[{"OA_type":"green","day":"01","issue":"5","publisher":"Wiley","month":"05","corr_author":"1","type":"journal_article","year":"2026","article_processing_charge":"No","department":[{"_id":"HeEd"},{"_id":"TaHa"}],"publication":"Proceedings of the London Mathematical Society","article_number":"e70163","external_id":{"arxiv":["2501.05315"]},"status":"public","date_updated":"2026-06-02T09:24:18Z","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"earlier_version","id":"21050","status":"public"}]},"arxiv":1,"citation":{"ieee":"H. Edelsbrunner, C. D. Fillmore, and G. Oliveira, “Counting equilibria of the electrostatic potential,” <i>Proceedings of the London Mathematical Society</i>, vol. 132, no. 5. Wiley, 2026.","ista":"Edelsbrunner H, Fillmore CD, Oliveira G. 2026. Counting equilibria of the electrostatic potential. Proceedings of the London Mathematical Society. 132(5), e70163.","apa":"Edelsbrunner, H., Fillmore, C. D., &#38; Oliveira, G. (2026). Counting equilibria of the electrostatic potential. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/plms.70163\">https://doi.org/10.1112/plms.70163</a>","ama":"Edelsbrunner H, Fillmore CD, Oliveira G. Counting equilibria of the electrostatic potential. <i>Proceedings of the London Mathematical Society</i>. 2026;132(5). doi:<a href=\"https://doi.org/10.1112/plms.70163\">10.1112/plms.70163</a>","chicago":"Edelsbrunner, Herbert, Christopher D Fillmore, and Goncalo Oliveira. “Counting Equilibria of the Electrostatic Potential.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2026. <a href=\"https://doi.org/10.1112/plms.70163\">https://doi.org/10.1112/plms.70163</a>.","short":"H. Edelsbrunner, C.D. Fillmore, G. Oliveira, Proceedings of the London Mathematical Society 132 (2026).","mla":"Edelsbrunner, Herbert, et al. “Counting Equilibria of the Electrostatic Potential.” <i>Proceedings of the London Mathematical Society</i>, vol. 132, no. 5, e70163, Wiley, 2026, doi:<a href=\"https://doi.org/10.1112/plms.70163\">10.1112/plms.70163</a>."},"oa":1,"date_published":"2026-05-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"first_name":"Christopher D","last_name":"Fillmore","full_name":"Fillmore, Christopher D","id":"35638A5C-AAC7-11E9-B0BF-5503E6697425"},{"full_name":"Oliveira, Goncalo","id":"58abbde8-f455-11eb-a497-98c8fd71b905","first_name":"Goncalo","last_name":"Oliveira"}],"date_created":"2026-05-31T22:02:13Z","doi":"10.1112/plms.70163","OA_place":"repository","scopus_import":"1","_id":"21931","article_type":"original","volume":132,"publication_identifier":{"issn":["0024-6115"],"eissn":["1460-244X"]},"intvolume":"       132","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2501.05315","open_access":"1"}],"publication_status":"published","oa_version":"Preprint","title":"Counting equilibria of the electrostatic potential","abstract":[{"lang":"eng","text":"In 1873, James C. Maxwell conjectured that the electric field generated by n point charges in generic position has at most (n-1)^2 isolated zeroes. The first (nonoptimal) upper bound was only obtained in 2007 by Gabrielov, Novikov, and Shapiro, who also posed two additional interesting conjectures. In this article, we give the best upper bound known to date on the number of zeroes of the electric field, and construct a counterexample to Conjecture 1.8 by Gabrielov, Novikov, and Shapiro that the number of equilibria cannot exceed those of the distance function defined by the unit point charges. Finally, we note that it is quite possible that Maxwell's quadratic upper bound is not tight, so it is prudent to find lower bounds. Hence, we also explore examples and construct configurations of charges achieving the highest ratios of the number of electric field zeroes by point charges found to this day."}]},{"oa":1,"date_published":"2024-03-01T00:00:00Z","arxiv":1,"citation":{"ista":"Lotay JD, Oliveira G. 2024. Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz. Journal of Differential Geometry. 126(3), 1121–1184.","ieee":"J. D. Lotay and G. Oliveira, “Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz,” <i>Journal of Differential Geometry</i>, vol. 126, no. 3. International Press, pp. 1121–1184, 2024.","ama":"Lotay JD, Oliveira G. Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz. <i>Journal of Differential Geometry</i>. 2024;126(3):1121-1184. doi:<a href=\"https://doi.org/10.4310/jdg/1717348872\">10.4310/jdg/1717348872</a>","chicago":"Lotay, Jason D., and Goncalo Oliveira. “Special Lagrangians, Lagrangian Mean Curvature Flow and the Gibbons-Hawking Ansatz.” <i>Journal of Differential Geometry</i>. International Press, 2024. <a href=\"https://doi.org/10.4310/jdg/1717348872\">https://doi.org/10.4310/jdg/1717348872</a>.","short":"J.D. Lotay, G. Oliveira, Journal of Differential Geometry 126 (2024) 1121–1184.","mla":"Lotay, Jason D., and Goncalo Oliveira. “Special Lagrangians, Lagrangian Mean Curvature Flow and the Gibbons-Hawking Ansatz.” <i>Journal of Differential Geometry</i>, vol. 126, no. 3, International Press, 2024, pp. 1121–84, doi:<a href=\"https://doi.org/10.4310/jdg/1717348872\">10.4310/jdg/1717348872</a>.","apa":"Lotay, J. D., &#38; Oliveira, G. (2024). Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz. <i>Journal of Differential Geometry</i>. International Press. <a href=\"https://doi.org/10.4310/jdg/1717348872\">https://doi.org/10.4310/jdg/1717348872</a>"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"full_name":"Lotay, Jason D.","last_name":"Lotay","first_name":"Jason D."},{"last_name":"Oliveira","first_name":"Goncalo","id":"58abbde8-f455-11eb-a497-98c8fd71b905","full_name":"Oliveira, Goncalo"}],"date_created":"2024-07-22T07:45:31Z","doi":"10.4310/jdg/1717348872","_id":"17292","OA_place":"repository","scopus_import":"1","publication_identifier":{"issn":["0022-040X"]},"volume":126,"article_type":"original","intvolume":"       126","quality_controlled":"1","page":"1121-1184","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2002.10391","open_access":"1"}],"publication_status":"published","oa_version":"Preprint","title":"Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz","abstract":[{"text":"The Gibbons-Hawking ansatz provides a large family of circle-invariant hyperkähler 4-manifolds, and thus Calabi-Yau 2-folds. In this setting, we prove versions of the Thomas conjecture on existence of special Lagrangian representatives of Hamiltonian isotopy classes of Lagrangians, and the Thomas-Yau conjecture on longtime existence of the Lagrangian mean curvature ow. We also make observations concerning closed geodesics, curve shortening flow and minimal surfaces.","lang":"eng"}],"issue":"3","day":"01","OA_type":"green","publisher":"International Press","corr_author":"1","month":"03","type":"journal_article","year":"2024","article_processing_charge":"No","publication":"Journal of Differential Geometry","isi":1,"department":[{"_id":"TaHa"}],"external_id":{"isi":["001271790200007"],"arxiv":["2002.10391"]},"status":"public","date_updated":"2025-09-08T08:27:51Z","language":[{"iso":"eng"}]},{"file_date_updated":"2023-01-23T07:53:23Z","quality_controlled":"1","oa_version":"Published Version","title":"New approaches to epidemic modeling on networks","publication_status":"published","abstract":[{"lang":"eng","text":"In this article, we develop two independent and new approaches to model epidemic spread in a network. Contrary to the most studied models, those developed here allow for contacts with different probabilities of transmitting the disease (transmissibilities). We then examine each of these models using some mean field type approximations. The first model looks at the late-stage effects of an epidemic outbreak and allows for the computation of the probability that a given vertex was infected. This computation is based on a mean field approximation and only depends on the number of contacts and their transmissibilities. This approach shares many similarities with percolation models in networks. The second model we develop is a dynamic model which we analyze using a mean field approximation which highly reduces the dimensionality of the system. In particular, the original system which individually analyses each vertex of the network is reduced to one with as many equations as different transmissibilities. Perhaps the greatest contribution of this article is the observation that, in both these models, the existence and size of an epidemic outbreak are linked to the properties of a matrix which we call the R-matrix. This is a generalization of the basic reproduction number which more precisely characterizes the main routes of infection."}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"short":"A. Gómez, G. Oliveira, Scientific Reports 13 (2023).","mla":"Gómez, Arturo, and Goncalo Oliveira. “New Approaches to Epidemic Modeling on Networks.” <i>Scientific Reports</i>, vol. 13, 468, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1038/s41598-022-19827-9\">10.1038/s41598-022-19827-9</a>.","chicago":"Gómez, Arturo, and Goncalo Oliveira. “New Approaches to Epidemic Modeling on Networks.” <i>Scientific Reports</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1038/s41598-022-19827-9\">https://doi.org/10.1038/s41598-022-19827-9</a>.","ama":"Gómez A, Oliveira G. New approaches to epidemic modeling on networks. <i>Scientific Reports</i>. 2023;13. doi:<a href=\"https://doi.org/10.1038/s41598-022-19827-9\">10.1038/s41598-022-19827-9</a>","apa":"Gómez, A., &#38; Oliveira, G. (2023). New approaches to epidemic modeling on networks. <i>Scientific Reports</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41598-022-19827-9\">https://doi.org/10.1038/s41598-022-19827-9</a>","ista":"Gómez A, Oliveira G. 2023. New approaches to epidemic modeling on networks. Scientific Reports. 13, 468.","ieee":"A. Gómez and G. Oliveira, “New approaches to epidemic modeling on networks,” <i>Scientific Reports</i>, vol. 13. Springer Nature, 2023."},"oa":1,"date_published":"2023-01-10T00:00:00Z","scopus_import":"1","_id":"12329","author":[{"last_name":"Gómez","first_name":"Arturo","full_name":"Gómez, Arturo"},{"last_name":"Oliveira","first_name":"Goncalo","id":"58abbde8-f455-11eb-a497-98c8fd71b905","full_name":"Oliveira, Goncalo"}],"doi":"10.1038/s41598-022-19827-9","date_created":"2023-01-22T23:00:55Z","article_type":"original","publication_identifier":{"eissn":["2045-2322"]},"volume":13,"acknowledgement":"Gonçalo Oliveira is supported by the NOMIS Foundation, Fundação Serrapilheira 1812-27395, by CNPq grants 428959/2018-0 and 307475/2018-2, and by FAPERJ through the grant Jovem Cientista do Nosso Estado E-26/202.793/2019.","intvolume":"        13","has_accepted_license":"1","department":[{"_id":"TaHa"}],"isi":1,"publication":"Scientific Reports","article_processing_charge":"No","status":"public","article_number":"468","external_id":{"isi":["001003345000051"]},"date_updated":"2024-10-09T21:03:29Z","file":[{"creator":"dernst","access_level":"open_access","date_created":"2023-01-23T07:53:23Z","checksum":"a8b83739f4a951e83e0b2a778f03b327","file_name":"2023_ScientificReports_Gomez.pdf","file_id":"12336","relation":"main_file","success":1,"file_size":2167792,"date_updated":"2023-01-23T07:53:23Z","content_type":"application/pdf"}],"ddc":["510"],"language":[{"iso":"eng"}],"day":"10","month":"01","corr_author":"1","publisher":"Springer Nature","year":"2023","type":"journal_article","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"}}]