[{"date_created":"2026-05-31T22:02:13Z","external_id":{"arxiv":["2501.05315"]},"article_number":"e70163","month":"05","article_processing_charge":"No","OA_place":"repository","OA_type":"green","department":[{"_id":"HeEd"},{"_id":"TaHa"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2501.05315"}],"publication_status":"published","fulldoi":"https://doi.org/10.1112/plms.70163","date_published":"2026-05-01T00:00:00Z","type":"journal_article","arxiv":1,"related_material":{"record":[{"relation":"earlier_version","id":"21050","status":"public"}]},"publisher":"Wiley","intvolume":"       132","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"first_name":"Christopher D","id":"35638A5C-AAC7-11E9-B0BF-5503E6697425","full_name":"Fillmore, Christopher D","last_name":"Fillmore"},{"last_name":"Oliveira","full_name":"Oliveira, Goncalo","first_name":"Goncalo","id":"58abbde8-f455-11eb-a497-98c8fd71b905"}],"corr_author":"1","oa":1,"year":"2026","title":"Counting equilibria of the electrostatic potential","date_updated":"2026-07-22T06:33:54Z","doi":"10.1112/plms.70163","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","_id":"21931","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.","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>.","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>","short":"H. Edelsbrunner, C.D. Fillmore, G. Oliveira, Proceedings of the London Mathematical Society 132 (2026).","ista":"Edelsbrunner H, Fillmore CD, Oliveira G. 2026. Counting equilibria of the electrostatic potential. Proceedings of the London Mathematical Society. 132(5), e70163.","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>.","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>"},"publication_identifier":{"issn":["0024-6115"],"eissn":["1460-244X"]},"language":[{"iso":"eng"}],"issue":"5","oa_version":"Preprint","publication":"Proceedings of the London Mathematical Society","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."}],"volume":132,"scopus_import":"1","day":"01","article_type":"original"},{"publication":"Proceedings of the London Mathematical Society","ddc":["500"],"abstract":[{"text":"A graph 𝐺 is said to be Ramsey for a tuple of graphs(𝐻 1 , … , 𝐻𝑟 ) if every 𝑟-coloring of the edges of 𝐺 con-tains a monochromatic copy of 𝐻𝑖 in color 𝑖, for some 𝑖.A fundamental question at the intersection of Ramseytheory and the theory of random graphs is to deter-mine the threshold at which the binomial randomgraph 𝐺𝑛,𝑝 becomes asymptotically almost surely Ram-sey for a fixed tuple (𝐻 1 , … , 𝐻𝑟 ), and a famous conjectureof Kohayakawa and Kreuter predicts this threshold.Earlier work of Mousset–Nenadov–Samotij, Bowtell–Hancock–Hyde, and Kuperwasser–Samotij–Wigdersonhas reduced this probabilistic problem to a determinis-tic graph decomposition conjecture. In this paper, weresolve this deterministic problem, thus proving theKohayakawa–Kreuter conjecture. Along the way, weprove a number of novel graph decomposition resultsthat may be of independent interest.","lang":"eng"}],"volume":130,"scopus_import":"1","day":"01","article_type":"original","citation":{"ama":"Christoph M, Martinsson A, Steiner R, Wigderson Y. Resolution of the Kohayakawa–Kreuter conjecture. <i>Proceedings of the London Mathematical Society</i>. 2025;130(1). doi:<a href=\"https://doi.org/10.1112/plms.70013\">10.1112/plms.70013</a>","ista":"Christoph M, Martinsson A, Steiner R, Wigderson Y. 2025. Resolution of the Kohayakawa–Kreuter conjecture. Proceedings of the London Mathematical Society. 130(1), e70013.","mla":"Christoph, Micha, et al. “Resolution of the Kohayakawa–Kreuter Conjecture.” <i>Proceedings of the London Mathematical Society</i>, vol. 130, no. 1, e70013, Wiley, 2025, doi:<a href=\"https://doi.org/10.1112/plms.70013\">10.1112/plms.70013</a>.","apa":"Christoph, M., Martinsson, A., Steiner, R., &#38; Wigderson, Y. (2025). Resolution of the Kohayakawa–Kreuter conjecture. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/plms.70013\">https://doi.org/10.1112/plms.70013</a>","short":"M. Christoph, A. Martinsson, R. Steiner, Y. Wigderson, Proceedings of the London Mathematical Society 130 (2025).","ieee":"M. Christoph, A. Martinsson, R. Steiner, and Y. Wigderson, “Resolution of the Kohayakawa–Kreuter conjecture,” <i>Proceedings of the London Mathematical Society</i>, vol. 130, no. 1. Wiley, 2025.","chicago":"Christoph, Micha, Anders Martinsson, Raphael Steiner, and Yuval Wigderson. “Resolution of the Kohayakawa–Kreuter Conjecture.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2025. <a href=\"https://doi.org/10.1112/plms.70013\">https://doi.org/10.1112/plms.70013</a>."},"publication_identifier":{"eissn":["1460-244X"],"issn":["0024-6115"]},"oa_version":"Preprint","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"language":[{"iso":"eng"}],"issue":"1","extern":"1","publisher":"Wiley","intvolume":"       130","author":[{"last_name":"Christoph","full_name":"Christoph, Micha","first_name":"Micha"},{"full_name":"Martinsson, Anders","last_name":"Martinsson","first_name":"Anders"},{"first_name":"Raphael","full_name":"Steiner, Raphael","last_name":"Steiner"},{"full_name":"Wigderson, Yuval","last_name":"Wigderson","first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5"}],"oa":1,"_id":"22157","title":"Resolution of the Kohayakawa–Kreuter conjecture","date_updated":"2026-07-08T10:24:21Z","mathsc":["05C70","05D10","05C80"],"year":"2025","doi":"10.1112/plms.70013","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","month":"01","article_processing_charge":"No","OA_place":"repository","OA_type":"green","publication_status":"published","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2402.03045"}],"date_created":"2026-06-29T10:50:35Z","external_id":{"arxiv":["2402.03045"]},"article_number":"e70013","type":"journal_article","date_published":"2025-01-01T00:00:00Z","arxiv":1,"fulldoi":"https://doi.org/10.1112/plms.70013"},{"publication_identifier":{"eissn":["1460-244X"],"issn":["0024-6115"]},"citation":{"ista":"Bloom TF, Kuperberg VZ. 2025. Odd moments and adding fractions. Proceedings of the London Mathematical Society. 131(1), e70068.","mla":"Bloom, Thomas F., and Vivian Zieve Kuperberg. “Odd Moments and Adding Fractions.” <i>Proceedings of the London Mathematical Society</i>, vol. 131, no. 1, e70068, Wiley, 2025, doi:<a href=\"https://doi.org/10.1112/plms.70068\">10.1112/plms.70068</a>.","ama":"Bloom TF, Kuperberg VZ. Odd moments and adding fractions. <i>Proceedings of the London Mathematical Society</i>. 2025;131(1). doi:<a href=\"https://doi.org/10.1112/plms.70068\">10.1112/plms.70068</a>","chicago":"Bloom, Thomas F., and Vivian Zieve Kuperberg. “Odd Moments and Adding Fractions.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2025. <a href=\"https://doi.org/10.1112/plms.70068\">https://doi.org/10.1112/plms.70068</a>.","ieee":"T. F. Bloom and V. Z. Kuperberg, “Odd moments and adding fractions,” <i>Proceedings of the London Mathematical Society</i>, vol. 131, no. 1. Wiley, 2025.","apa":"Bloom, T. F., &#38; Kuperberg, V. Z. (2025). Odd moments and adding fractions. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/plms.70068\">https://doi.org/10.1112/plms.70068</a>","short":"T.F. Bloom, V.Z. Kuperberg, Proceedings of the London Mathematical Society 131 (2025)."},"oa_version":"Preprint","issue":"1","language":[{"iso":"eng"}],"publication":"Proceedings of the London Mathematical Society","article_type":"original","day":"01","scopus_import":"1","volume":131,"abstract":[{"lang":"eng","text":"We prove near-optimal upper bounds for the oddmoments of the distribution of coprime residues inshort intervals, confirming a conjecture of Montgomeryand Vaughan. As an application, we prove near-optimalupper bounds for the average of the refined singularseries in the Hardy–Littlewood conjectures concerningthe number of prime 𝑘-tuples for 𝑘 odd. The mainnew ingredient is a near-optimal upper bound for thenumber of solutions to ∑1 ⩽𝑖 ⩽𝑘𝑎 𝑖𝑞𝑖∈ ℤ when 𝑘 is odd,with gcd(𝑎𝑖 , 𝑞𝑖 ) = 1 and restrictions on the size of thenumerators and denominators, which is of indepen-dent interest."}],"publication_status":"published","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2312.09021"}],"OA_type":"green","OA_place":"repository","article_processing_charge":"No","month":"07","article_number":"e70068","external_id":{"arxiv":["2312.09021"]},"date_created":"2026-06-29T13:00:46Z","arxiv":1,"type":"journal_article","date_published":"2025-07-01T00:00:00Z","fulldoi":"https://doi.org/10.1112/plms.70068","extern":"1","author":[{"last_name":"Bloom","full_name":"Bloom, Thomas F.","first_name":"Thomas F."},{"first_name":"Vivian Zieve","id":"c3bac823-112d-11f0-a3f5-c264f852e697","last_name":"Kuperberg","full_name":"Kuperberg, Vivian Zieve"}],"oa":1,"intvolume":"       131","publisher":"Wiley","_id":"22203","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","doi":"10.1112/plms.70068","title":"Odd moments and adding fractions","mathsc":["11N69","11N05","14G05"],"year":"2025","date_updated":"2026-07-14T11:45:18Z"},{"date_created":"2023-08-27T22:01:18Z","external_id":{"isi":["001049312700001"],"arxiv":["1807.04057"]},"article_processing_charge":"Yes (via OA deal)","month":"10","department":[{"_id":"TaHa"}],"publication_status":"published","fulldoi":"https://doi.org/10.1112/plms.12555","date_published":"2023-10-01T00:00:00Z","type":"journal_article","arxiv":1,"publisher":"Wiley","intvolume":"       127","author":[{"orcid":"0000-0002-9582-2634","first_name":"Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Hausel, Tamás","last_name":"Hausel"},{"last_name":"Wong","full_name":"Wong, Michael Lennox","first_name":"Michael Lennox"},{"full_name":"Wyss, Dimitri","last_name":"Wyss","first_name":"Dimitri"}],"oa":1,"corr_author":"1","date_updated":"2025-04-14T09:12:46Z","year":"2023","title":"Arithmetic and metric aspects of open de Rham spaces","doi":"10.1112/plms.12555","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","has_accepted_license":"1","status":"public","_id":"14244","isi":1,"citation":{"chicago":"Hausel, Tamás, Michael Lennox Wong, and Dimitri Wyss. “Arithmetic and Metric Aspects of Open de Rham Spaces.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2023. <a href=\"https://doi.org/10.1112/plms.12555\">https://doi.org/10.1112/plms.12555</a>.","ieee":"T. Hausel, M. L. Wong, and D. Wyss, “Arithmetic and metric aspects of open de Rham spaces,” <i>Proceedings of the London Mathematical Society</i>, vol. 127, no. 4. Wiley, pp. 958–1027, 2023.","short":"T. Hausel, M.L. Wong, D. Wyss, Proceedings of the London Mathematical Society 127 (2023) 958–1027.","apa":"Hausel, T., Wong, M. L., &#38; Wyss, D. (2023). Arithmetic and metric aspects of open de Rham spaces. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/plms.12555\">https://doi.org/10.1112/plms.12555</a>","mla":"Hausel, Tamás, et al. “Arithmetic and Metric Aspects of Open de Rham Spaces.” <i>Proceedings of the London Mathematical Society</i>, vol. 127, no. 4, Wiley, 2023, pp. 958–1027, doi:<a href=\"https://doi.org/10.1112/plms.12555\">10.1112/plms.12555</a>.","ista":"Hausel T, Wong ML, Wyss D. 2023. Arithmetic and metric aspects of open de Rham spaces. Proceedings of the London Mathematical Society. 127(4), 958–1027.","ama":"Hausel T, Wong ML, Wyss D. Arithmetic and metric aspects of open de Rham spaces. <i>Proceedings of the London Mathematical Society</i>. 2023;127(4):958-1027. doi:<a href=\"https://doi.org/10.1112/plms.12555\">10.1112/plms.12555</a>"},"publication_identifier":{"issn":["0024-6115"],"eissn":["1460-244X"]},"file":[{"date_updated":"2024-01-30T12:56:00Z","access_level":"open_access","success":1,"creator":"dernst","file_size":651335,"relation":"main_file","file_id":"14910","date_created":"2024-01-30T12:56:00Z","file_name":"2023_ProcLondonMathSoc_Hausel.pdf","checksum":"2af4d2d6a8ae42f7d3fba0188e79ae82","content_type":"application/pdf"}],"file_date_updated":"2024-01-30T12:56:00Z","language":[{"iso":"eng"}],"acknowledgement":"We would like to thank Gergely Bérczy, Roger Bielawski, Philip Boalch, Sergey Cherkis, Andrew Dancer, Brent Doran, Eloïse Hamilton, Frances Kirwan, Bernard Leclerc, Emmanuel Letellier, Alessia Mandini, Maxence Mayrand, András Némethi, Szilárd Szabó, and Daisuke Yamakawa for discussions related to the paper. We especially thank the referee for an extensive list of very careful comments. At various stages of this project, the authors were supported by the Advanced Grant “Arithmetic and physics of Higgs moduli spaces” no. 320593 of the European Research Council, by grant no. 153627 and NCCR SwissMAP, both funded by the Swiss National Science Foundation as well as by EPF Lausanne and IST Austria. In the final stages of this project, MLW was supported by SFB/TR 45 “Periods, moduli and arithmetic of algebraic varieties,” subproject M08-10 “Moduli of vector bundles on higher-dimensional varieties.” DW was also supported by the Fondation Sciences Mathématiques de Paris, as well as public grants overseen by the Agence national de la recherche (ANR) of France as part of the Investissements d'avenir program, under reference numbers ANR-10-LABX-0098 and ANR-15-CE40-0008 (Défigéo).","issue":"4","oa_version":"Published Version","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"ddc":["510"],"publication":"Proceedings of the London Mathematical Society","page":"958-1027","ec_funded":1,"abstract":[{"lang":"eng","text":"In this paper, we determine the motivic class — in particular, the weight polynomial and conjecturally the Poincaré polynomial — of the open de Rham space, defined and studied by Boalch, of certain moduli spaces of irregular meromorphic connections on the trivial rank \r\n bundle on P1. The computation is by motivic Fourier transform. We show that the result satisfies the purity conjecture, that is, it agrees with the pure part of the conjectured mixed Hodge polynomial of the corresponding wild character variety. We also identify the open de Rham spaces with quiver varieties with multiplicities of Yamakawa and Geiss–Leclerc–Schröer. We finish with constructing natural complete hyperkähler metrics on them, which in the four-dimensional cases are expected to be of type ALF."}],"volume":127,"scopus_import":"1","day":"01","article_type":"original","project":[{"name":"Arithmetic and physics of Higgs moduli spaces","grant_number":"320593","call_identifier":"FP7","_id":"25E549F4-B435-11E9-9278-68D0E5697425"},{"_id":"25E6C798-B435-11E9-9278-68D0E5697425","grant_number":"153627","name":"Arithmetic quantization of character and quiver varities"}]},{"doi":"10.1112/plms.12373","title":"Almost all Steiner triple systems have perfect matchings","date_updated":"2023-02-23T14:01:43Z","year":"2020","quality_controlled":"1","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","status":"public","_id":"9581","publisher":"Wiley","intvolume":"       121","oa":1,"author":[{"last_name":"Kwan","full_name":"Kwan, Matthew Alan","first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","orcid":"0000-0002-4003-7567"}],"extern":"1","fulldoi":"https://doi.org/10.1112/plms.12373","type":"journal_article","date_published":"2020-12-01T00:00:00Z","arxiv":1,"date_created":"2021-06-22T06:35:16Z","external_id":{"arxiv":["1611.02246"]},"month":"12","article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1611.02246"}],"publication_status":"published","volume":121,"abstract":[{"text":"We show that for any  𝑛  divisible by 3, almost all order-  𝑛  Steiner triple systems have a perfect matching (also known as a parallel class or resolution class). In fact, we prove a general upper bound on the number of perfect matchings in a Steiner triple system and show that almost all Steiner triple systems essentially attain this maximum. We accomplish this via a general theorem comparing a uniformly random Steiner triple system to the outcome of the triangle removal process, which we hope will be useful for other problems. Our methods can also be adapted to other types of designs; for example, we sketch a proof of the theorem that almost all Latin squares have transversals.","lang":"eng"}],"article_type":"original","day":"01","scopus_import":"1","publication":"Proceedings of the London Mathematical Society","page":"1468-1495","language":[{"iso":"eng"}],"issue":"6","oa_version":"Preprint","citation":{"ama":"Kwan MA. Almost all Steiner triple systems have perfect matchings. <i>Proceedings of the London Mathematical Society</i>. 2020;121(6):1468-1495. doi:<a href=\"https://doi.org/10.1112/plms.12373\">10.1112/plms.12373</a>","mla":"Kwan, Matthew Alan. “Almost All Steiner Triple Systems Have Perfect Matchings.” <i>Proceedings of the London Mathematical Society</i>, vol. 121, no. 6, Wiley, 2020, pp. 1468–95, doi:<a href=\"https://doi.org/10.1112/plms.12373\">10.1112/plms.12373</a>.","ista":"Kwan MA. 2020. Almost all Steiner triple systems have perfect matchings. Proceedings of the London Mathematical Society. 121(6), 1468–1495.","short":"M.A. Kwan, Proceedings of the London Mathematical Society 121 (2020) 1468–1495.","apa":"Kwan, M. A. (2020). Almost all Steiner triple systems have perfect matchings. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/plms.12373\">https://doi.org/10.1112/plms.12373</a>","chicago":"Kwan, Matthew Alan. “Almost All Steiner Triple Systems Have Perfect Matchings.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2020. <a href=\"https://doi.org/10.1112/plms.12373\">https://doi.org/10.1112/plms.12373</a>.","ieee":"M. A. Kwan, “Almost all Steiner triple systems have perfect matchings,” <i>Proceedings of the London Mathematical Society</i>, vol. 121, no. 6. Wiley, pp. 1468–1495, 2020."},"publication_identifier":{"issn":["0024-6115"],"eissn":["1460-244X"]}},{"date_created":"2018-12-11T11:52:10Z","external_id":{"arxiv":["0003093"]},"OA_place":"repository","month":"05","article_processing_charge":"No","OA_type":"green","publication_status":"published","main_file_link":[{"url":"http://arxiv.org/abs/math/0003093","open_access":"1"}],"fulldoi":"https://doi.org/10.1112/S0024611503014618","type":"journal_article","date_published":"2004-05-01T00:00:00Z","arxiv":1,"publisher":"Oxford University Press","intvolume":"        88","publist_id":"5736","author":[{"full_name":"Hausel, Tamas","last_name":"Hausel","orcid":"0000-0002-9582-2634","first_name":"Tamas","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Michael","full_name":"Thaddeus, Michael","last_name":"Thaddeus"}],"oa":1,"extern":"1","date_updated":"2026-09-30T13:24:04Z","year":"2004","title":"Generators for the cohomology ring of the moduli space of rank 2 higgs bundles","doi":"10.1112/S0024611503014618","status":"public","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"1464","citation":{"chicago":"Hausel, Tamás, and Michael Thaddeus. “Generators for the Cohomology Ring of the Moduli Space of Rank 2 Higgs Bundles.” <i>Proceedings of the London Mathematical Society</i>. Oxford University Press, 2004. <a href=\"https://doi.org/10.1112/S0024611503014618\">https://doi.org/10.1112/S0024611503014618</a>.","ieee":"T. Hausel and M. Thaddeus, “Generators for the cohomology ring of the moduli space of rank 2 higgs bundles,” <i>Proceedings of the London Mathematical Society</i>, vol. 88, no. 3. Oxford University Press, pp. 632–658, 2004.","short":"T. Hausel, M. Thaddeus, Proceedings of the London Mathematical Society 88 (2004) 632–658.","apa":"Hausel, T., &#38; Thaddeus, M. (2004). Generators for the cohomology ring of the moduli space of rank 2 higgs bundles. <i>Proceedings of the London Mathematical Society</i>. Oxford University Press. <a href=\"https://doi.org/10.1112/S0024611503014618\">https://doi.org/10.1112/S0024611503014618</a>","mla":"Hausel, Tamás, and Michael Thaddeus. “Generators for the Cohomology Ring of the Moduli Space of Rank 2 Higgs Bundles.” <i>Proceedings of the London Mathematical Society</i>, vol. 88, no. 3, Oxford University Press, 2004, pp. 632–58, doi:<a href=\"https://doi.org/10.1112/S0024611503014618\">10.1112/S0024611503014618</a>.","ista":"Hausel T, Thaddeus M. 2004. Generators for the cohomology ring of the moduli space of rank 2 higgs bundles. Proceedings of the London Mathematical Society. 88(3), 632–658.","ama":"Hausel T, Thaddeus M. Generators for the cohomology ring of the moduli space of rank 2 higgs bundles. <i>Proceedings of the London Mathematical Society</i>. 2004;88(3):632-658. doi:<a href=\"https://doi.org/10.1112/S0024611503014618\">10.1112/S0024611503014618</a>"},"publication_identifier":{"eissn":["1460-244X"],"issn":["0024-6115"]},"language":[{"iso":"eng"}],"issue":"3","oa_version":"None","publication":"Proceedings of the London Mathematical Society","page":"632 - 658","abstract":[{"lang":"eng","text":"The moduli space of stable vector bundles on a Riemann surface is smooth when the rank and degree are coprime, and is diffeomorphic to the space of unitary connections of central constant curvature. A classic result of Newstead and Atiyah and Bott asserts that its rational cohomology ring is generated by the universal classes, that is, by the Kunneth components of the Chern classes of the universal bundle.\r\n\r\nThis paper studies the larger, non-compact moduli space of Higgs bundles, as introduced by Hitchin and Simpson, with values in the canonical bundle K. This is diffeomorphic to the space of all connections of central constant curvature, whether unitary or not. The main result of the paper is that, in the rank 2 case, the rational cohomology ring of this space is again generated by universal classes.\r\n\r\nThe spaces of Higgs bundles with values in K(n) for n &gt; 0 turn out to be essential to the story. Indeed, we show that their direct limit has the homotopy type of the classifying space of the gauge group, and hence has cohomology generated by universal classes. 2000 Mathematics Subject Classification 14H60 (primary), 14D20, 14H81, 32Q55, 58D27 (secondary). "}],"volume":88,"day":"01","article_type":"original"}]