[{"citation":{"ama":"Ernst A, Schmidt K-U. Intersection theorems for finite general linear groups. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. 2023;175(1):129-160. doi:<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>","bibtex":"@article{Ernst_Schmidt_2023, title={Intersection theorems for finite general linear groups}, volume={175}, DOI={<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>}, 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} }","mla":"Ernst, Alena, and Kai-Uwe Schmidt. “Intersection Theorems for Finite General Linear Groups.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 175, no. 1, Cambridge University Press (CUP), 2023, pp. 129–60, doi:<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>.","short":"A. Ernst, K.-U. Schmidt, Mathematical Proceedings of the Cambridge Philosophical Society 175 (2023) 129–160.","chicago":"Ernst, Alena, and Kai-Uwe Schmidt. “Intersection Theorems for Finite General Linear Groups.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i> 175, no. 1 (2023): 129–60. <a href=\"https://doi.org/10.1017/s0305004123000075\">https://doi.org/10.1017/s0305004123000075</a>.","apa":"Ernst, A., &#38; Schmidt, K.-U. (2023). Intersection theorems for finite general linear groups. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, <i>175</i>(1), 129–160. <a href=\"https://doi.org/10.1017/s0305004123000075\">https://doi.org/10.1017/s0305004123000075</a>","ieee":"A. Ernst and K.-U. Schmidt, “Intersection theorems for finite general linear groups,” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 175, no. 1, pp. 129–160, 2023, doi: <a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>."},"volume":175,"user_id":"46953","publisher":"Cambridge University Press (CUP)","_id":"53533","page":"129-160","status":"public","department":[{"_id":"100"}],"type":"journal_article","keyword":["General Mathematics"],"date_created":"2024-04-17T12:23:18Z","issue":"1","publication":"Mathematical Proceedings of the Cambridge Philosophical Society","doi":"10.1017/s0305004123000075","language":[{"iso":"eng"}],"intvolume":"       175","date_updated":"2024-05-07T08:29:59Z","publication_status":"published","author":[{"id":"46953","last_name":"Ernst","first_name":"Alena","full_name":"Ernst, Alena"},{"first_name":"Kai-Uwe","last_name":"Schmidt","full_name":"Schmidt, Kai-Uwe"}],"publication_identifier":{"issn":["0305-0041","1469-8064"]},"title":"Intersection theorems for finite general linear groups","year":"2023"},{"doi":"10.1017/S0305004123000518","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2026-07-09T07:11:55Z","intvolume":"       176","year":"2023","title":"Abelian tropical covers","publication_identifier":{"issn":["0305-0041","1469-8064"]},"author":[{"last_name":"Len","first_name":"Yoav","full_name":"Len, Yoav"},{"id":"114697","full_name":"Ulirsch, Martin","last_name":"Ulirsch","first_name":"Martin"},{"full_name":"Zakharov, Dmitry","first_name":"Dmitry","last_name":"Zakharov"}],"type":"journal_article","date_created":"2026-07-08T06:50:59Z","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Let<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0305004123000518_inline1.png\"/><jats:tex-math>$\\mathfrak{A}$</jats:tex-math></jats:alternatives></jats:inline-formula>be a finite abelian group. In this paper, we classify harmonic<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0305004123000518_inline2.png\"/><jats:tex-math>$\\mathfrak{A}$</jats:tex-math></jats:alternatives></jats:inline-formula>-covers of a tropical curve<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0305004123000518_inline3.png\"/><jats:tex-math>$\\Gamma$</jats:tex-math></jats:alternatives></jats:inline-formula>(which allow dilation along edges and at vertices) in terms of the cohomology group of a suitably defined sheaf on<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0305004123000518_inline4.png\"/><jats:tex-math>$\\Gamma$</jats:tex-math></jats:alternatives></jats:inline-formula>. We give a realisability criterion for harmonic<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0305004123000518_inline5.png\"/><jats:tex-math>$\\mathfrak{A}$</jats:tex-math></jats:alternatives></jats:inline-formula>-covers by patching local monodromy data in an extended homology group on<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0305004123000518_inline6.png\"/><jats:tex-math>$\\Gamma$</jats:tex-math></jats:alternatives></jats:inline-formula>. As an explicit example, we work out the case<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0305004123000518_inline7.png\"/><jats:tex-math>$\\mathfrak{A}=\\mathbb{Z}/p\\mathbb{Z}$</jats:tex-math></jats:alternatives></jats:inline-formula>and explain how realisability for such covers is related to the nowhere-zero flow problem from graph theory.</jats:p>","lang":"eng"}],"issue":"2","publication":"Mathematical Proceedings of the Cambridge Philosophical Society","user_id":"82981","volume":176,"page":"395-416","_id":"66325","publisher":"Cambridge University Press (CUP)","status":"public","citation":{"short":"Y. Len, M. Ulirsch, D. Zakharov, Mathematical Proceedings of the Cambridge Philosophical Society 176 (2023) 395–416.","chicago":"Len, Yoav, Martin Ulirsch, and Dmitry Zakharov. “Abelian Tropical Covers.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i> 176, no. 2 (2023): 395–416. <a href=\"https://doi.org/10.1017/S0305004123000518\">https://doi.org/10.1017/S0305004123000518</a>.","ieee":"Y. Len, M. Ulirsch, and D. Zakharov, “Abelian tropical covers,” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 176, no. 2, pp. 395–416, 2023, doi: <a href=\"https://doi.org/10.1017/S0305004123000518\">10.1017/S0305004123000518</a>.","apa":"Len, Y., Ulirsch, M., &#38; Zakharov, D. (2023). Abelian tropical covers. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, <i>176</i>(2), 395–416. <a href=\"https://doi.org/10.1017/S0305004123000518\">https://doi.org/10.1017/S0305004123000518</a>","bibtex":"@article{Len_Ulirsch_Zakharov_2023, title={Abelian tropical covers}, volume={176}, DOI={<a href=\"https://doi.org/10.1017/S0305004123000518\">10.1017/S0305004123000518</a>}, 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} }","ama":"Len Y, Ulirsch M, Zakharov D. Abelian tropical covers. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. 2023;176(2):395-416. doi:<a href=\"https://doi.org/10.1017/S0305004123000518\">10.1017/S0305004123000518</a>","mla":"Len, Yoav, et al. “Abelian Tropical Covers.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 176, no. 2, Cambridge University Press (CUP), 2023, pp. 395–416, doi:<a href=\"https://doi.org/10.1017/S0305004123000518\">10.1017/S0305004123000518</a>."}},{"date_updated":"2022-01-06T06:52:53Z","publication_status":"published","author":[{"first_name":"Ian","last_name":"Melbourne","full_name":"Melbourne, Ian"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}],"publication_identifier":{"issn":["0305-0041","1469-8064"]},"status":"public","year":"1993","title":"Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group","doi":"10.1017/s0305004100071577","user_id":"15701","language":[{"iso":"eng"}],"_id":"16633","page":"235-268","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>We 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.</jats:p><jats:p>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.</jats:p>","lang":"eng"}],"citation":{"ieee":"I. Melbourne and M. Dellnitz, “Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group,” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, pp. 235–268, 1993.","apa":"Melbourne, I., &#38; Dellnitz, M. (1993). Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, 235–268. <a href=\"https://doi.org/10.1017/s0305004100071577\">https://doi.org/10.1017/s0305004100071577</a>","short":"I. Melbourne, M. Dellnitz, Mathematical Proceedings of the Cambridge Philosophical Society (1993) 235–268.","chicago":"Melbourne, Ian, and Michael Dellnitz. “Normal Forms for Linear Hamiltonian Vector Fields Commuting with the Action of a Compact Lie Group.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, 1993, 235–68. <a href=\"https://doi.org/10.1017/s0305004100071577\">https://doi.org/10.1017/s0305004100071577</a>.","mla":"Melbourne, Ian, and Michael Dellnitz. “Normal Forms for Linear Hamiltonian Vector Fields Commuting with the Action of a Compact Lie Group.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, 1993, pp. 235–68, doi:<a href=\"https://doi.org/10.1017/s0305004100071577\">10.1017/s0305004100071577</a>.","bibtex":"@article{Melbourne_Dellnitz_1993, title={Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group}, DOI={<a href=\"https://doi.org/10.1017/s0305004100071577\">10.1017/s0305004100071577</a>}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, author={Melbourne, Ian and Dellnitz, Michael}, year={1993}, pages={235–268} }","ama":"Melbourne I, Dellnitz M. Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. 1993:235-268. doi:<a href=\"https://doi.org/10.1017/s0305004100071577\">10.1017/s0305004100071577</a>"},"publication":"Mathematical Proceedings of the Cambridge Philosophical Society","department":[{"_id":"101"}],"type":"journal_article","date_created":"2020-04-16T08:31:40Z"}]