":"Hana","last_name":"Kourimska","full_name":"Kourimska, Hana"},{"first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa"},{"last_name":"Percival","full_name":"Percival, Sarah","first_name":"Sarah"},{"full_name":"Ziegelmeier, Lori","last_name":"Ziegelmeier","first_name":"Lori"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"mla":"Adams, Henry, et al. “How to Tutorial-a-Thon.” Notices of the American Mathematical Society, vol. 68, no. 9, American Mathematical Society, 2021, pp. 1511–14, doi:10.1090/noti2349.","short":"H. Adams, H. Kourimska, T. Heiss, S. Percival, L. Ziegelmeier, Notices of the American Mathematical Society 68 (2021) 1511–1514.","ieee":"H. Adams, H. Kourimska, T. Heiss, S. Percival, and L. Ziegelmeier, “How to tutorial-a-thon,” Notices of the American Mathematical Society, vol. 68, no. 9. American Mathematical Society, pp. 1511–1514, 2021.","ama":"Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. How to tutorial-a-thon. Notices of the American Mathematical Society. 2021;68(9):1511-1514. doi:10.1090/noti2349","apa":"Adams, H., Kourimska, H., Heiss, T., Percival, S., & Ziegelmeier, L. (2021). How to tutorial-a-thon. Notices of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/noti2349","chicago":"Adams, Henry, Hana Kourimska, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier. “How to Tutorial-a-Thon.” Notices of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/noti2349.","ista":"Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. 2021. How to tutorial-a-thon. Notices of the American Mathematical Society. 68(9), 1511–1514."},"date_created":"2021-10-03T22:01:22Z","doi":"10.1090/noti2349","date_published":"2021-10-01T00:00:00Z","page":"1511-1514","publication":"Notices of the American Mathematical Society","day":"01","year":"2021","oa":1,"quality_controlled":"1","publisher":"American Mathematical Society"},{"citation":{"ama":"Ilharco C, Shirazi A, Gopalan A, et al. Recognizing multimodal entailment. In: 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts. Association for Computational Linguistics; 2021:29-30. doi:10.18653/v1/2021.acl-tutorials.6","apa":"Ilharco, C., Shirazi, A., Gopalan, A., Nagrani, A., Bratanič, B., Bregler, C., … Imbrasaite, V. (2021). Recognizing multimodal entailment. In 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts (pp. 29–30). Bangkok, Thailand: Association for Computational Linguistics. https://doi.org/10.18653/v1/2021.acl-tutorials.6","ieee":"C. Ilharco et al., “Recognizing multimodal entailment,” in 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Bangkok, Thailand, 2021, pp. 29–30.","short":"C. Ilharco, A. Shirazi, A. Gopalan, A. Nagrani, B. Bratanič, C. Bregler, C. Liu, F. Ferreira, G. Barcik, G. Ilharco, G.F. Osang, J. Bulian, J. Frank, L. Smaira, Q. Cao, R. Marino, R. Patel, T. Leung, V. Imbrasaite, in:, 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Association for Computational Linguistics, 2021, pp. 29–30.","mla":"Ilharco, Cesar, et al. “Recognizing Multimodal Entailment.” 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Association for Computational Linguistics, 2021, pp. 29–30, doi:10.18653/v1/2021.acl-tutorials.6.","ista":"Ilharco C, Shirazi A, Gopalan A, Nagrani A, Bratanič B, Bregler C, Liu C, Ferreira F, Barcik G, Ilharco G, Osang GF, Bulian J, Frank J, Smaira L, Cao Q, Marino R, Patel R, Leung T, Imbrasaite V. 2021. Recognizing multimodal entailment. 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts. ACL: Association for Computational Linguistics ; IJCNLP: International Joint Conference on Natural Language Processing, 29–30.","chicago":"Ilharco, Cesar, Afsaneh Shirazi, Arjun Gopalan, Arsha Nagrani, Blaž Bratanič, Chris Bregler, Christina Liu, et al. “Recognizing Multimodal Entailment.” In 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, 29–30. Association for Computational Linguistics, 2021. https://doi.org/10.18653/v1/2021.acl-tutorials.6."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","author":[{"last_name":"Ilharco","full_name":"Ilharco, Cesar","first_name":"Cesar"},{"full_name":"Shirazi, Afsaneh","last_name":"Shirazi","first_name":"Afsaneh"},{"last_name":"Gopalan","full_name":"Gopalan, Arjun","first_name":"Arjun"},{"first_name":"Arsha","full_name":"Nagrani, Arsha","last_name":"Nagrani"},{"first_name":"Blaž","last_name":"Bratanič","full_name":"Bratanič, Blaž"},{"full_name":"Bregler, Chris","last_name":"Bregler","first_name":"Chris"},{"first_name":"Christina","full_name":"Liu, Christina","last_name":"Liu"},{"first_name":"Felipe","full_name":"Ferreira, Felipe","last_name":"Ferreira"},{"first_name":"Gabriek","last_name":"Barcik","full_name":"Barcik, Gabriek"},{"full_name":"Ilharco, Gabriel","last_name":"Ilharco","first_name":"Gabriel"},{"first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","full_name":"Osang, Georg F"},{"first_name":"Jannis","last_name":"Bulian","full_name":"Bulian, Jannis"},{"first_name":"Jared","full_name":"Frank, Jared","last_name":"Frank"},{"full_name":"Smaira, Lucas","last_name":"Smaira","first_name":"Lucas"},{"full_name":"Cao, Qin","last_name":"Cao","first_name":"Qin"},{"first_name":"Ricardo","full_name":"Marino, Ricardo","last_name":"Marino"},{"first_name":"Roma","full_name":"Patel, Roma","last_name":"Patel"},{"first_name":"Thomas","full_name":"Leung, Thomas","last_name":"Leung"},{"full_name":"Imbrasaite, Vaiva","last_name":"Imbrasaite","first_name":"Vaiva"}],"article_processing_charge":"No","title":"Recognizing multimodal entailment","has_accepted_license":"1","year":"2021","day":"01","publication":"59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts","page":"29-30","doi":"10.18653/v1/2021.acl-tutorials.6","date_published":"2021-08-01T00:00:00Z","date_created":"2021-11-28T23:01:30Z","acknowledgement":"We would like to thank Abby Schantz, Abe Ittycheriah, Aliaksei Severyn, Allan Heydon, Aly\r\nGrealish, Andrey Vlasov, Arkaitz Zubiaga, Ashwin Kakarla, Chen Sun, Clayton Williams, Cong\r\nYu, Cordelia Schmid, Da-Cheng Juan, Dan Finnie, Dani Valevski, Daniel Rocha, David Price, David Sklar, Devi Krishna, Elena Kochkina, Enrique Alfonseca, Franc¸oise Beaufays, Isabelle Augenstein, Jialu Liu, John Cantwell, John Palowitch, Jordan Boyd-Graber, Lei Shi, Luis Valente, Maria Voitovich, Mehmet Aktuna, Mogan Brown, Mor Naaman, Natalia P, Nidhi Hebbar, Pete Aykroyd, Rahul Sukthankar, Richa Dixit, Steve Pucci, Tania Bedrax-Weiss, Tobias Kaufmann, Tom Boulos, Tu Tsao, Vladimir Chtchetkine, Yair Kurzion, Yifan Xu and Zach Hynes.","publisher":"Association for Computational Linguistics","quality_controlled":"1","oa":1,"date_updated":"2022-01-26T14:26:36Z","ddc":["000"],"department":[{"_id":"HeEd"}],"file_date_updated":"2021-11-29T08:41:00Z","_id":"10367","type":"conference","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"name":"ACL: Association for Computational Linguistics ; IJCNLP: International Joint Conference on Natural Language Processing","end_date":"2021-08-06","location":"Bangkok, Thailand","start_date":"2021-08-01"},"status":"public","publication_identifier":{"isbn":["9-781-9540-8557-2"]},"publication_status":"published","file":[{"date_created":"2021-11-29T08:41:00Z","file_name":"2021_ACL_Ilharco.pdf","date_updated":"2021-11-29T08:41:00Z","file_size":1227703,"creator":"cchlebak","checksum":"b14052a025a6ecf675bdfe51db98c0d7","file_id":"10368","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"abstract":[{"text":"How information is created, shared and consumed has changed rapidly in recent decades, in part thanks to new social platforms and technologies on the web. With ever-larger amounts of unstructured and limited labels, organizing and reconciling information from different sources and modalities is a central challenge in machine learning. This cutting-edge tutorial aims to introduce the multimodal entailment task, which can be useful for detecting semantic alignments when a single modality alone does not suffice for a whole content understanding. Starting with a brief overview of natural language processing, computer vision, structured data and neural graph learning, we lay the foundations for the multimodal sections to follow. We then discuss recent multimodal learning literature covering visual, audio and language streams, and explore case studies focusing on tasks which require fine-grained understanding of visual and linguistic semantics question answering, veracity and hatred classification. Finally, we introduce a new dataset for recognizing multimodal entailment, exploring it in a hands-on collaborative section. Overall, this tutorial gives an overview of multimodal learning, introduces a multimodal entailment dataset, and encourages future research in the topic.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","main_file_link":[{"url":"https://aclanthology.org/2021.acl-tutorials.6/","open_access":"1"}],"month":"08"},{"file":[{"date_updated":"2022-01-10T08:33:22Z","file_size":384908,"creator":"cchlebak","date_created":"2022-01-10T08:33:22Z","file_name":"2021_EuJournalMath_Weighill.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"c435dcfa1ad3aadc5cdd7366bc7f4e98","file_id":"10610","success":1}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"publication_status":"published","month":"12","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider infinite-dimensional properties in coarse geometry for hyperspaces consisting of finite subsets of metric spaces with the Hausdorff metric. We see that several infinite-dimensional properties are preserved by taking the hyperspace of subsets with at most n points. On the other hand, we prove that, if a metric space contains a sequence of long intervals coarsely, then its hyperspace of finite subsets is not coarsely embeddable into any uniformly convex Banach space. As a corollary, the hyperspace of finite subsets of the real line is not coarsely embeddable into any uniformly convex Banach space. It is also shown that every (not necessarily bounded geometry) metric space with straight finite decomposition complexity has metric sparsification property."}],"department":[{"_id":"HeEd"}],"file_date_updated":"2022-01-10T08:33:22Z","ddc":["500"],"date_updated":"2022-01-10T08:36:55Z","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"10608","date_published":"2021-12-30T00:00:00Z","doi":"10.1007/s40879-021-00515-3","date_created":"2022-01-09T23:01:27Z","day":"30","publication":"European Journal of Mathematics","has_accepted_license":"1","year":"2021","quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"We would like to thank the referees for their careful reading and the comments that improved our work. The third named author would like to thank the Division of Mathematics, Physics and Earth Sciences of the Graduate School of Science and Engineering of Ehime University and the second named author for hosting his visit in June 2018. Open access funding provided by Institute of Science and Technology (IST Austria).","title":"Coarse infinite-dimensionality of hyperspaces of finite subsets","author":[{"full_name":"Weighill, Thomas","last_name":"Weighill","first_name":"Thomas"},{"last_name":"Yamauchi","full_name":"Yamauchi, Takamitsu","first_name":"Takamitsu"},{"id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","first_name":"Nicolò","full_name":"Zava, Nicolò","last_name":"Zava"}],"article_processing_charge":"Yes (via OA deal)","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"ista":"Weighill T, Yamauchi T, Zava N. 2021. Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics.","chicago":"Weighill, Thomas, Takamitsu Yamauchi, and Nicolò Zava. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” European Journal of Mathematics. Springer Nature, 2021. https://doi.org/10.1007/s40879-021-00515-3.","ieee":"T. Weighill, T. Yamauchi, and N. Zava, “Coarse infinite-dimensionality of hyperspaces of finite subsets,” European Journal of Mathematics. Springer Nature, 2021.","short":"T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics (2021).","apa":"Weighill, T., Yamauchi, T., & Zava, N. (2021). Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-021-00515-3","ama":"Weighill T, Yamauchi T, Zava N. Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics. 2021. doi:10.1007/s40879-021-00515-3","mla":"Weighill, Thomas, et al. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” European Journal of Mathematics, Springer Nature, 2021, doi:10.1007/s40879-021-00515-3."}},{"acknowledgement":"A.A. funded by the Marie Skłodowska-Curie grant agreement No. 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE).","oa":1,"quality_controlled":"1","publisher":"Springer Nature","publication":"15th International Conference on Algorithms and Computation","day":"16","year":"2021","date_created":"2021-03-28T22:01:41Z","doi":"10.1007/978-3-030-68211-8_18","date_published":"2021-02-16T00:00:00Z","page":"221-233","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"name":"The Wittgenstein Prize","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307","call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425"},{"name":"Modern Graph Algorithmic Techniques in Formal Verification","grant_number":"P 23499-N23","_id":"2584A770-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"S11407","name":"Game Theory","_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” In 15th International Conference on Algorithms and Computation, 12635:221–33. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-68211-8_18.","ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2021. On compatible matchings. 15th International Conference on Algorithms and Computation. WALCOM: Algorithms and Computation, LNCS, vol. 12635, 221–233.","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” 15th International Conference on Algorithms and Computation, vol. 12635, Springer Nature, 2021, pp. 221–33, doi:10.1007/978-3-030-68211-8_18.","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2021). On compatible matchings. In 15th International Conference on Algorithms and Computation (Vol. 12635, pp. 221–233). Yangon, Myanmar: Springer Nature. https://doi.org/10.1007/978-3-030-68211-8_18","ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. In: 15th International Conference on Algorithms and Computation. Vol 12635. Springer Nature; 2021:221-233. doi:10.1007/978-3-030-68211-8_18","ieee":"O. Aichholzer et al., “On compatible matchings,” in 15th International Conference on Algorithms and Computation, Yangon, Myanmar, 2021, vol. 12635, pp. 221–233.","short":"O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, in:, 15th International Conference on Algorithms and Computation, Springer Nature, 2021, pp. 221–233."},"title":"On compatible matchings","article_processing_charge":"No","external_id":{"arxiv":["2101.03928"]},"author":[{"first_name":"Oswin","full_name":"Aichholzer, Oswin","last_name":"Aichholzer"},{"last_name":"Arroyo Guevara","orcid":"0000-0003-2401-8670","full_name":"Arroyo Guevara, Alan M","first_name":"Alan M","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","last_name":"Masárová","first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Parada, Irene","last_name":"Parada","first_name":"Irene"},{"last_name":"Perz","full_name":"Perz, Daniel","first_name":"Daniel"},{"first_name":"Alexander","last_name":"Pilz","full_name":"Pilz, Alexander"},{"last_name":"Tkadlec","full_name":"Tkadlec, Josef","orcid":"0000-0002-1097-9684","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","first_name":"Josef"},{"full_name":"Vogtenhuber, Birgit","last_name":"Vogtenhuber","first_name":"Birgit"}],"oa_version":"Preprint","abstract":[{"text":" matching is compatible to two or more labeled point sets of size n with labels {1,…,n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of n points there exists a compatible matching with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(logn) copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge.","lang":"eng"}],"intvolume":" 12635","month":"02","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2101.03928"}],"scopus_import":"1","alternative_title":["LNCS"],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["03029743"],"eissn":["16113349"],"isbn":["9783030682101"]},"ec_funded":1,"volume":12635,"related_material":{"record":[{"status":"public","id":"11938","relation":"later_version"}]},"_id":"9296","status":"public","conference":{"start_date":"2021-02-28","location":"Yangon, Myanmar","end_date":"2021-03-02","name":"WALCOM: Algorithms and Computation"},"type":"conference","date_updated":"2023-02-21T16:33:44Z","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}]},{"_id":"9465","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"date_updated":"2022-05-12T11:41:45Z","department":[{"_id":"HeEd"}],"file_date_updated":"2021-06-11T13:16:26Z","oa_version":"Published Version","abstract":[{"text":"Given a locally finite set 𝑋⊆ℝ𝑑 and an integer 𝑘≥0, we consider the function 𝐰𝑘:Del𝑘(𝑋)→ℝ on the dual of the order-k Voronoi tessellation, whose sublevel sets generalize the notion of alpha shapes from order-1 to order-k (Edelsbrunner et al. in IEEE Trans Inf Theory IT-29:551–559, 1983; Krasnoshchekov and Polishchuk in Inf Process Lett 114:76–83, 2014). While this function is not necessarily generalized discrete Morse, in the sense of Forman (Adv Math 134:90–145, 1998) and Freij (Discrete Math 309:3821–3829, 2009), we prove that it satisfies similar properties so that its increments can be meaningfully classified into critical and non-critical steps. This result extends to the case of weighted points and sheds light on k-fold covers with balls in Euclidean space.","lang":"eng"}],"month":"04","intvolume":" 112","scopus_import":"1","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"e52a832f1def52a2b23d21bcc09e646f","file_id":"9544","file_size":694706,"date_updated":"2021-06-11T13:16:26Z","creator":"kschuh","file_name":"2021_Geometry_Edelsbrunner.pdf","date_created":"2021-06-11T13:16:26Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["00472468"],"eissn":["14208997"]},"publication_status":"published","volume":112,"issue":"1","article_number":"15","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Edelsbrunner, Herbert, et al. “A Step in the Delaunay Mosaic of Order K.” Journal of Geometry, vol. 112, no. 1, 15, Springer Nature, 2021, doi:10.1007/s00022-021-00577-4.","short":"H. Edelsbrunner, A. Nikitenko, G.F. Osang, Journal of Geometry 112 (2021).","ieee":"H. Edelsbrunner, A. Nikitenko, and G. F. Osang, “A step in the Delaunay mosaic of order k,” Journal of Geometry, vol. 112, no. 1. Springer Nature, 2021.","ama":"Edelsbrunner H, Nikitenko A, Osang GF. A step in the Delaunay mosaic of order k. Journal of Geometry. 2021;112(1). doi:10.1007/s00022-021-00577-4","apa":"Edelsbrunner, H., Nikitenko, A., & Osang, G. F. (2021). A step in the Delaunay mosaic of order k. Journal of Geometry. Springer Nature. https://doi.org/10.1007/s00022-021-00577-4","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, and Georg F Osang. “A Step in the Delaunay Mosaic of Order K.” Journal of Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00022-021-00577-4.","ista":"Edelsbrunner H, Nikitenko A, Osang GF. 2021. A step in the Delaunay mosaic of order k. Journal of Geometry. 112(1), 15."},"title":"A step in the Delaunay mosaic of order k","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","full_name":"Nikitenko, Anton"},{"first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","full_name":"Osang, Georg F","last_name":"Osang"}],"article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","quality_controlled":"1","oa":1,"day":"01","publication":"Journal of Geometry","has_accepted_license":"1","year":"2021","doi":"10.1007/s00022-021-00577-4","date_published":"2021-04-01T00:00:00Z","date_created":"2021-06-06T22:01:29Z"},{"status":"public","type":"conference","conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2021-06-07","end_date":"2021-06-11","location":"Virtual"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"9345","file_date_updated":"2021-04-22T08:08:14Z","department":[{"_id":"HeEd"}],"ddc":["004","516"],"date_updated":"2023-02-23T13:55:40Z","month":"06","intvolume":" 189","alternative_title":["LIPIcs"],"oa_version":"Published Version","abstract":[{"text":"Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functionsthat facilitates the efficient search for new materials and material properties. We prove invarianceunder isometries, continuity, and completeness in the generic case, which are necessary featuresfor the reliable comparison of crystals. The proof of continuity integrates methods from discretegeometry and lattice theory, while the proof of generic completeness combines techniques fromgeometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and relatedinclusion-exclusion formulae. We have implemented the algorithm and describe its application tocrystal structure prediction.","lang":"eng"}],"volume":189,"ec_funded":1,"file":[{"file_name":"df_socg_final_version.pdf","date_created":"2021-04-22T08:08:14Z","file_size":3117435,"date_updated":"2021-04-22T08:08:14Z","creator":"mwintrae","success":1,"checksum":"1787baef1523d6d93753b90d0c109a6d","file_id":"9346","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1868-8969"]},"publication_status":"published","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Discretization in Geometry and Dynamics","grant_number":"I4887"},{"name":"The Wittgenstein Prize","grant_number":"Z00312","call_identifier":"FWF","_id":"25C5A090-B435-11E9-9278-68D0E5697425"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"title":"The density fingerprint of a periodic point set","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689","last_name":"Heiss"},{"first_name":"Vitaliy","last_name":" Kurlin ","full_name":" Kurlin , Vitaliy"},{"first_name":"Philip","last_name":"Smith","full_name":"Smith, Philip"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220"}],"article_processing_charge":"No","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"mla":"Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point Set.” 37th International Symposium on Computational Geometry (SoCG 2021), vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16, doi:10.4230/LIPIcs.SoCG.2021.32.","apa":"Edelsbrunner, H., Heiss, T., Kurlin , V., Smith, P., & Wintraecken, M. (2021). The density fingerprint of a periodic point set. In 37th International Symposium on Computational Geometry (SoCG 2021) (Vol. 189, p. 32:1-32:16). Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.32","ama":"Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. The density fingerprint of a periodic point set. In: 37th International Symposium on Computational Geometry (SoCG 2021). Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:32:1-32:16. doi:10.4230/LIPIcs.SoCG.2021.32","ieee":"H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, and M. Wintraecken, “The density fingerprint of a periodic point set,” in 37th International Symposium on Computational Geometry (SoCG 2021), Virtual, 2021, vol. 189, p. 32:1-32:16.","short":"H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, M. Wintraecken, in:, 37th International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16.","chicago":"Edelsbrunner, Herbert, Teresa Heiss, Vitaliy Kurlin , Philip Smith, and Mathijs Wintraecken. “The Density Fingerprint of a Periodic Point Set.” In 37th International Symposium on Computational Geometry (SoCG 2021), 189:32:1-32:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.32.","ista":"Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. 2021. The density fingerprint of a periodic point set. 37th International Symposium on Computational Geometry (SoCG 2021). SoCG: Symposium on Computational Geometry, LIPIcs, vol. 189, 32:1-32:16."},"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","oa":1,"acknowledgement":"The authors thank Janos Pach for insightful discussions on the topic of thispaper, Morteza Saghafian for finding the one-dimensional counterexample mentioned in Section 5,and Larry Andrews for generously sharing his crystallographic perspective.","date_published":"2021-06-02T00:00:00Z","doi":"10.4230/LIPIcs.SoCG.2021.32","date_created":"2021-04-22T08:09:58Z","page":"32:1-32:16","day":"02","publication":"37th International Symposium on Computational Geometry (SoCG 2021)","has_accepted_license":"1","year":"2021"},{"ddc":["516"],"date_updated":"2023-02-23T14:02:28Z","file_date_updated":"2021-06-28T13:11:39Z","department":[{"_id":"HeEd"}],"_id":"9604","status":"public","type":"conference","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"start_date":"2021-06-07","end_date":"2021-06-11","location":"Online","name":"SoCG: International Symposium on Computational Geometry"},"file":[{"date_created":"2021-06-28T13:11:39Z","file_name":"2021_LIPIcs_Biswas.pdf","date_updated":"2021-06-28T13:11:39Z","file_size":727817,"creator":"asandaue","checksum":"22b11a719018b22ecba2471b51f2eb40","file_id":"9611","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["18688969"],"isbn":["9783959771849"]},"publication_status":"published","volume":189,"ec_funded":1,"oa_version":"Published Version","abstract":[{"text":"Generalizing Lee’s inductive argument for counting the cells of higher order Voronoi tessellations in ℝ² to ℝ³, we get precise relations in terms of Morse theoretic quantities for piecewise constant functions on planar arrangements. Specifically, we prove that for a generic set of n ≥ 5 points in ℝ³, the number of regions in the order-k Voronoi tessellation is N_{k-1} - binom(k,2)n + n, for 1 ≤ k ≤ n-1, in which N_{k-1} is the sum of Euler characteristics of these function’s first k-1 sublevel sets. We get similar expressions for the vertices, edges, and polygons of the order-k Voronoi tessellation.","lang":"eng"}],"month":"06","intvolume":" 189","alternative_title":["LIPIcs"],"scopus_import":"1","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2021. Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 16.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Counting Cells of Order-k Voronoi Tessellations in ℝ3 with Morse Theory.” In Leibniz International Proceedings in Informatics, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.16.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. In: Leibniz International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.16","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2021). Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. In Leibniz International Proceedings in Informatics (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.16","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. 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We propose a characterization of 3D discrete analytical planes with their topological features (in the Cartesian and in the new coordinate system) such as the interrelation between the thickness of the plane and the separability constraint we aim to obtain.","lang":"eng"}],"oa_version":"None","volume":12708,"ec_funded":1,"publication_identifier":{"issn":["03029743"],"isbn":["9783030766566"],"eissn":["16113349"]},"publication_status":"published","language":[{"iso":"eng"}],"project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"author":[{"last_name":"Čomić","full_name":"Čomić, Lidija","first_name":"Lidija"},{"full_name":"Zrour, Rita","last_name":"Zrour","first_name":"Rita"},{"full_name":"Largeteau-Skapin, Gaëlle","last_name":"Largeteau-Skapin","first_name":"Gaëlle"},{"orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita"},{"first_name":"Eric","full_name":"Andres, Eric","last_name":"Andres"}],"article_processing_charge":"No","title":"Body centered cubic grid - coordinate system and discrete analytical plane definition","citation":{"mla":"Čomić, Lidija, et al. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” Discrete Geometry and Mathematical Morphology, vol. 12708, Springer Nature, 2021, pp. 152–63, doi:10.1007/978-3-030-76657-3_10.","ieee":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, and E. Andres, “Body centered cubic grid - coordinate system and discrete analytical plane definition,” in Discrete Geometry and Mathematical Morphology, Uppsala, Sweden, 2021, vol. 12708, pp. 152–163.","short":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.","apa":"Čomić, L., Zrour, R., Largeteau-Skapin, G., Biswas, R., & Andres, E. (2021). Body centered cubic grid - coordinate system and discrete analytical plane definition. In Discrete Geometry and Mathematical Morphology (Vol. 12708, pp. 152–163). Uppsala, Sweden: Springer Nature. https://doi.org/10.1007/978-3-030-76657-3_10","ama":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. Body centered cubic grid - coordinate system and discrete analytical plane definition. In: Discrete Geometry and Mathematical Morphology. Vol 12708. Springer Nature; 2021:152-163. doi:10.1007/978-3-030-76657-3_10","chicago":"Čomić, Lidija, Rita Zrour, Gaëlle Largeteau-Skapin, Ranita Biswas, and Eric Andres. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” In Discrete Geometry and Mathematical Morphology, 12708:152–63. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-76657-3_10.","ista":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. 2021. Body centered cubic grid - coordinate system and discrete analytical plane definition. Discrete Geometry and Mathematical Morphology. DGMM: International Conference on Discrete Geometry and Mathematical Morphology, LNCS, vol. 12708, 152–163."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publisher":"Springer Nature","acknowledgement":"This work has been partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia through the project no. 451-03-68/2020-14/200156: “Innovative scientific and artistic research from the FTS (activity) domain” (LČ), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183 (RB), and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35 (RB).","page":"152-163","doi":"10.1007/978-3-030-76657-3_10","date_published":"2021-05-16T00:00:00Z","date_created":"2021-08-08T22:01:29Z","year":"2021","day":"16","publication":"Discrete Geometry and Mathematical Morphology"},{"department":[{"_id":"HeEd"}],"date_updated":"2023-08-04T10:57:42Z","type":"journal_article","article_type":"original","status":"public","_id":"8317","related_material":{"record":[{"id":"6989","status":"public","relation":"shorter_version"}]},"volume":93,"publication_status":"published","publication_identifier":{"issn":["09257721"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.09917v3"}],"scopus_import":"1","intvolume":" 93","month":"02","abstract":[{"text":"When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability.","lang":"eng"}],"oa_version":"Preprint","article_processing_charge":"No","external_id":{"arxiv":["1910.09917"],"isi":["000579185100004"]},"author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"full_name":"Akitaya, Hugo A.","last_name":"Akitaya","first_name":"Hugo A."},{"full_name":"Cheung, Kenneth C.","last_name":"Cheung","first_name":"Kenneth C."},{"first_name":"Erik D.","last_name":"Demaine","full_name":"Demaine, Erik D."},{"last_name":"Demaine","full_name":"Demaine, Martin L.","first_name":"Martin L."},{"full_name":"Fekete, Sándor P.","last_name":"Fekete","first_name":"Sándor P."},{"first_name":"Linda","last_name":"Kleist","full_name":"Kleist, Linda"},{"first_name":"Irina","last_name":"Kostitsyna","full_name":"Kostitsyna, Irina"},{"last_name":"Löffler","full_name":"Löffler, Maarten","first_name":"Maarten"},{"orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana"},{"last_name":"Mundilova","full_name":"Mundilova, Klara","first_name":"Klara"},{"last_name":"Schmidt","full_name":"Schmidt, Christiane","first_name":"Christiane"}],"title":"Folding polyominoes with holes into a cube","citation":{"chicago":"Aichholzer, Oswin, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” Computational Geometry: Theory and Applications. Elsevier, 2021. https://doi.org/10.1016/j.comgeo.2020.101700.","ista":"Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2021. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 93, 101700.","mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Computational Geometry: Theory and Applications, vol. 93, 101700, Elsevier, 2021, doi:10.1016/j.comgeo.2020.101700.","ieee":"O. Aichholzer et al., “Folding polyominoes with holes into a cube,” Computational Geometry: Theory and Applications, vol. 93. Elsevier, 2021.","short":"O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P. Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt, Computational Geometry: Theory and Applications 93 (2021).","ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 2021;93. doi:10.1016/j.comgeo.2020.101700","apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2021). Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2020.101700"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize","grant_number":"Z00342"}],"article_number":"101700","date_created":"2020-08-30T22:01:09Z","doi":"10.1016/j.comgeo.2020.101700","date_published":"2021-02-01T00:00:00Z","year":"2021","isi":1,"publication":"Computational Geometry: Theory and Applications","day":"01","oa":1,"publisher":"Elsevier","quality_controlled":"1","acknowledgement":"This research was performed in part at the 33rd Bellairs Winter Workshop on Computational Geometry. We thank all other participants for a fruitful atmosphere. H. Akitaya was supported by NSF CCF-1422311 & 1423615. Z. Masárová was partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31."},{"citation":{"mla":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society, vol. 149, no. 1, American Mathematical Society, 2021, pp. 37–52, doi:10.1090/proc/15205.","short":"A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2021) 37–52.","ieee":"A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” Proceedings of the American Mathematical Society, vol. 149, no. 1. American Mathematical Society, pp. 37–52, 2021.","apa":"Brown, A., & Romanov, A. (2021). Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/15205","ama":"Brown A, Romanov A. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 2021;149(1):37-52. doi:10.1090/proc/15205","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/proc/15205.","ista":"Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown","full_name":"Brown, Adam"},{"first_name":"Anna","last_name":"Romanov","full_name":"Romanov, Anna"}],"article_processing_charge":"No","external_id":{"arxiv":["1910.08286"],"isi":["000600416300004"]},"title":"Contravariant forms on Whittaker modules","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"isi":1,"year":"2021","day":"01","publication":"Proceedings of the American Mathematical Society","page":"37-52","doi":"10.1090/proc/15205","date_published":"2021-01-01T00:00:00Z","date_created":"2020-11-19T10:17:40Z","acknowledgement":"We would like to thank Peter Trapa for useful discussions, and Dragan Milicic and Arun Ram for valuable feedback on the structure of the paper. The first author acknowledges the support of the European Unions Horizon 2020 research and innovation programme under the Marie Skodowska-Curie Grant Agreement No. 754411. The second author is\r\nsupported by the National Science Foundation Award No. 1803059.","publisher":"American Mathematical Society","quality_controlled":"1","oa":1,"date_updated":"2023-08-04T11:11:47Z","department":[{"_id":"HeEd"}],"_id":"8773","type":"journal_article","article_type":"original","status":"public","keyword":["Applied Mathematics","General Mathematics"],"publication_identifier":{"eissn":["1088-6826"],"issn":["0002-9939"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":149,"issue":"1","ec_funded":1,"abstract":[{"lang":"eng","text":"Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.08286"}],"month":"01","intvolume":" 149"}]