[{"publication":"Proceedings of the London Mathematical Society","external_id":{"isi":["001049312700001"],"arxiv":["1807.04057"]},"file":[{"creator":"dernst","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_name":"2023_ProcLondonMathSoc_Hausel.pdf","file_size":651335,"checksum":"2af4d2d6a8ae42f7d3fba0188e79ae82","file_id":"14910","date_created":"2024-01-30T12:56:00Z","date_updated":"2024-01-30T12:56:00Z","success":1}],"title":"Arithmetic and metric aspects of open de Rham spaces","issue":"4","scopus_import":"1","has_accepted_license":"1","project":[{"_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces","grant_number":"320593","call_identifier":"FP7"},{"_id":"25E6C798-B435-11E9-9278-68D0E5697425","name":"Arithmetic quantization of character and quiver varities","grant_number":"153627"}],"arxiv":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.","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.","short":"T. Hausel, M.L. Wong, D. Wyss, Proceedings of the London Mathematical Society 127 (2023) 958–1027.","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>.","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>","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_status":"published","oa_version":"Published Version","page":"958-1027","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"01","ec_funded":1,"abstract":[{"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.","lang":"eng"}],"status":"public","date_updated":"2024-01-30T12:56:10Z","isi":1,"volume":127,"article_type":"original","month":"10","quality_controlled":"1","publication_identifier":{"issn":["0024-6115"],"eissn":["1460-244X"]},"article_processing_charge":"Yes (via OA deal)","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2024-01-30T12:56:00Z","intvolume":"       127","date_created":"2023-08-27T22:01:18Z","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).","department":[{"_id":"TaHa"}],"date_published":"2023-10-01T00:00:00Z","author":[{"id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel","first_name":"Tamás","full_name":"Hausel, Tamás"},{"last_name":"Wong","full_name":"Wong, Michael Lennox","first_name":"Michael Lennox"},{"last_name":"Wyss","first_name":"Dimitri","full_name":"Wyss, Dimitri"}],"oa":1,"_id":"14244","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1112/plms.12555","publisher":"Wiley","year":"2023"},{"project":[{"name":"Arithmetic and physics of Higgs moduli spaces","_id":"25E549F4-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"320593"}],"citation":{"chicago":"Mirković, Ivan, Yaping Yang, and Gufang Zhao. “Loop Grassmannians of Quivers and Affine Quantum Groups.” In <i>Representation Theory and Algebraic Geometry</i>, edited by Vladimir Baranovskky, Nicolas Guay, and Travis Schedler, 1st ed., 347–92. TM. Cham: Springer Nature; Birkhäuser, 2022. <a href=\"https://doi.org/10.1007/978-3-030-82007-7_8\">https://doi.org/10.1007/978-3-030-82007-7_8</a>.","ieee":"I. Mirković, Y. Yang, and G. Zhao, “Loop Grassmannians of Quivers and Affine Quantum Groups,” in <i>Representation Theory and Algebraic Geometry</i>, 1st ed., V. Baranovskky, N. Guay, and T. Schedler, Eds. Cham: Springer Nature; Birkhäuser, 2022, pp. 347–392.","mla":"Mirković, Ivan, et al. “Loop Grassmannians of Quivers and Affine Quantum Groups.” <i>Representation Theory and Algebraic Geometry</i>, edited by Vladimir Baranovskky et al., 1st ed., Springer Nature; Birkhäuser, 2022, pp. 347–92, doi:<a href=\"https://doi.org/10.1007/978-3-030-82007-7_8\">10.1007/978-3-030-82007-7_8</a>.","ista":"Mirković I, Yang Y, Zhao G. 2022.Loop Grassmannians of Quivers and Affine Quantum Groups. In: Representation Theory and Algebraic Geometry. Trends in Mathematics, , 347–392.","apa":"Mirković, I., Yang, Y., &#38; Zhao, G. (2022). Loop Grassmannians of Quivers and Affine Quantum Groups. In V. Baranovskky, N. Guay, &#38; T. Schedler (Eds.), <i>Representation Theory and Algebraic Geometry</i> (1st ed., pp. 347–392). Cham: Springer Nature; Birkhäuser. <a href=\"https://doi.org/10.1007/978-3-030-82007-7_8\">https://doi.org/10.1007/978-3-030-82007-7_8</a>","short":"I. Mirković, Y. Yang, G. Zhao, in:, V. Baranovskky, N. Guay, T. Schedler (Eds.), Representation Theory and Algebraic Geometry, 1st ed., Springer Nature; Birkhäuser, Cham, 2022, pp. 347–392.","ama":"Mirković I, Yang Y, Zhao G. Loop Grassmannians of Quivers and Affine Quantum Groups. In: Baranovskky V, Guay N, Schedler T, eds. <i>Representation Theory and Algebraic Geometry</i>. 1st ed. TM. Cham: Springer Nature; Birkhäuser; 2022:347-392. doi:<a href=\"https://doi.org/10.1007/978-3-030-82007-7_8\">10.1007/978-3-030-82007-7_8</a>"},"arxiv":1,"scopus_import":"1","editor":[{"last_name":"Baranovskky","full_name":"Baranovskky, Vladimir","first_name":"Vladimir"},{"first_name":"Nicolas","full_name":"Guay, Nicolas","last_name":"Guay"},{"last_name":"Schedler","first_name":"Travis","full_name":"Schedler, Travis"}],"alternative_title":["Trends in Mathematics"],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1810.10095"}],"publication":"Representation Theory and Algebraic Geometry","series_title":"TM","external_id":{"arxiv":["1810.10095"]},"title":"Loop Grassmannians of Quivers and Affine Quantum Groups","date_updated":"2023-01-27T07:07:31Z","status":"public","publication_status":"published","oa_version":"Preprint","page":"347-392","day":"16","ec_funded":1,"abstract":[{"lang":"eng","text":"We construct for each choice of a quiver Q, a cohomology theory A, and a poset P a “loop Grassmannian” GP(Q,A). This generalizes loop Grassmannians of semisimple groups and the loop Grassmannians of based quadratic forms. The addition of a “dilation” torus D⊆G2m gives a quantization GPD(Q,A). This construction is motivated by the program of introducing an inner cohomology theory in algebraic geometry adequate for the Geometric Langlands program (Mirković, Some extensions of the notion of loop Grassmannians. Rad Hrvat. Akad. Znan. Umjet. Mat. Znan., the Mardešić issue. No. 532, 53–74, 2017) and on the construction of affine quantum groups from generalized cohomology theories (Yang and Zhao, Quiver varieties and elliptic quantum groups, preprint. arxiv1708.01418)."}],"edition":"1","date_created":"2023-01-16T10:06:41Z","acknowledgement":"I.M. thanks Zhijie Dong for long-term discussions on the material that entered this work. We thank Misha Finkelberg for pointing out errors in earlier versions. His advice and his insistence have led to a much better paper. A part of the writing was done at the conference at IST (Vienna) attended by all coauthors. We therefore thank the organizers of the conference and the support of ERC Advanced Grant Arithmetic and Physics of Higgs moduli spaces No. 320593. The work of I.M. was partially supported by NSF grants. The work of Y.Y. was partially supported by the Australian Research Council (ARC) via the award DE190101231. The work of G.Z. was partially supported by ARC via the award DE190101222.","department":[{"_id":"TaHa"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","place":"Cham","month":"06","quality_controlled":"1","publication_identifier":{"isbn":["9783030820060"],"eisbn":["9783030820077"],"issn":["2297-0215"],"eissn":["2297-024X"]},"language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-82007-7_8","publisher":"Springer Nature; Birkhäuser","year":"2022","type":"book_chapter","author":[{"full_name":"Mirković, Ivan","first_name":"Ivan","last_name":"Mirković"},{"first_name":"Yaping","full_name":"Yang, Yaping","last_name":"Yang"},{"id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","last_name":"Zhao","full_name":"Zhao, Gufang","first_name":"Gufang"}],"oa":1,"_id":"12303","date_published":"2022-06-16T00:00:00Z"},{"_id":"9359","oa":1,"author":[{"first_name":"Quoc P","full_name":"Ho, Quoc P","id":"3DD82E3C-F248-11E8-B48F-1D18A9856A87","last_name":"Ho"}],"date_published":"2021-04-27T00:00:00Z","year":"2021","publisher":"Mathematical Sciences Publishers","doi":"10.2140/gt.2021.25.813","language":[{"iso":"eng"}],"type":"journal_article","publication_identifier":{"issn":["1364-0380"]},"quality_controlled":"1","month":"04","article_type":"original","volume":25,"isi":1,"acknowledgement":"This paper owes an obvious intellectual debt to the illuminating treatments of factorization homology by J.\r\nFrancis, D. Gaitsgory, and J. Lurie in [GL,G1, FG]. The author would like to thank B. Farb and J. Wolfson for\r\nbringing the question of explaining coincidences in homological densities to his attention. Moreover, the author\r\nthanks J. Wolfson for many helpful conversations on the subject, O. Randal-Williams for many comments which\r\ngreatly help improve the exposition, and G. C. Drummond-Cole for many useful conversations on L∞-algebras.\r\nFinally, the author is grateful to the anonymous referee for carefully reading the manuscript and for providing\r\nnumerous comments which greatly helped improve the clarity and precision of the exposition.\r\nThis work is supported by the Advanced Grant “Arithmetic and Physics of Higgs moduli spaces” No. 320593 of\r\nthe European Research Council and the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization\r\nHomology,” Austrian Science Fund (FWF): M 2751.","department":[{"_id":"TaHa"}],"date_created":"2021-05-02T06:59:33Z","intvolume":"        25","keyword":["Generalized configuration spaces","homological stability","homological densities","chiral algebras","chiral homology","factorization algebras","Koszul duality","Ran space"],"file_date_updated":"2021-05-03T06:54:06Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","ddc":["514","516","512"],"abstract":[{"lang":"eng","text":"We prove that the factorization homologies of a scheme with coefficients in truncated polynomial algebras compute the cohomologies of its generalized configuration spaces. Using Koszul duality between commutative algebras and Lie algebras, we obtain new expressions for the cohomologies of the latter. As a consequence, we obtain a uniform and conceptual approach for treating homological stability, homological densities, and arithmetic densities of generalized configuration spaces. Our results categorify, generalize, and in fact provide a conceptual understanding of the coincidences appearing in the work of Farb--Wolfson--Wood. Our computation of the stable homological densities also yields rational homotopy types, answering a question posed by Vakil--Wood. Our approach hinges on the study of homological stability of cohomological Chevalley complexes, which is of independent interest.\r\n"}],"ec_funded":1,"day":"27","page":"813-912","oa_version":"Submitted Version","publication_status":"published","date_updated":"2023-08-08T13:28:59Z","status":"public","title":"Homological stability and densities of generalized configuration spaces","file":[{"checksum":"643a8d2d6f06f0888dcd7503f55d0920","date_created":"2021-05-03T06:54:06Z","file_id":"9366","date_updated":"2021-05-03T06:54:06Z","success":1,"file_name":"densities.pdf","file_size":479268,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","creator":"qho"}],"external_id":{"isi":["000682738600005"],"arxiv":["1802.07948"]},"publication":"Geometry & Topology","citation":{"ama":"Ho QP. Homological stability and densities of generalized configuration spaces. <i>Geometry &#38; Topology</i>. 2021;25(2):813-912. doi:<a href=\"https://doi.org/10.2140/gt.2021.25.813\">10.2140/gt.2021.25.813</a>","apa":"Ho, Q. P. (2021). Homological stability and densities of generalized configuration spaces. <i>Geometry &#38; Topology</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/gt.2021.25.813\">https://doi.org/10.2140/gt.2021.25.813</a>","ista":"Ho QP. 2021. Homological stability and densities of generalized configuration spaces. Geometry &#38; Topology. 25(2), 813–912.","mla":"Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration Spaces.” <i>Geometry &#38; Topology</i>, vol. 25, no. 2, Mathematical Sciences Publishers, 2021, pp. 813–912, doi:<a href=\"https://doi.org/10.2140/gt.2021.25.813\">10.2140/gt.2021.25.813</a>.","short":"Q.P. Ho, Geometry &#38; Topology 25 (2021) 813–912.","ieee":"Q. P. Ho, “Homological stability and densities of generalized configuration spaces,” <i>Geometry &#38; Topology</i>, vol. 25, no. 2. Mathematical Sciences Publishers, pp. 813–912, 2021.","chicago":"Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration Spaces.” <i>Geometry &#38; Topology</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/gt.2021.25.813\">https://doi.org/10.2140/gt.2021.25.813</a>."},"arxiv":1,"project":[{"grant_number":"320593","call_identifier":"FP7","_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces"},{"_id":"26B96266-B435-11E9-9278-68D0E5697425","name":"Algebro-Geometric Applications of Factorization Homology","call_identifier":"FWF","grant_number":"M02751"}],"has_accepted_license":"1","issue":"2"},{"project":[{"grant_number":"320593","call_identifier":"FP7","_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces"}],"arxiv":1,"citation":{"mla":"Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” <i>Transformation Groups</i>, vol. 25, Springer Nature, 2020, pp. 1371–85, doi:<a href=\"https://doi.org/10.1007/s00031-020-09572-6\">10.1007/s00031-020-09572-6</a>.","ista":"Yang Y, Zhao G. 2020. The PBW theorem for affine Yangians. Transformation Groups. 25, 1371–1385.","short":"Y. Yang, G. Zhao, Transformation Groups 25 (2020) 1371–1385.","apa":"Yang, Y., &#38; Zhao, G. (2020). The PBW theorem for affine Yangians. <i>Transformation Groups</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00031-020-09572-6\">https://doi.org/10.1007/s00031-020-09572-6</a>","ama":"Yang Y, Zhao G. The PBW theorem for affine Yangians. <i>Transformation Groups</i>. 2020;25:1371-1385. doi:<a href=\"https://doi.org/10.1007/s00031-020-09572-6\">10.1007/s00031-020-09572-6</a>","chicago":"Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” <i>Transformation Groups</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00031-020-09572-6\">https://doi.org/10.1007/s00031-020-09572-6</a>.","ieee":"Y. Yang and G. Zhao, “The PBW theorem for affine Yangians,” <i>Transformation Groups</i>, vol. 25. Springer Nature, pp. 1371–1385, 2020."},"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.04375"}],"publication":"Transformation Groups","external_id":{"isi":["000534874300003"],"arxiv":["1804.04375"]},"title":"The PBW theorem for affine Yangians","date_updated":"2023-08-21T07:06:21Z","status":"public","publication_status":"published","oa_version":"Preprint","page":"1371-1385","day":"01","ec_funded":1,"abstract":[{"text":"We prove that the Yangian associated to an untwisted symmetric affine Kac–Moody Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter is constructed in [YZ14] as an algebraic formalism of cohomological Hall algebras. As a consequence, we obtain the Poincare–Birkhoff–Witt (PBW) theorem for this class of affine Yangians. Another independent proof of the PBW theorem is given recently by Guay, Regelskis, and Wendlandt [GRW18].","lang":"eng"}],"date_created":"2020-06-07T22:00:55Z","department":[{"_id":"TaHa"}],"acknowledgement":"Gufang Zhao is affiliated to IST Austria, Hausel group until July of 2018. Supported by the Advanced Grant Arithmetic and Physics of Higgs moduli spaces No. 320593 of the European Research Council.","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"        25","month":"12","quality_controlled":"1","publication_identifier":{"eissn":["1531586X"],"issn":["10834362"]},"isi":1,"article_type":"original","volume":25,"language":[{"iso":"eng"}],"doi":"10.1007/s00031-020-09572-6","publisher":"Springer Nature","year":"2020","type":"journal_article","author":[{"first_name":"Yaping","full_name":"Yang, Yaping","last_name":"Yang","id":"360D8648-F248-11E8-B48F-1D18A9856A87"},{"id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","last_name":"Zhao","full_name":"Zhao, Gufang","first_name":"Gufang"}],"oa":1,"_id":"7940","date_published":"2020-12-01T00:00:00Z"},{"intvolume":"       376","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"TaHa"}],"date_created":"2019-11-12T14:01:27Z","article_type":"original","volume":376,"isi":1,"quality_controlled":"1","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"month":"06","type":"journal_article","publisher":"Springer Nature","year":"2020","language":[{"iso":"eng"}],"doi":"10.1007/s00220-019-03575-5","date_published":"2020-06-01T00:00:00Z","oa":1,"_id":"7004","author":[{"last_name":"Rapcak","full_name":"Rapcak, Miroslav","first_name":"Miroslav"},{"first_name":"Yan","full_name":"Soibelman, Yan","last_name":"Soibelman"},{"last_name":"Yang","first_name":"Yaping","full_name":"Yang, Yaping"},{"last_name":"Zhao","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","full_name":"Zhao, Gufang","first_name":"Gufang"}],"scopus_import":"1","project":[{"_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces","call_identifier":"FP7","grant_number":"320593"}],"citation":{"chicago":"Rapcak, Miroslav, Yan Soibelman, Yaping Yang, and Gufang Zhao. “Cohomological Hall Algebras, Vertex Algebras and Instantons.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03575-5\">https://doi.org/10.1007/s00220-019-03575-5</a>.","ieee":"M. Rapcak, Y. Soibelman, Y. Yang, and G. Zhao, “Cohomological Hall algebras, vertex algebras and instantons,” <i>Communications in Mathematical Physics</i>, vol. 376. Springer Nature, pp. 1803–1873, 2020.","short":"M. Rapcak, Y. Soibelman, Y. Yang, G. Zhao, Communications in Mathematical Physics 376 (2020) 1803–1873.","apa":"Rapcak, M., Soibelman, Y., Yang, Y., &#38; Zhao, G. (2020). Cohomological Hall algebras, vertex algebras and instantons. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03575-5\">https://doi.org/10.1007/s00220-019-03575-5</a>","ista":"Rapcak M, Soibelman Y, Yang Y, Zhao G. 2020. Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics. 376, 1803–1873.","mla":"Rapcak, Miroslav, et al. “Cohomological Hall Algebras, Vertex Algebras and Instantons.” <i>Communications in Mathematical Physics</i>, vol. 376, Springer Nature, 2020, pp. 1803–73, doi:<a href=\"https://doi.org/10.1007/s00220-019-03575-5\">10.1007/s00220-019-03575-5</a>.","ama":"Rapcak M, Soibelman Y, Yang Y, Zhao G. Cohomological Hall algebras, vertex algebras and instantons. <i>Communications in Mathematical Physics</i>. 2020;376:1803-1873. doi:<a href=\"https://doi.org/10.1007/s00220-019-03575-5\">10.1007/s00220-019-03575-5</a>"},"arxiv":1,"external_id":{"isi":["000536255500004"],"arxiv":["1810.10402"]},"title":"Cohomological Hall algebras, vertex algebras and instantons","publication":"Communications in Mathematical Physics","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1810.10402"}],"status":"public","date_updated":"2023-08-17T14:02:59Z","ec_funded":1,"abstract":[{"text":"We define an action of the (double of) Cohomological Hall algebra of Kontsevich and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov. We identify this action with the one of the affine Yangian of gl(1). Based on that we derive the vertex algebra at the corner Wr1,r2,r3 of Gaiotto and Rapčák. We conjecture that our approach works for a big class of Calabi–Yau categories, including those associated with toric Calabi–Yau 3-folds.","lang":"eng"}],"publication_status":"published","page":"1803-1873","oa_version":"Preprint","day":"01"},{"date_created":"2019-11-04T16:10:50Z","department":[{"_id":"TaHa"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","intvolume":"       147","month":"11","publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"quality_controlled":"1","isi":1,"article_type":"original","volume":147,"doi":"10.1090/proc/14586","language":[{"iso":"eng"}],"year":"2019","publisher":"AMS","type":"journal_article","author":[{"full_name":"Li, Penghui","first_name":"Penghui","last_name":"Li","id":"42A24CCC-F248-11E8-B48F-1D18A9856A87"}],"_id":"6986","oa":1,"date_published":"2019-11-01T00:00:00Z","arxiv":1,"citation":{"ieee":"P. Li, “A colimit of traces of reflection groups,” <i>Proceedings of the American Mathematical Society</i>, vol. 147, no. 11. AMS, pp. 4597–4604, 2019.","chicago":"Li, Penghui. “A Colimit of Traces of Reflection Groups.” <i>Proceedings of the American Mathematical Society</i>. AMS, 2019. <a href=\"https://doi.org/10.1090/proc/14586\">https://doi.org/10.1090/proc/14586</a>.","ama":"Li P. A colimit of traces of reflection groups. <i>Proceedings of the American Mathematical Society</i>. 2019;147(11):4597-4604. doi:<a href=\"https://doi.org/10.1090/proc/14586\">10.1090/proc/14586</a>","ista":"Li P. 2019. A colimit of traces of reflection groups. Proceedings of the American Mathematical Society. 147(11), 4597–4604.","apa":"Li, P. (2019). A colimit of traces of reflection groups. <i>Proceedings of the American Mathematical Society</i>. AMS. <a href=\"https://doi.org/10.1090/proc/14586\">https://doi.org/10.1090/proc/14586</a>","short":"P. Li, Proceedings of the American Mathematical Society 147 (2019) 4597–4604.","mla":"Li, Penghui. “A Colimit of Traces of Reflection Groups.” <i>Proceedings of the American Mathematical Society</i>, vol. 147, no. 11, AMS, 2019, pp. 4597–604, doi:<a href=\"https://doi.org/10.1090/proc/14586\">10.1090/proc/14586</a>."},"project":[{"_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces","call_identifier":"FP7","grant_number":"320593"}],"scopus_import":"1","issue":"11","main_file_link":[{"url":"https://arxiv.org/abs/1810.07039","open_access":"1"}],"publication":"Proceedings of the American Mathematical Society","title":"A colimit of traces of reflection groups","external_id":{"arxiv":["1810.07039"],"isi":["000488621700004"]},"date_updated":"2023-09-05T12:22:21Z","status":"public","day":"01","oa_version":"Preprint","publication_status":"published","page":"4597-4604","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. "}],"ec_funded":1},{"abstract":[{"text":"We count points over a finite field on wild character varieties,of Riemann surfaces for singularities with regular semisimple leading term. The new feature in our counting formulas is the appearance of characters of Yokonuma–Hecke algebras. Our result leads to the conjecture that the mixed Hodge polynomials of these character varieties agree with previously conjectured perverse Hodge polynomials of certain twisted parabolic Higgs moduli spaces, indicating the\r\npossibility of a P = W conjecture for a suitable wild Hitchin system.","lang":"eng"}],"ec_funded":1,"day":"01","page":"2995-3052","publication_status":"published","oa_version":"Preprint","date_updated":"2023-08-24T14:24:49Z","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1604.03382"}],"title":"Arithmetic and representation theory of wild character varieties","external_id":{"isi":["000480413600002"],"arxiv":["1604.03382"]},"publication":"Journal of the European Mathematical Society","citation":{"ama":"Hausel T, Mereb M, Wong M. Arithmetic and representation theory of wild character varieties. <i>Journal of the European Mathematical Society</i>. 2019;21(10):2995-3052. doi:<a href=\"https://doi.org/10.4171/JEMS/896\">10.4171/JEMS/896</a>","apa":"Hausel, T., Mereb, M., &#38; Wong, M. (2019). Arithmetic and representation theory of wild character varieties. <i>Journal of the European Mathematical Society</i>. European Mathematical Society. <a href=\"https://doi.org/10.4171/JEMS/896\">https://doi.org/10.4171/JEMS/896</a>","mla":"Hausel, Tamás, et al. “Arithmetic and Representation Theory of Wild Character Varieties.” <i>Journal of the European Mathematical Society</i>, vol. 21, no. 10, European Mathematical Society, 2019, pp. 2995–3052, doi:<a href=\"https://doi.org/10.4171/JEMS/896\">10.4171/JEMS/896</a>.","ista":"Hausel T, Mereb M, Wong M. 2019. Arithmetic and representation theory of wild character varieties. Journal of the European Mathematical Society. 21(10), 2995–3052.","short":"T. Hausel, M. Mereb, M. Wong, Journal of the European Mathematical Society 21 (2019) 2995–3052.","ieee":"T. Hausel, M. Mereb, and M. Wong, “Arithmetic and representation theory of wild character varieties,” <i>Journal of the European Mathematical Society</i>, vol. 21, no. 10. European Mathematical Society, pp. 2995–3052, 2019.","chicago":"Hausel, Tamás, Martin Mereb, and Michael Wong. “Arithmetic and Representation Theory of Wild Character Varieties.” <i>Journal of the European Mathematical Society</i>. European Mathematical Society, 2019. <a href=\"https://doi.org/10.4171/JEMS/896\">https://doi.org/10.4171/JEMS/896</a>."},"arxiv":1,"project":[{"name":"Arithmetic and physics of Higgs moduli spaces","_id":"25E549F4-B435-11E9-9278-68D0E5697425","grant_number":"320593","call_identifier":"FP7"}],"scopus_import":"1","issue":"10","_id":"439","oa":1,"author":[{"last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Hausel, Tamas","first_name":"Tamas"},{"last_name":"Mereb","id":"43D735EE-F248-11E8-B48F-1D18A9856A87","first_name":"Martin","full_name":"Mereb, Martin"},{"last_name":"Wong","first_name":"Michael","full_name":"Wong, Michael"}],"date_published":"2019-10-01T00:00:00Z","year":"2019","publisher":"European Mathematical Society","doi":"10.4171/JEMS/896","language":[{"iso":"eng"}],"type":"journal_article","publist_id":"7384","publication_identifier":{"eissn":["1435-9855"]},"quality_controlled":"1","month":"10","volume":21,"article_type":"original","isi":1,"department":[{"_id":"TaHa"}],"date_created":"2018-12-11T11:46:29Z","intvolume":"        21","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"doi":"10.1016/j.jalgebra.2018.03.015","language":[{"iso":"eng"}],"year":"2018","publisher":"World Scientific Publishing","type":"journal_article","author":[{"first_name":"Iordan V","full_name":"Ganev, Iordan V","id":"447491B8-F248-11E8-B48F-1D18A9856A87","last_name":"Ganev"}],"_id":"322","oa":1,"date_published":"2018-07-15T00:00:00Z","date_created":"2018-12-11T11:45:49Z","acknowledgement":"National Science Foundation: Graduate Research Fellowship and grant No.0932078000; ERC Advanced Grant “Arithmetic and Physics of Higgs moduli spaces” No. 320593 \r\nThe author is grateful to David Jordan for suggesting this project and providing guidance throughout, particularly for the formulation of Frobenius quantum moment maps and key ideas in the proofs of Theorems 3.12 and 4.8. Special thanks to David Ben-Zvi (the author's PhD advisor) for numerous discussions and constant encouragement, and for suggesting the term ‘hypertoric quantum group.’ Many results appearing in the current paper were proven independently by Nicholas Cooney; the author is grateful to Nicholas for sharing his insight on various topics, including Proposition 3.8. The author also thanks Nicholas Proudfoot for relating the definition of multiplicative hypertoric varieties, as well as the content of Remark 2.14. The author also benefited immensely from the close reading and detailed comments of an anonymous referee, and from conversations with Justin Hilburn, Kobi Kremnitzer, Michael McBreen, Tom Nevins, Travis Schedler, and Ben Webster. \r\n\r\n\r\n\r\n","department":[{"_id":"TaHa"}],"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","intvolume":"       506","month":"07","publist_id":"7543","quality_controlled":"1","isi":1,"volume":506,"date_updated":"2023-09-15T12:08:38Z","status":"public","day":"15","oa_version":"Preprint","page":"92 - 128","publication_status":"published","abstract":[{"text":"We construct quantizations of multiplicative hypertoric varieties using an algebra of q-difference operators on affine space, where q is a root of unity in C. The quantization defines a matrix bundle (i.e. Azumaya algebra) over the multiplicative hypertoric variety and admits an explicit finite étale splitting. The global sections of this Azumaya algebra is a hypertoric quantum group, and we prove a localization theorem. We introduce a general framework of Frobenius quantum moment maps and their Hamiltonian reductions; our results shed light on an instance of this framework.","lang":"eng"}],"ec_funded":1,"citation":{"ama":"Ganev IV. Quantizations of multiplicative hypertoric varieties at a root of unity. <i>Journal of Algebra</i>. 2018;506:92-128. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2018.03.015\">10.1016/j.jalgebra.2018.03.015</a>","short":"I.V. Ganev, Journal of Algebra 506 (2018) 92–128.","ista":"Ganev IV. 2018. Quantizations of multiplicative hypertoric varieties at a root of unity. Journal of Algebra. 506, 92–128.","mla":"Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties at a Root of Unity.” <i>Journal of Algebra</i>, vol. 506, World Scientific Publishing, 2018, pp. 92–128, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2018.03.015\">10.1016/j.jalgebra.2018.03.015</a>.","apa":"Ganev, I. V. (2018). Quantizations of multiplicative hypertoric varieties at a root of unity. <i>Journal of Algebra</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1016/j.jalgebra.2018.03.015\">https://doi.org/10.1016/j.jalgebra.2018.03.015</a>","ieee":"I. V. Ganev, “Quantizations of multiplicative hypertoric varieties at a root of unity,” <i>Journal of Algebra</i>, vol. 506. World Scientific Publishing, pp. 92–128, 2018.","chicago":"Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties at a Root of Unity.” <i>Journal of Algebra</i>. World Scientific Publishing, 2018. <a href=\"https://doi.org/10.1016/j.jalgebra.2018.03.015\">https://doi.org/10.1016/j.jalgebra.2018.03.015</a>."},"arxiv":1,"project":[{"_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces","call_identifier":"FP7","grant_number":"320593"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1412.7211"}],"publication":"Journal of Algebra","title":"Quantizations of multiplicative hypertoric varieties at a root of unity","external_id":{"arxiv":["1412.7211"],"isi":["000433270600005"]}},{"project":[{"call_identifier":"FP7","grant_number":"320593","name":"Arithmetic and physics of Higgs moduli spaces","_id":"25E549F4-B435-11E9-9278-68D0E5697425"}],"citation":{"short":"B. Davison, Quarterly Journal of Mathematics 68 (2017) 635–703.","apa":"Davison, B. (2017). The critical CoHA of a quiver with potential. <i>Quarterly Journal of Mathematics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/qmath/haw053\">https://doi.org/10.1093/qmath/haw053</a>","ista":"Davison B. 2017. The critical CoHA of a quiver with potential. Quarterly Journal of Mathematics. 68(2), 635–703.","mla":"Davison, Ben. “The Critical CoHA of a Quiver with Potential.” <i>Quarterly Journal of Mathematics</i>, vol. 68, no. 2, Oxford University Press, 2017, pp. 635–703, doi:<a href=\"https://doi.org/10.1093/qmath/haw053\">10.1093/qmath/haw053</a>.","ama":"Davison B. The critical CoHA of a quiver with potential. <i>Quarterly Journal of Mathematics</i>. 2017;68(2):635-703. doi:<a href=\"https://doi.org/10.1093/qmath/haw053\">10.1093/qmath/haw053</a>","chicago":"Davison, Ben. “The Critical CoHA of a Quiver with Potential.” <i>Quarterly Journal of Mathematics</i>. Oxford University Press, 2017. <a href=\"https://doi.org/10.1093/qmath/haw053\">https://doi.org/10.1093/qmath/haw053</a>.","ieee":"B. Davison, “The critical CoHA of a quiver with potential,” <i>Quarterly Journal of Mathematics</i>, vol. 68, no. 2. Oxford University Press, pp. 635–703, 2017."},"issue":"2","scopus_import":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1311.7172"}],"publication":"Quarterly Journal of Mathematics","title":"The critical CoHA of a quiver with potential","date_updated":"2021-01-12T08:09:24Z","status":"public","page":"635 - 703","oa_version":"Submitted Version","publication_status":"published","day":"01","ec_funded":1,"abstract":[{"lang":"eng","text":"Pursuing the similarity between the Kontsevich-Soibelman construction of the cohomological Hall algebra (CoHA) of BPS states and Lusztig's construction of canonical bases for quantum enveloping algebras, and the similarity between the integrality conjecture for motivic Donaldson-Thomas invariants and the PBW theorem for quantum enveloping algebras, we build a coproduct on the CoHA associated to a quiver with potential. We also prove a cohomological dimensional reduction theorem, further linking a special class of CoHAs with Yangians, and explaining how to connect the study of character varieties with the study of CoHAs."}],"date_created":"2018-12-11T11:47:55Z","department":[{"_id":"TaHa"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        68","month":"06","quality_controlled":"1","publist_id":"7022","publication_identifier":{"issn":["00335606"]},"volume":68,"language":[{"iso":"eng"}],"doi":"10.1093/qmath/haw053","publisher":"Oxford University Press","year":"2017","type":"journal_article","author":[{"id":"4634AB1E-F248-11E8-B48F-1D18A9856A87","last_name":"Davison","orcid":"0000-0002-8944-4390","first_name":"Ben","full_name":"Davison, Ben"}],"oa":1,"_id":"687","date_published":"2017-06-01T00:00:00Z"}]