--- _id: '12427' abstract: - lang: eng text: 'Let k be a number field and X a smooth, geometrically integral quasi-projective variety over k. For any linear algebraic group G over k and any G-torsor g : Z → X, we observe that if the étale-Brauer obstruction is the only one for strong approximation off a finite set of places S for all twists of Z by elements in H^1(k, G), then the étale-Brauer obstruction is the only one for strong approximation off a finite set of places S for X. As an application, we show that any homogeneous space of the form G/H with G a connected linear algebraic group over k satisfies strong approximation off the infinite places with étale-Brauer obstruction, under some compactness assumptions when k is totally real. We also prove more refined strong approximation results for homogeneous spaces of the form G/H with G semisimple simply connected and H finite, using the theory of torsors and descent.' article_processing_charge: No article_type: original author: - first_name: Francesca full_name: Balestrieri, Francesca id: 3ACCD756-F248-11E8-B48F-1D18A9856A87 last_name: Balestrieri citation: ama: Balestrieri F. Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups. Proceedings of the American Mathematical Society. 2023;151(3):907-914. doi:10.1090/proc/15239 apa: Balestrieri, F. (2023). Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/15239 chicago: Balestrieri, Francesca. “Some Remarks on Strong Approximation and Applications to Homogeneous Spaces of Linear Algebraic Groups.” Proceedings of the American Mathematical Society. American Mathematical Society, 2023. https://doi.org/10.1090/proc/15239. ieee: F. Balestrieri, “Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups,” Proceedings of the American Mathematical Society, vol. 151, no. 3. American Mathematical Society, pp. 907–914, 2023. ista: Balestrieri F. 2023. Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups. Proceedings of the American Mathematical Society. 151(3), 907–914. mla: Balestrieri, Francesca. “Some Remarks on Strong Approximation and Applications to Homogeneous Spaces of Linear Algebraic Groups.” Proceedings of the American Mathematical Society, vol. 151, no. 3, American Mathematical Society, 2023, pp. 907–14, doi:10.1090/proc/15239. short: F. Balestrieri, Proceedings of the American Mathematical Society 151 (2023) 907–914. date_created: 2023-01-29T23:00:58Z date_published: 2023-01-01T00:00:00Z date_updated: 2023-08-01T13:03:32Z day: '01' department: - _id: TiBr doi: 10.1090/proc/15239 external_id: isi: - '000898440000001' intvolume: ' 151' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://hal.science/hal-03013498/ month: '01' oa: 1 oa_version: Preprint page: 907-914 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' scopus_import: '1' status: public title: Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 151 year: '2023' ... --- _id: '13177' abstract: - lang: eng text: In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established. acknowledgement: The second author was supported by the priority program SPP2026 of the German Research Foundation (DFG). The fourth author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2. article_processing_charge: No article_type: original author: - first_name: Bobo full_name: Hua, Bobo last_name: Hua - first_name: Matthias full_name: Keller, Matthias last_name: Keller - first_name: Michael full_name: Schwarz, Michael last_name: Schwarz - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 citation: ama: Hua B, Keller M, Schwarz M, Wirth M. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. 2023;151(8):3401-3414. doi:10.1090/proc/14361 apa: Hua, B., Keller, M., Schwarz, M., & Wirth, M. (2023). Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/14361 chicago: Hua, Bobo, Matthias Keller, Michael Schwarz, and Melchior Wirth. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” Proceedings of the American Mathematical Society. American Mathematical Society, 2023. https://doi.org/10.1090/proc/14361. ieee: B. Hua, M. Keller, M. Schwarz, and M. Wirth, “Sobolev-type inequalities and eigenvalue growth on graphs with finite measure,” Proceedings of the American Mathematical Society, vol. 151, no. 8. American Mathematical Society, pp. 3401–3414, 2023. ista: Hua B, Keller M, Schwarz M, Wirth M. 2023. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. 151(8), 3401–3414. mla: Hua, Bobo, et al. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” Proceedings of the American Mathematical Society, vol. 151, no. 8, American Mathematical Society, 2023, pp. 3401–14, doi:10.1090/proc/14361. short: B. Hua, M. Keller, M. Schwarz, M. Wirth, Proceedings of the American Mathematical Society 151 (2023) 3401–3414. date_created: 2023-07-02T22:00:43Z date_published: 2023-08-01T00:00:00Z date_updated: 2023-11-14T13:07:09Z day: '01' department: - _id: JaMa doi: 10.1090/proc/14361 external_id: arxiv: - '1804.08353' isi: - '000988204400001' intvolume: ' 151' isi: 1 issue: '8' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.1804.08353' month: '08' oa: 1 oa_version: Preprint page: 3401-3414 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' scopus_import: '1' status: public title: Sobolev-type inequalities and eigenvalue growth on graphs with finite measure type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 151 year: '2023' ... --- _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' ... --- _id: '6986' abstract: - lang: eng text: 'Li-Nadler proposed a conjecture about traces of Hecke categories, which implies the semistable part of the Betti geometric Langlands conjecture of Ben-Zvi-Nadler in genus 1. We prove a Weyl group analogue of this conjecture. Our theorem holds in the natural generality of reflection groups in Euclidean or hyperbolic space. As a corollary, we give an expression of the centralizer of a finite order element in a reflection group using homotopy theory. ' article_processing_charge: No article_type: original author: - first_name: Penghui full_name: Li, Penghui id: 42A24CCC-F248-11E8-B48F-1D18A9856A87 last_name: Li citation: ama: Li P. A colimit of traces of reflection groups. Proceedings of the American Mathematical Society. 2019;147(11):4597-4604. doi:10.1090/proc/14586 apa: Li, P. (2019). A colimit of traces of reflection groups. Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14586 chicago: Li, Penghui. “A Colimit of Traces of Reflection Groups.” Proceedings of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14586. ieee: P. Li, “A colimit of traces of reflection groups,” Proceedings of the American Mathematical Society, vol. 147, no. 11. AMS, pp. 4597–4604, 2019. ista: Li P. 2019. A colimit of traces of reflection groups. Proceedings of the American Mathematical Society. 147(11), 4597–4604. mla: Li, Penghui. “A Colimit of Traces of Reflection Groups.” Proceedings of the American Mathematical Society, vol. 147, no. 11, AMS, 2019, pp. 4597–604, doi:10.1090/proc/14586. short: P. Li, Proceedings of the American Mathematical Society 147 (2019) 4597–4604. date_created: 2019-11-04T16:10:50Z date_published: 2019-11-01T00:00:00Z date_updated: 2023-09-05T12:22:21Z day: '01' department: - _id: TaHa doi: 10.1090/proc/14586 ec_funded: 1 external_id: arxiv: - '1810.07039' isi: - '000488621700004' intvolume: ' 147' isi: 1 issue: '11' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1810.07039 month: '11' oa: 1 oa_version: Preprint page: 4597-4604 project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces publication: Proceedings of the American Mathematical Society publication_identifier: eissn: - 1088-6826 issn: - 0002-9939 publication_status: published publisher: AMS quality_controlled: '1' scopus_import: '1' status: public title: A colimit of traces of reflection groups type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 147 year: '2019' ...