--- _id: '6050' abstract: - lang: eng text: 'We answer a question of David Hilbert: given two circles it is not possible in general to construct their centers using only a straightedge. On the other hand, we give infinitely many families of pairs of circles for which such construction is possible. ' article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Roman full_name: Fedorov, Roman last_name: Fedorov citation: ama: Akopyan A, Fedorov R. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 2019;147:91-102. doi:10.1090/proc/14240 apa: Akopyan, A., & Fedorov, R. (2019). Two circles and only a straightedge. Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14240 chicago: Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14240. ieee: A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” Proceedings of the American Mathematical Society, vol. 147. AMS, pp. 91–102, 2019. ista: Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102. mla: Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society, vol. 147, AMS, 2019, pp. 91–102, doi:10.1090/proc/14240. short: A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102. date_created: 2019-02-24T22:59:19Z date_published: 2019-01-01T00:00:00Z date_updated: 2023-08-24T14:48:59Z day: '01' department: - _id: HeEd doi: 10.1090/proc/14240 external_id: arxiv: - '1709.02562' isi: - '000450363900008' intvolume: ' 147' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1709.02562 month: '01' oa: 1 oa_version: Preprint page: 91-102 publication: Proceedings of the American Mathematical Society publication_status: published publisher: AMS quality_controlled: '1' scopus_import: '1' status: public title: Two circles and only a straightedge type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 147 year: '2019' ... --- _id: '6634' abstract: - lang: eng text: In this paper we prove several new results around Gromov's waist theorem. We give a simple proof of Vaaler's theorem on sections of the unit cube using the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective spaces, flat tori, convex bodies in Euclidean space; and establish waist-type results in terms of the Hausdorff measure. article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Alfredo full_name: Hubard, Alfredo last_name: Hubard - first_name: Roman full_name: Karasev, Roman last_name: Karasev citation: ama: Akopyan A, Hubard A, Karasev R. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 2019;53(2):457-490. doi:10.12775/TMNA.2019.008 apa: Akopyan, A., Hubard, A., & Karasev, R. (2019). Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. Akademicka Platforma Czasopism. https://doi.org/10.12775/TMNA.2019.008 chicago: Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis. Akademicka Platforma Czasopism, 2019. https://doi.org/10.12775/TMNA.2019.008. ieee: A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists of different spaces,” Topological Methods in Nonlinear Analysis, vol. 53, no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019. ista: Akopyan A, Hubard A, Karasev R. 2019. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 53(2), 457–490. mla: Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis, vol. 53, no. 2, Akademicka Platforma Czasopism, 2019, pp. 457–90, doi:10.12775/TMNA.2019.008. short: A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490. date_created: 2019-07-14T21:59:19Z date_published: 2019-06-01T00:00:00Z date_updated: 2023-08-29T06:32:48Z day: '01' department: - _id: HeEd doi: 10.12775/TMNA.2019.008 ec_funded: 1 external_id: arxiv: - '1612.06926' isi: - '000472541600004' intvolume: ' 53' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1612.06926 month: '06' oa: 1 oa_version: Preprint page: 457-490 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Topological Methods in Nonlinear Analysis publication_status: published publisher: Akademicka Platforma Czasopism quality_controlled: '1' scopus_import: '1' status: public title: Lower and upper bounds for the waists of different spaces type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 53 year: '2019' ... --- _id: '6756' abstract: - lang: eng text: "We study the topology generated by the temperature fluctuations of the cosmic microwave background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the ΛCDM paradigm with Gaussian distributed fluctuations. The comparison is multi-scale, being performed on a sequence of degraded maps with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over \U0001D54A2 is incomplete due to obfuscation effects by bright point sources and other extended foreground objects like our own galaxy. To deal with such situations, where analysis in the presence of “masks” is of importance, we introduce the concept of relative homology. The parametric χ2-test shows differences between observations and simulations, yielding p-values at percent to less than permil levels roughly between 2 and 7°, with the difference in the number of components and holes peaking at more than 3σ sporadically at these scales. The highest observed deviation between the observations and simulations for b0 and b1 is approximately between 3σ and 4σ at scales of 3–7°. There are reports of mildly unusual behaviour of the Euler characteristic at 3.66° in the literature, computed from independent measurements of the CMB temperature fluctuations by Planck’s predecessor, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite. The mildly anomalous behaviour of the Euler characteristic is phenomenologically related to the strongly anomalous behaviour of components and holes, or the zeroth and first Betti numbers, respectively. Further, since these topological descriptors show consistent anomalous behaviour over independent measurements of Planck and WMAP, instrumental and systematic errors may be an unlikely source. These are also the scales at which the observed maps exhibit low variance compared to the simulations, and approximately the range of scales at which the power spectrum exhibits a dip with respect to the theoretical model. Non-parametric tests show even stronger differences at almost all scales. Crucially, Gaussian simulations based on power-spectrum matching the characteristics of the observed dipped power spectrum are not able to resolve the anomaly. Understanding the origin of the anomalies in the CMB, whether cosmological in nature or arising due to late-time effects, is an extremely challenging task. Regardless, beyond the trivial possibility that this may still be a manifestation of an extreme Gaussian case, these observations, along with the super-horizon scales involved, may motivate the study of primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology, including topological defect models." article_number: A163 article_processing_charge: No article_type: original author: - first_name: Pratyush full_name: Pranav, Pratyush last_name: Pranav - first_name: Robert J. full_name: Adler, Robert J. last_name: Adler - first_name: Thomas full_name: Buchert, Thomas last_name: Buchert - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Bernard J.T. full_name: Jones, Bernard J.T. last_name: Jones - first_name: Armin full_name: Schwartzman, Armin last_name: Schwartzman - first_name: Hubert full_name: Wagner, Hubert id: 379CA8B8-F248-11E8-B48F-1D18A9856A87 last_name: Wagner - first_name: Rien full_name: Van De Weygaert, Rien last_name: Van De Weygaert citation: ama: Pranav P, Adler RJ, Buchert T, et al. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. 2019;627. doi:10.1051/0004-6361/201834916 apa: Pranav, P., Adler, R. J., Buchert, T., Edelsbrunner, H., Jones, B. J. T., Schwartzman, A., … Van De Weygaert, R. (2019). Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. EDP Sciences. https://doi.org/10.1051/0004-6361/201834916 chicago: Pranav, Pratyush, Robert J. Adler, Thomas Buchert, Herbert Edelsbrunner, Bernard J.T. Jones, Armin Schwartzman, Hubert Wagner, and Rien Van De Weygaert. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics. EDP Sciences, 2019. https://doi.org/10.1051/0004-6361/201834916. ieee: P. Pranav et al., “Unexpected topology of the temperature fluctuations in the cosmic microwave background,” Astronomy and Astrophysics, vol. 627. EDP Sciences, 2019. ista: Pranav P, Adler RJ, Buchert T, Edelsbrunner H, Jones BJT, Schwartzman A, Wagner H, Van De Weygaert R. 2019. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. 627, A163. mla: Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics, vol. 627, A163, EDP Sciences, 2019, doi:10.1051/0004-6361/201834916. short: P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman, H. Wagner, R. Van De Weygaert, Astronomy and Astrophysics 627 (2019). date_created: 2019-08-04T21:59:18Z date_published: 2019-07-17T00:00:00Z date_updated: 2023-08-29T07:01:48Z day: '17' ddc: - '520' - '530' department: - _id: HeEd doi: 10.1051/0004-6361/201834916 external_id: arxiv: - '1812.07678' isi: - '000475839300003' file: - access_level: open_access checksum: 83b9209ed9eefbdcefd89019c5a97805 content_type: application/pdf creator: dernst date_created: 2019-08-05T08:08:59Z date_updated: 2020-07-14T12:47:39Z file_id: '6766' file_name: 2019_AstronomyAstrophysics_Pranav.pdf file_size: 14420451 relation: main_file file_date_updated: 2020-07-14T12:47:39Z has_accepted_license: '1' intvolume: ' 627' isi: 1 language: - iso: eng month: '07' oa: 1 oa_version: Published Version project: - _id: 265683E4-B435-11E9-9278-68D0E5697425 grant_number: M62909-18-1-2038 name: Toward Computational Information Topology - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Astronomy and Astrophysics publication_identifier: eissn: - '14320746' issn: - '00046361' publication_status: published publisher: EDP Sciences quality_controlled: '1' scopus_import: '1' status: public title: Unexpected topology of the temperature fluctuations in the cosmic microwave background 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 627 year: '2019' ... --- _id: '6793' abstract: - lang: eng text: The Regge symmetry is a set of remarkable relations between two tetrahedra whose edge lengths are related in a simple fashion. It was first discovered as a consequence of an asymptotic formula in mathematical physics. Here, we give a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic geometry. article_processing_charge: No article_type: original author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Ivan full_name: Izmestiev, Ivan last_name: Izmestiev citation: ama: Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. 2019;51(5):765-775. doi:10.1112/blms.12276 apa: Akopyan, A., & Izmestiev, I. (2019). The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/blms.12276 chicago: Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” Bulletin of the London Mathematical Society. London Mathematical Society, 2019. https://doi.org/10.1112/blms.12276. ieee: A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the Schläfli formula,” Bulletin of the London Mathematical Society, vol. 51, no. 5. London Mathematical Society, pp. 765–775, 2019. ista: Akopyan A, Izmestiev I. 2019. The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. 51(5), 765–775. mla: Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” Bulletin of the London Mathematical Society, vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:10.1112/blms.12276. short: A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 765–775. date_created: 2019-08-11T21:59:23Z date_published: 2019-10-01T00:00:00Z date_updated: 2023-08-29T07:08:34Z day: '01' department: - _id: HeEd doi: 10.1112/blms.12276 ec_funded: 1 external_id: arxiv: - '1903.04929' isi: - '000478560200001' intvolume: ' 51' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1903.04929 month: '10' oa: 1 oa_version: Preprint page: 765-775 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended publication: Bulletin of the London Mathematical Society publication_identifier: eissn: - '14692120' issn: - '00246093' publication_status: published publisher: London Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: The Regge symmetry, confocal conics, and the Schläfli formula type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 51 year: '2019' ... --- _id: '6828' abstract: - lang: eng text: In this paper we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type to the category of finite-dimensional modules of the graded affine Hecke algebra of type . Using results of Backelin [2] and of Arakawa-Suzuki [1], we prove that these functors map standard modules to standard modules (or zero) and simple modules to simple modules (or zero). Moreover, we show that each simple module of the graded affine Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker category contains the BGG category as a full subcategory, our results generalize results of Arakawa-Suzuki [1], which in turn generalize Schur-Weyl duality between finite-dimensional representations of and representations of the symmetric group . article_processing_charge: No article_type: original author: - first_name: Adam full_name: Brown, Adam id: 70B7FDF6-608D-11E9-9333-8535E6697425 last_name: Brown citation: ama: Brown A. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 2019;538:261-289. doi:10.1016/j.jalgebra.2019.07.027 apa: Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2019.07.027 chicago: Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra. Elsevier, 2019. https://doi.org/10.1016/j.jalgebra.2019.07.027. ieee: A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” Journal of Algebra, vol. 538. Elsevier, pp. 261–289, 2019. ista: Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 538, 261–289. mla: Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra, vol. 538, Elsevier, 2019, pp. 261–89, doi:10.1016/j.jalgebra.2019.07.027. short: A. Brown, Journal of Algebra 538 (2019) 261–289. date_created: 2019-08-22T07:54:13Z date_published: 2019-11-15T00:00:00Z date_updated: 2023-08-29T07:11:47Z day: '15' department: - _id: HeEd doi: 10.1016/j.jalgebra.2019.07.027 external_id: arxiv: - '1805.04676' isi: - '000487176300011' intvolume: ' 538' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1805.04676 month: '11' oa: 1 oa_version: Preprint page: 261-289 publication: Journal of Algebra publication_identifier: issn: - 0021-8693 publication_status: published publisher: Elsevier quality_controlled: '1' status: public title: Arakawa-Suzuki functors for Whittaker modules type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 538 year: '2019' ...