--- _id: '53533' author: - first_name: Alena full_name: Ernst, Alena id: '46953' last_name: Ernst - first_name: Kai-Uwe full_name: Schmidt, Kai-Uwe last_name: Schmidt citation: ama: Ernst A, Schmidt K-U. Intersection theorems for finite general linear groups. Mathematical Proceedings of the Cambridge Philosophical Society. 2023;175(1):129-160. doi:10.1017/s0305004123000075 apa: Ernst, A., & Schmidt, K.-U. (2023). Intersection theorems for finite general linear groups. Mathematical Proceedings of the Cambridge Philosophical Society, 175(1), 129–160. https://doi.org/10.1017/s0305004123000075 bibtex: '@article{Ernst_Schmidt_2023, title={Intersection theorems for finite general linear groups}, volume={175}, DOI={10.1017/s0305004123000075}, number={1}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, publisher={Cambridge University Press (CUP)}, author={Ernst, Alena and Schmidt, Kai-Uwe}, year={2023}, pages={129–160} }' chicago: 'Ernst, Alena, and Kai-Uwe Schmidt. “Intersection Theorems for Finite General Linear Groups.” Mathematical Proceedings of the Cambridge Philosophical Society 175, no. 1 (2023): 129–60. https://doi.org/10.1017/s0305004123000075.' ieee: 'A. Ernst and K.-U. Schmidt, “Intersection theorems for finite general linear groups,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 175, no. 1, pp. 129–160, 2023, doi: 10.1017/s0305004123000075.' mla: Ernst, Alena, and Kai-Uwe Schmidt. “Intersection Theorems for Finite General Linear Groups.” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 175, no. 1, Cambridge University Press (CUP), 2023, pp. 129–60, doi:10.1017/s0305004123000075. short: A. Ernst, K.-U. Schmidt, Mathematical Proceedings of the Cambridge Philosophical Society 175 (2023) 129–160. date_created: 2024-04-17T12:23:18Z date_updated: 2024-05-07T08:29:59Z department: - _id: '100' doi: 10.1017/s0305004123000075 intvolume: ' 175' issue: '1' keyword: - General Mathematics language: - iso: eng page: 129-160 publication: Mathematical Proceedings of the Cambridge Philosophical Society publication_identifier: issn: - 0305-0041 - 1469-8064 publication_status: published publisher: Cambridge University Press (CUP) status: public title: Intersection theorems for finite general linear groups type: journal_article user_id: '46953' volume: 175 year: '2023' ... --- _id: '66325' abstract: - lang: eng text: AbstractLet

$\mathfrak{A}$

be a finite abelian group. In this paper, we classify harmonic

$\mathfrak{A}$

-covers of a tropical curve

$\Gamma$

(which allow dilation along edges and at vertices) in terms of the cohomology group of a suitably defined sheaf on

$\Gamma$

. We give a realisability criterion for harmonic

$\mathfrak{A}$

-covers by patching local monodromy data in an extended homology group on

$\Gamma$

. As an explicit example, we work out the case

$\mathfrak{A}=\mathbb{Z}/p\mathbb{Z}$

and explain how realisability for such covers is related to the nowhere-zero flow problem from graph theory. author: - first_name: Yoav full_name: Len, Yoav last_name: Len - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch - first_name: Dmitry full_name: Zakharov, Dmitry last_name: Zakharov citation: ama: Len Y, Ulirsch M, Zakharov D. Abelian tropical covers. Mathematical Proceedings of the Cambridge Philosophical Society. 2023;176(2):395-416. doi:10.1017/S0305004123000518 apa: Len, Y., Ulirsch, M., & Zakharov, D. (2023). Abelian tropical covers. Mathematical Proceedings of the Cambridge Philosophical Society, 176(2), 395–416. https://doi.org/10.1017/S0305004123000518 bibtex: '@article{Len_Ulirsch_Zakharov_2023, title={Abelian tropical covers}, volume={176}, DOI={10.1017/S0305004123000518}, number={2}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, publisher={Cambridge University Press (CUP)}, author={Len, Yoav and Ulirsch, Martin and Zakharov, Dmitry}, year={2023}, pages={395–416} }' chicago: 'Len, Yoav, Martin Ulirsch, and Dmitry Zakharov. “Abelian Tropical Covers.” Mathematical Proceedings of the Cambridge Philosophical Society 176, no. 2 (2023): 395–416. https://doi.org/10.1017/S0305004123000518.' ieee: 'Y. Len, M. Ulirsch, and D. Zakharov, “Abelian tropical covers,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 176, no. 2, pp. 395–416, 2023, doi: 10.1017/S0305004123000518.' mla: Len, Yoav, et al. “Abelian Tropical Covers.” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 176, no. 2, Cambridge University Press (CUP), 2023, pp. 395–416, doi:10.1017/S0305004123000518. short: Y. Len, M. Ulirsch, D. Zakharov, Mathematical Proceedings of the Cambridge Philosophical Society 176 (2023) 395–416. date_created: 2026-07-08T06:50:59Z date_updated: 2026-07-09T07:11:55Z doi: 10.1017/S0305004123000518 intvolume: ' 176' issue: '2' language: - iso: eng page: 395-416 publication: Mathematical Proceedings of the Cambridge Philosophical Society publication_identifier: issn: - 0305-0041 - 1469-8064 publication_status: published publisher: Cambridge University Press (CUP) status: public title: Abelian tropical covers type: journal_article user_id: '82981' volume: 176 year: '2023' ... --- _id: '16633' abstract: - lang: eng text: AbstractWe obtain normal forms for infinitesimally symplectic matrices (or linear Hamiltonian vector fields) that commute with the symplectic action of a compact Lie group of symmetries. In doing so we extend Williamson's theorem on normal forms when there is no symmetry present.Using standard representation-theoretic results the symmetry can be factored out and we reduce to finding normal forms over a real division ring. There are three real division rings consisting of the real, complex and quaternionic numbers. Of these, only the real case is covered in Williamson's original work. author: - first_name: Ian full_name: Melbourne, Ian last_name: Melbourne - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz citation: ama: Melbourne I, Dellnitz M. Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group. Mathematical Proceedings of the Cambridge Philosophical Society. 1993:235-268. doi:10.1017/s0305004100071577 apa: Melbourne, I., & Dellnitz, M. (1993). Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group. Mathematical Proceedings of the Cambridge Philosophical Society, 235–268. https://doi.org/10.1017/s0305004100071577 bibtex: '@article{Melbourne_Dellnitz_1993, title={Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group}, DOI={10.1017/s0305004100071577}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, author={Melbourne, Ian and Dellnitz, Michael}, year={1993}, pages={235–268} }' chicago: Melbourne, Ian, and Michael Dellnitz. “Normal Forms for Linear Hamiltonian Vector Fields Commuting with the Action of a Compact Lie Group.” Mathematical Proceedings of the Cambridge Philosophical Society, 1993, 235–68. https://doi.org/10.1017/s0305004100071577. ieee: I. Melbourne and M. Dellnitz, “Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group,” Mathematical Proceedings of the Cambridge Philosophical Society, pp. 235–268, 1993. mla: Melbourne, Ian, and Michael Dellnitz. “Normal Forms for Linear Hamiltonian Vector Fields Commuting with the Action of a Compact Lie Group.” Mathematical Proceedings of the Cambridge Philosophical Society, 1993, pp. 235–68, doi:10.1017/s0305004100071577. short: I. Melbourne, M. Dellnitz, Mathematical Proceedings of the Cambridge Philosophical Society (1993) 235–268. date_created: 2020-04-16T08:31:40Z date_updated: 2022-01-06T06:52:53Z department: - _id: '101' doi: 10.1017/s0305004100071577 language: - iso: eng page: 235-268 publication: Mathematical Proceedings of the Cambridge Philosophical Society publication_identifier: issn: - 0305-0041 - 1469-8064 publication_status: published status: public title: Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group type: journal_article user_id: '15701' year: '1993' ...