{"abstract":[{"lang":"eng","text":"The first part of this paper is a survey of mathematical results on mirror symmetry phenomena between Hitchin systems for Langlands dual groups. The second part introduces\r\nand discusses multiplicity algebras of the Hitchin system on Lagrangians, and considers\r\ncorresponding conjectural structures on their mirror."}],"article_processing_charge":"No","department":[{"_id":"TaHa"}],"external_id":{"arxiv":["2112.09455"]},"oa_version":"Published Version","publication":"International Congress of Mathematicians","year":"2022","publication_identifier":{"isbn":["9783985470587"],"eisbn":["9783985475582"]},"file":[{"date_created":"2025-09-24T09:05:05Z","access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_name":"2022_ICM_Hausel.pdf","date_updated":"2025-09-24T09:05:05Z","relation":"main_file","checksum":"d2b9d4cf51c854f1082d8dc18c5853b1","file_id":"20387","success":1,"file_size":655370}],"_id":"19984","citation":{"ieee":"T. Hausel, “Enhanced mirror symmetry for Langlands dual Hitchin systems,” in <i>International Congress of Mathematicians</i>, EMS Press, 2022, pp. 2228–2249.","apa":"Hausel, T. (2022). Enhanced mirror symmetry for Langlands dual Hitchin systems. In <i>International Congress of Mathematicians</i> (pp. 2228–2249). virtuel: EMS Press. <a href=\"https://doi.org/10.4171/icm2022/164\">https://doi.org/10.4171/icm2022/164</a>","mla":"Hausel, Tamás. “Enhanced Mirror Symmetry for Langlands Dual Hitchin Systems.” <i>International Congress of Mathematicians</i>, EMS Press, 2022, pp. 2228–49, doi:<a href=\"https://doi.org/10.4171/icm2022/164\">10.4171/icm2022/164</a>.","chicago":"Hausel, Tamás. “Enhanced Mirror Symmetry for Langlands Dual Hitchin Systems.” In <i>International Congress of Mathematicians</i>, 2228–49. EMS Press, 2022. <a href=\"https://doi.org/10.4171/icm2022/164\">https://doi.org/10.4171/icm2022/164</a>.","ama":"Hausel T. Enhanced mirror symmetry for Langlands dual Hitchin systems. In: <i>International Congress of Mathematicians</i>. EMS Press; 2022:2228-2249. doi:<a href=\"https://doi.org/10.4171/icm2022/164\">10.4171/icm2022/164</a>","short":"T. Hausel, in:, International Congress of Mathematicians, EMS Press, 2022, pp. 2228–2249.","ista":"Hausel T. 2022.Enhanced mirror symmetry for Langlands dual Hitchin systems. In: International Congress of Mathematicians. , 2228–2249."},"language":[{"iso":"eng"}],"conference":{"end_date":"2022-07-14","name":"ICM: International Congress of Mathematicians","start_date":"2022-07-06","location":"virtuel"},"page":"2228-2249","month":"07","ddc":["510"],"has_accepted_license":"1","OA_type":"gold","title":"Enhanced mirror symmetry for Langlands dual Hitchin systems","corr_author":"1","type":"book_chapter","arxiv":1,"file_date_updated":"2025-09-24T09:05:05Z","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"day":"15","date_updated":"2025-09-24T09:12:13Z","author":[{"last_name":"Hausel","orcid":"0000-0002-9582-2634","first_name":"Tamás","full_name":"Hausel, Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87"}],"OA_place":"publisher","date_created":"2025-07-10T13:13:36Z","date_published":"2022-07-15T00:00:00Z","quality_controlled":"1","acknowledgement":"The author thanks Nigel Hitchin for introducing him to Higgs bundles during 1995–1998,\r\nsuggesting the SYZ picture for Langlands dual Hitchin systems in 1996, and for the\r\nmore recent collaborations [29, 30]. He also thanks David Ben-Zvi, Pierre-Henri Chaudouard, Pierre Deligne, Ron Donagi, Sergei Gukov, Jochen Heinloth, Vadim Kaloshin,\r\nJoel Kamnitzer, Gérard Laumon, Anton Mellit, David Nadler, Andy Neitzke, Ngô Bao\r\nChâu, Michael Thaddeus, Tony Pantev, Du Pei, Richárd Rimányi, Leonid Rybnikov, Vivek\r\nShende, Balázs Szendrői, András Szenes, Fernando Rodriguez-Villegas, Edward Witten,\r\nand Zhiwei Yun for discussions about the subjects in this paper over the years. Thanks are\r\nalso due to Hülya Argüz, Jakub Löwit, Balázs Szendrői, and Nigel Hitchin for the careful\r\nreading of the paper.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","doi":"10.4171/icm2022/164","publisher":"EMS Press"}