---
_id: '10071'
alternative_title:
- Early Career
article_processing_charge: No
article_type: letter_note
author:
- first_name: Henry
full_name: Adams, Henry
last_name: Adams
- first_name: Hana
full_name: Kourimska, Hana
id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
last_name: Kourimska
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Sarah
full_name: Percival, Sarah
last_name: Percival
- first_name: Lori
full_name: Ziegelmeier, Lori
last_name: Ziegelmeier
citation:
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.
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.
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.
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.
date_created: 2021-10-03T22:01:22Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2021-12-03T07:31:26Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/noti2349
intvolume: ' 68'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ams.org/notices/
month: '10'
oa: 1
oa_version: Published Version
page: 1511-1514
publication: Notices of the American Mathematical Society
publication_identifier:
eissn:
- 1088-9477
issn:
- 0002-9920
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: How to tutorial-a-thon
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 68
year: '2021'
...
---
_id: '10367'
abstract:
- lang: eng
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.
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."
article_processing_charge: No
author:
- first_name: Cesar
full_name: Ilharco, Cesar
last_name: Ilharco
- first_name: Afsaneh
full_name: Shirazi, Afsaneh
last_name: Shirazi
- first_name: Arjun
full_name: Gopalan, Arjun
last_name: Gopalan
- first_name: Arsha
full_name: Nagrani, Arsha
last_name: Nagrani
- first_name: Blaž
full_name: Bratanič, Blaž
last_name: Bratanič
- first_name: Chris
full_name: Bregler, Chris
last_name: Bregler
- first_name: Christina
full_name: Liu, Christina
last_name: Liu
- first_name: Felipe
full_name: Ferreira, Felipe
last_name: Ferreira
- first_name: Gabriek
full_name: Barcik, Gabriek
last_name: Barcik
- first_name: Gabriel
full_name: Ilharco, Gabriel
last_name: Ilharco
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
- first_name: Jannis
full_name: Bulian, Jannis
last_name: Bulian
- first_name: Jared
full_name: Frank, Jared
last_name: Frank
- first_name: Lucas
full_name: Smaira, Lucas
last_name: Smaira
- first_name: Qin
full_name: Cao, Qin
last_name: Cao
- 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
- first_name: Vaiva
full_name: Imbrasaite, Vaiva
last_name: Imbrasaite
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'
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.
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.
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.'
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.
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.
conference:
end_date: 2021-08-06
location: Bangkok, Thailand
name: 'ACL: Association for Computational Linguistics ; IJCNLP: International Joint
Conference on Natural Language Processing'
start_date: 2021-08-01
date_created: 2021-11-28T23:01:30Z
date_published: 2021-08-01T00:00:00Z
date_updated: 2022-01-26T14:26:36Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.18653/v1/2021.acl-tutorials.6
file:
- access_level: open_access
checksum: b14052a025a6ecf675bdfe51db98c0d7
content_type: application/pdf
creator: cchlebak
date_created: 2021-11-29T08:41:00Z
date_updated: 2021-11-29T08:41:00Z
file_id: '10368'
file_name: 2021_ACL_Ilharco.pdf
file_size: 1227703
relation: main_file
success: 1
file_date_updated: 2021-11-29T08:41:00Z
has_accepted_license: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
- open_access: '1'
url: https://aclanthology.org/2021.acl-tutorials.6/
month: '08'
oa: 1
oa_version: Published Version
page: 29-30
publication: 59th Annual Meeting of the Association for Computational Linguistics
and the 11th International Joint Conference on Natural Language Processing, Tutorial
Abstracts
publication_identifier:
isbn:
- 9-781-9540-8557-2
publication_status: published
publisher: Association for Computational Linguistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Recognizing multimodal entailment
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)
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2021'
...
---
_id: '10608'
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.
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).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Thomas
full_name: Weighill, Thomas
last_name: Weighill
- first_name: Takamitsu
full_name: Yamauchi, Takamitsu
last_name: Yamauchi
- first_name: Nicolò
full_name: Zava, Nicolò
id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
last_name: Zava
citation:
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
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
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.
ista: Weighill T, Yamauchi T, Zava N. 2021. Coarse infinite-dimensionality of hyperspaces
of finite subsets. European Journal of Mathematics.
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.
short: T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics (2021).
date_created: 2022-01-09T23:01:27Z
date_published: 2021-12-30T00:00:00Z
date_updated: 2022-01-10T08:36:55Z
day: '30'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1007/s40879-021-00515-3
file:
- access_level: open_access
checksum: c435dcfa1ad3aadc5cdd7366bc7f4e98
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-10T08:33:22Z
date_updated: 2022-01-10T08:33:22Z
file_id: '10610'
file_name: 2021_EuJournalMath_Weighill.pdf
file_size: 384908
relation: main_file
success: 1
file_date_updated: 2022-01-10T08:33:22Z
has_accepted_license: '1'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
publication: European Journal of Mathematics
publication_identifier:
eissn:
- 2199-6768
issn:
- 2199-675X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Coarse infinite-dimensionality of hyperspaces of finite subsets
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)
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2021'
...
---
_id: '9296'
abstract:
- lang: eng
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.'
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).'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Alan M
full_name: Arroyo Guevara, Alan M
id: 3207FDC6-F248-11E8-B48F-1D18A9856A87
last_name: Arroyo Guevara
orcid: 0000-0003-2401-8670
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Irene
full_name: Parada, Irene
last_name: Parada
- first_name: Daniel
full_name: Perz, Daniel
last_name: Perz
- first_name: Alexander
full_name: Pilz, Alexander
last_name: Pilz
- first_name: Josef
full_name: Tkadlec, Josef
id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87
last_name: Tkadlec
orcid: 0000-0002-1097-9684
- first_name: Birgit
full_name: Vogtenhuber, Birgit
last_name: Vogtenhuber
citation:
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'
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'
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.
ieee: O. Aichholzer et al., “On compatible matchings,” in 15th International
Conference on Algorithms and Computation, Yangon, Myanmar, 2021, vol. 12635,
pp. 221–233.
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.
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.
conference:
end_date: 2021-03-02
location: Yangon, Myanmar
name: 'WALCOM: Algorithms and Computation'
start_date: 2021-02-28
date_created: 2021-03-28T22:01:41Z
date_published: 2021-02-16T00:00:00Z
date_updated: 2023-02-21T16:33:44Z
day: '16'
department:
- _id: UlWa
- _id: HeEd
- _id: KrCh
doi: 10.1007/978-3-030-68211-8_18
ec_funded: 1
external_id:
arxiv:
- '2101.03928'
intvolume: ' 12635'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2101.03928
month: '02'
oa: 1
oa_version: Preprint
page: 221-233
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
publication: 15th International Conference on Algorithms and Computation
publication_identifier:
eissn:
- '16113349'
isbn:
- '9783030682101'
issn:
- '03029743'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '11938'
relation: later_version
status: public
scopus_import: '1'
status: public
title: On compatible matchings
type: conference
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 12635
year: '2021'
...
---
_id: '9465'
abstract:
- lang: eng
text: "Given a locally finite set \U0001D44B⊆ℝ\U0001D451 and an integer \U0001D458≥0,
we consider the function \U0001D430\U0001D458:Del\U0001D458(\U0001D44B)→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."
article_number: '15'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
citation:
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.
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.
ista: Edelsbrunner H, Nikitenko A, Osang GF. 2021. A step in the Delaunay mosaic
of order k. Journal of Geometry. 112(1), 15.
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).
date_created: 2021-06-06T22:01:29Z
date_published: 2021-04-01T00:00:00Z
date_updated: 2022-05-12T11:41:45Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00022-021-00577-4
file:
- access_level: open_access
checksum: e52a832f1def52a2b23d21bcc09e646f
content_type: application/pdf
creator: kschuh
date_created: 2021-06-11T13:16:26Z
date_updated: 2021-06-11T13:16:26Z
file_id: '9544'
file_name: 2021_Geometry_Edelsbrunner.pdf
file_size: 694706
relation: main_file
success: 1
file_date_updated: 2021-06-11T13:16:26Z
has_accepted_license: '1'
intvolume: ' 112'
issue: '1'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
publication: Journal of Geometry
publication_identifier:
eissn:
- '14208997'
issn:
- '00472468'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A step in the Delaunay mosaic of order k
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)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 112
year: '2021'
...
---
_id: '9345'
abstract:
- lang: eng
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.
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.
alternative_title:
- LIPIcs
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Vitaliy
full_name: ' Kurlin , Vitaliy'
last_name: ' Kurlin '
- first_name: Philip
full_name: Smith, Philip
last_name: Smith
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
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'
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'
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.
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.
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.'
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.
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.
conference:
end_date: 2021-06-11
location: Virtual
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2021-06-07
date_created: 2021-04-22T08:09:58Z
date_published: 2021-06-02T00:00:00Z
date_updated: 2023-02-23T13:55:40Z
day: '02'
ddc:
- '004'
- '516'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2021.32
ec_funded: 1
file:
- access_level: open_access
checksum: 1787baef1523d6d93753b90d0c109a6d
content_type: application/pdf
creator: mwintrae
date_created: 2021-04-22T08:08:14Z
date_updated: 2021-04-22T08:08:14Z
file_id: '9346'
file_name: df_socg_final_version.pdf
file_size: 3117435
relation: main_file
success: 1
file_date_updated: 2021-04-22T08:08:14Z
has_accepted_license: '1'
intvolume: ' 189'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 32:1-32:16
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
- _id: 25C5A090-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00312
name: The Wittgenstein Prize
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 37th International Symposium on Computational Geometry (SoCG 2021)
publication_identifier:
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
status: public
title: The density fingerprint of a periodic point set
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)
type: conference
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 189
year: '2021'
...
---
_id: '9604'
abstract:
- lang: eng
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.
alternative_title:
- LIPIcs
article_number: '16'
article_processing_charge: No
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Sebastiano
full_name: Cultrera di Montesano, Sebastiano
id: 34D2A09C-F248-11E8-B48F-1D18A9856A87
last_name: Cultrera di Montesano
orcid: 0000-0001-6249-0832
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Morteza
full_name: Saghafian, Morteza
last_name: Saghafian
citation:
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'
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.
ieee: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Counting
cells of order-k voronoi tessellations in ℝ3 with morse theory,” in
Leibniz International Proceedings in Informatics, Online, 2021, vol. 189.
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.'
mla: Biswas, Ranita, et al. “Counting Cells of Order-k Voronoi Tessellations in
ℝ3 with Morse Theory.” Leibniz International Proceedings in Informatics,
vol. 189, 16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi: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.
conference:
end_date: 2021-06-11
location: Online
name: 'SoCG: International Symposium on Computational Geometry'
start_date: 2021-06-07
date_created: 2021-06-27T22:01:48Z
date_published: 2021-06-02T00:00:00Z
date_updated: 2023-02-23T14:02:28Z
day: '02'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2021.16
ec_funded: 1
file:
- access_level: open_access
checksum: 22b11a719018b22ecba2471b51f2eb40
content_type: application/pdf
creator: asandaue
date_created: 2021-06-28T13:11:39Z
date_updated: 2021-06-28T13:11:39Z
file_id: '9611'
file_name: 2021_LIPIcs_Biswas.pdf
file_size: 727817
relation: main_file
success: 1
file_date_updated: 2021-06-28T13:11:39Z
has_accepted_license: '1'
intvolume: ' 189'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Discretization in Geometry and Dynamics
publication: Leibniz International Proceedings in Informatics
publication_identifier:
isbn:
- '9783959771849'
issn:
- '18688969'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Counting cells of order-k voronoi tessellations in ℝ3 with morse
theory
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)
type: conference
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 189
year: '2021'
...
---
_id: '9824'
abstract:
- lang: eng
text: We define a new compact coordinate system in which each integer triplet addresses
a voxel in the BCC grid, and we investigate some of its properties. 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.
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).'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Lidija
full_name: Čomić, Lidija
last_name: Čomić
- first_name: Rita
full_name: Zrour, Rita
last_name: Zrour
- first_name: Gaëlle
full_name: Largeteau-Skapin, Gaëlle
last_name: Largeteau-Skapin
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Eric
full_name: Andres, Eric
last_name: Andres
citation:
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'
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'
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.
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.
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.'
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.
short: L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete
Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.
conference:
end_date: 2021-05-27
location: Uppsala, Sweden
name: 'DGMM: International Conference on Discrete Geometry and Mathematical Morphology'
start_date: 2021-05-24
date_created: 2021-08-08T22:01:29Z
date_published: 2021-05-16T00:00:00Z
date_updated: 2022-05-31T06:58:21Z
day: '16'
department:
- _id: HeEd
doi: 10.1007/978-3-030-76657-3_10
ec_funded: 1
intvolume: ' 12708'
language:
- iso: eng
month: '05'
oa_version: None
page: 152-163
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Discrete Geometry and Mathematical Morphology
publication_identifier:
eissn:
- '16113349'
isbn:
- '9783030766566'
issn:
- '03029743'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Body centered cubic grid - coordinate system and discrete analytical plane
definition
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12708
year: '2021'
...
---
_id: '8317'
abstract:
- lang: eng
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.
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.
article_number: '101700'
article_processing_charge: No
article_type: original
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Hugo A.
full_name: Akitaya, Hugo A.
last_name: Akitaya
- first_name: Kenneth C.
full_name: Cheung, Kenneth C.
last_name: Cheung
- first_name: Erik D.
full_name: Demaine, Erik D.
last_name: Demaine
- first_name: Martin L.
full_name: Demaine, Martin L.
last_name: Demaine
- first_name: Sándor P.
full_name: Fekete, Sándor P.
last_name: Fekete
- first_name: Linda
full_name: Kleist, Linda
last_name: Kleist
- first_name: Irina
full_name: Kostitsyna, Irina
last_name: Kostitsyna
- first_name: Maarten
full_name: Löffler, Maarten
last_name: Löffler
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Klara
full_name: Mundilova, Klara
last_name: Mundilova
- first_name: Christiane
full_name: Schmidt, Christiane
last_name: Schmidt
citation:
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'
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.'
ieee: 'O. Aichholzer et al., “Folding polyominoes with holes into a cube,”
Computational Geometry: Theory and Applications, vol. 93. Elsevier, 2021.'
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.'
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).'
date_created: 2020-08-30T22:01:09Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2023-08-04T10:57:42Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2020.101700
external_id:
arxiv:
- '1910.09917'
isi:
- '000579185100004'
intvolume: ' 93'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.09917v3
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
publication: 'Computational Geometry: Theory and Applications'
publication_identifier:
issn:
- '09257721'
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
record:
- id: '6989'
relation: shorter_version
status: public
scopus_import: '1'
status: public
title: Folding polyominoes with holes into a cube
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 93
year: '2021'
...
---
_id: '8773'
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.
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."
article_processing_charge: No
article_type: original
author:
- first_name: Adam
full_name: Brown, Adam
id: 70B7FDF6-608D-11E9-9333-8535E6697425
last_name: Brown
- first_name: Anna
full_name: Romanov, Anna
last_name: Romanov
citation:
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
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
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.
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.
ista: Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings
of the American Mathematical Society. 149(1), 37–52.
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.
date_created: 2020-11-19T10:17:40Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-08-04T11:11:47Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/15205
ec_funded: 1
external_id:
arxiv:
- '1910.08286'
isi:
- '000600416300004'
intvolume: ' 149'
isi: 1
issue: '1'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.08286
month: '01'
oa: 1
oa_version: Preprint
page: 37-52
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Proceedings of the American Mathematical Society
publication_identifier:
eissn:
- 1088-6826
issn:
- 0002-9939
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: Contravariant forms on Whittaker modules
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 149
year: '2021'
...