--- _id: '14244' 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." 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). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Michael Lennox full_name: Wong, Michael Lennox last_name: Wong - first_name: Dimitri full_name: Wyss, Dimitri last_name: Wyss citation: ama: Hausel T, Wong ML, Wyss D. Arithmetic and metric aspects of open de Rham spaces. Proceedings of the London Mathematical Society. 2023;127(4):958-1027. doi:10.1112/plms.12555 apa: Hausel, T., Wong, M. L., & Wyss, D. (2023). Arithmetic and metric aspects of open de Rham spaces. Proceedings of the London Mathematical Society. Wiley. https://doi.org/10.1112/plms.12555 chicago: Hausel, Tamás, Michael Lennox Wong, and Dimitri Wyss. “Arithmetic and Metric Aspects of Open de Rham Spaces.” Proceedings of the London Mathematical Society. Wiley, 2023. https://doi.org/10.1112/plms.12555. ieee: T. Hausel, M. L. Wong, and D. Wyss, “Arithmetic and metric aspects of open de Rham spaces,” Proceedings of the London Mathematical Society, 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. mla: Hausel, Tamás, et al. “Arithmetic and Metric Aspects of Open de Rham Spaces.” Proceedings of the London Mathematical Society, vol. 127, no. 4, Wiley, 2023, pp. 958–1027, doi:10.1112/plms.12555. short: T. Hausel, M.L. Wong, D. Wyss, Proceedings of the London Mathematical Society 127 (2023) 958–1027. date_created: 2023-08-27T22:01:18Z date_published: 2023-10-01T00:00:00Z date_updated: 2024-01-30T12:56:10Z day: '01' ddc: - '510' department: - _id: TaHa doi: 10.1112/plms.12555 ec_funded: 1 external_id: arxiv: - '1807.04057' isi: - '001049312700001' file: - access_level: open_access checksum: 2af4d2d6a8ae42f7d3fba0188e79ae82 content_type: application/pdf creator: dernst date_created: 2024-01-30T12:56:00Z date_updated: 2024-01-30T12:56:00Z file_id: '14910' file_name: 2023_ProcLondonMathSoc_Hausel.pdf file_size: 651335 relation: main_file success: 1 file_date_updated: 2024-01-30T12:56:00Z has_accepted_license: '1' intvolume: ' 127' isi: 1 issue: '4' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 958-1027 project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces - _id: 25E6C798-B435-11E9-9278-68D0E5697425 grant_number: '153627' name: Arithmetic quantization of character and quiver varities publication: Proceedings of the London Mathematical Society publication_identifier: eissn: - 1460-244X issn: - 0024-6115 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: Arithmetic and metric aspects of open de Rham spaces tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 127 year: '2023' ... --- _id: '9581' abstract: - lang: eng text: "We show that for any \U0001D45B divisible by 3, almost all order- \U0001D45B \ 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." article_processing_charge: No article_type: original author: - first_name: Matthew Alan full_name: Kwan, Matthew Alan id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3 last_name: Kwan orcid: 0000-0002-4003-7567 citation: ama: Kwan MA. Almost all Steiner triple systems have perfect matchings. Proceedings of the London Mathematical Society. 2020;121(6):1468-1495. doi:10.1112/plms.12373 apa: Kwan, M. A. (2020). Almost all Steiner triple systems have perfect matchings. Proceedings of the London Mathematical Society. Wiley. https://doi.org/10.1112/plms.12373 chicago: Kwan, Matthew Alan. “Almost All Steiner Triple Systems Have Perfect Matchings.” Proceedings of the London Mathematical Society. Wiley, 2020. https://doi.org/10.1112/plms.12373. ieee: M. A. Kwan, “Almost all Steiner triple systems have perfect matchings,” Proceedings of the London Mathematical Society, vol. 121, no. 6. Wiley, pp. 1468–1495, 2020. ista: Kwan MA. 2020. Almost all Steiner triple systems have perfect matchings. Proceedings of the London Mathematical Society. 121(6), 1468–1495. mla: Kwan, Matthew Alan. “Almost All Steiner Triple Systems Have Perfect Matchings.” Proceedings of the London Mathematical Society, vol. 121, no. 6, Wiley, 2020, pp. 1468–95, doi:10.1112/plms.12373. short: M.A. Kwan, Proceedings of the London Mathematical Society 121 (2020) 1468–1495. date_created: 2021-06-22T06:35:16Z date_published: 2020-12-01T00:00:00Z date_updated: 2023-02-23T14:01:43Z day: '01' doi: 10.1112/plms.12373 extern: '1' external_id: arxiv: - '1611.02246' intvolume: ' 121' issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1611.02246 month: '12' oa: 1 oa_version: Preprint page: 1468-1495 publication: Proceedings of the London Mathematical Society publication_identifier: eissn: - 1460-244X issn: - 0024-6115 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: Almost all Steiner triple systems have perfect matchings type: journal_article user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf volume: 121 year: '2020' ... --- _id: '5999' abstract: - lang: eng text: "We introduce for each quiver Q and each algebraic oriented cohomology theory A, the cohomological Hall algebra (CoHA) of Q, as the A-homology of the moduli of representations of the preprojective algebra of Q. This generalizes the K-theoretic Hall algebra of commuting varieties defined by Schiffmann-Vasserot. When A is the Morava K-theory, we show evidence that this algebra is a candidate for Lusztig's reformulated conjecture on modular representations of algebraic groups.\r\nWe construct an action of the preprojective CoHA on the A-homology of Nakajima quiver varieties. We compare this with the action of the Borel subalgebra of Yangian when A is the intersection theory. We also give a shuffle algebra description of this CoHA in terms of the underlying formal group law of A. As applications, we obtain a shuffle description of the Yangian. " article_processing_charge: No author: - first_name: Yaping full_name: Yang, Yaping last_name: Yang - first_name: Gufang full_name: Zhao, Gufang id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87 last_name: Zhao citation: ama: Yang Y, Zhao G. The cohomological Hall algebra of a preprojective algebra. Proceedings of the London Mathematical Society. 2018;116(5):1029-1074. doi:10.1112/plms.12111 apa: Yang, Y., & Zhao, G. (2018). The cohomological Hall algebra of a preprojective algebra. Proceedings of the London Mathematical Society. Oxford University Press. https://doi.org/10.1112/plms.12111 chicago: Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” Proceedings of the London Mathematical Society. Oxford University Press, 2018. https://doi.org/10.1112/plms.12111. ieee: Y. Yang and G. Zhao, “The cohomological Hall algebra of a preprojective algebra,” Proceedings of the London Mathematical Society, vol. 116, no. 5. Oxford University Press, pp. 1029–1074, 2018. ista: Yang Y, Zhao G. 2018. The cohomological Hall algebra of a preprojective algebra. Proceedings of the London Mathematical Society. 116(5), 1029–1074. mla: Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” Proceedings of the London Mathematical Society, vol. 116, no. 5, Oxford University Press, 2018, pp. 1029–74, doi:10.1112/plms.12111. short: Y. Yang, G. Zhao, Proceedings of the London Mathematical Society 116 (2018) 1029–1074. date_created: 2019-02-14T13:14:22Z date_published: 2018-05-01T00:00:00Z date_updated: 2023-09-19T14:37:19Z day: '01' department: - _id: TaHa doi: 10.1112/plms.12111 external_id: arxiv: - '1407.7994' isi: - '000431506400001' intvolume: ' 116' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1407.7994 month: '05' oa: 1 oa_version: Preprint page: 1029-1074 publication: Proceedings of the London Mathematical Society publication_identifier: issn: - 0024-6115 publication_status: published publisher: Oxford University Press quality_controlled: '1' scopus_import: '1' status: public title: The cohomological Hall algebra of a preprojective algebra type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 116 year: '2018' ... --- _id: '270' abstract: - lang: eng text: Given a symmetric variety Y defined over Q and a non-zero polynomial with integer coefficients, we use techniques from homogeneous dynamics to establish conditions under which the polynomial can be made r-free for a Zariski dense set of integral points on Y . We also establish an asymptotic counting formula for this set. In the special case that Y is a quadric hypersurface, we give explicit bounds on the size of r by combining the argument with a uniform upper bound for the density of integral points on general affine quadrics defined over Q. acknowledgement: While working on this paper the authors were supported by ERC grants 306457 and 239606, respectively. article_processing_charge: No article_type: original author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Alexander full_name: Gorodnik, Alexander last_name: Gorodnik citation: ama: Browning TD, Gorodnik A. Power-free values of polynomials on symmetric varieties. Proceedings of the London Mathematical Society. 2017;114(6):1044-1080. doi:10.1112/plms.12030 apa: Browning, T. D., & Gorodnik, A. (2017). Power-free values of polynomials on symmetric varieties. Proceedings of the London Mathematical Society. Wiley. https://doi.org/10.1112/plms.12030 chicago: Browning, Timothy D, and Alexander Gorodnik. “Power-Free Values of Polynomials on Symmetric Varieties.” Proceedings of the London Mathematical Society. Wiley, 2017. https://doi.org/10.1112/plms.12030. ieee: T. D. Browning and A. Gorodnik, “Power-free values of polynomials on symmetric varieties,” Proceedings of the London Mathematical Society, vol. 114, no. 6. Wiley, pp. 1044–1080, 2017. ista: Browning TD, Gorodnik A. 2017. Power-free values of polynomials on symmetric varieties. Proceedings of the London Mathematical Society. 114(6), 1044–1080. mla: Browning, Timothy D., and Alexander Gorodnik. “Power-Free Values of Polynomials on Symmetric Varieties.” Proceedings of the London Mathematical Society, vol. 114, no. 6, Wiley, 2017, pp. 1044–80, doi:10.1112/plms.12030. short: T.D. Browning, A. Gorodnik, Proceedings of the London Mathematical Society 114 (2017) 1044–1080. date_created: 2018-12-11T11:45:32Z date_published: 2017-06-01T00:00:00Z date_updated: 2024-03-05T11:58:25Z day: '01' doi: 10.1112/plms.12030 extern: '1' external_id: arxiv: - '1606.06342' intvolume: ' 114' issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1606.06342 month: '06' oa: 1 oa_version: Preprint page: 1044 - 1080 publication: Proceedings of the London Mathematical Society publication_identifier: issn: - 0024-6115 publication_status: published publisher: Wiley publist_id: '7632' quality_controlled: '1' status: public title: Power-free values of polynomials on symmetric varieties type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 114 year: '2017' ...