[{"type":"journal_article","_id":"14930","date_updated":"2024-02-05T12:58:21Z","publisher":"Springer Nature","article_processing_charge":"No","doi":"10.1007/s00029-023-00914-2","quality_controlled":"1","year":"2024","acknowledgement":"Special thanks go to Christof Geiss, Bernard Leclerc and Jan Schröer for explaining their work but also for sharing some unpublished results with us. We also thank the referee for many useful suggestions. We would like to thank Tommaso Scognamiglio for pointing out a mistake in the proof of Proposition 5.17 in an earlier version of the paper. We would like also to thank Alexander Beilinson, Bill Crawley-Boevey, Joel Kamnitzer, and Peng Shan for useful discussions.","date_published":"2024-01-27T00:00:00Z","publication":"Selecta Mathematica","status":"public","date_created":"2024-02-04T23:00:53Z","article_type":"original","volume":30,"oa_version":"None","title":"Locally free representations of quivers over commutative Frobenius algebras","day":"27","scopus_import":"1","author":[{"last_name":"Hausel","full_name":"Hausel, Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamás"},{"last_name":"Letellier","full_name":"Letellier, Emmanuel","first_name":"Emmanuel"},{"last_name":"Rodriguez-Villegas","full_name":"Rodriguez-Villegas, Fernando","first_name":"Fernando"}],"publication_identifier":{"eissn":["1420-9020"],"issn":["1022-1824"]},"publication_status":"epub_ahead","abstract":[{"lang":"eng","text":"In this paper we investigate locally free representations of a quiver Q over a commutative Frobenius algebra R by arithmetic Fourier transform. When the base field is finite we prove that the number of isomorphism classes of absolutely indecomposable locally free representations of fixed rank is independent of the orientation of Q. We also prove that the number of isomorphism classes of locally free absolutely indecomposable representations of the preprojective algebra of Q over R equals the number of isomorphism classes of locally free absolutely indecomposable representations of Q over R[t]/(t2). Using these results together with results of Geiss, Leclerc and Schröer we give, when k is algebraically closed, a classification of pairs (Q, R) such that the set of isomorphism classes of indecomposable locally free representations of Q over R is finite. Finally when the representation is free of rank 1 at each vertex of Q, we study the function that counts the number of isomorphism classes of absolutely indecomposable locally free representations of Q over the Frobenius algebra Fq[t]/(tr). We prove that they are polynomial in q and their generating function is rational and satisfies a functional equation."}],"intvolume":"        30","article_number":"20","department":[{"_id":"TaHa"}],"month":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Hausel, Tamás, Emmanuel Letellier, and Fernando Rodriguez-Villegas. “Locally Free Representations of Quivers over Commutative Frobenius Algebras.” <i>Selecta Mathematica</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00029-023-00914-2\">https://doi.org/10.1007/s00029-023-00914-2</a>.","ista":"Hausel T, Letellier E, Rodriguez-Villegas F. 2024. Locally free representations of quivers over commutative Frobenius algebras. Selecta Mathematica. 30(2), 20.","apa":"Hausel, T., Letellier, E., &#38; Rodriguez-Villegas, F. (2024). Locally free representations of quivers over commutative Frobenius algebras. <i>Selecta Mathematica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00029-023-00914-2\">https://doi.org/10.1007/s00029-023-00914-2</a>","mla":"Hausel, Tamás, et al. “Locally Free Representations of Quivers over Commutative Frobenius Algebras.” <i>Selecta Mathematica</i>, vol. 30, no. 2, 20, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00029-023-00914-2\">10.1007/s00029-023-00914-2</a>.","ama":"Hausel T, Letellier E, Rodriguez-Villegas F. Locally free representations of quivers over commutative Frobenius algebras. <i>Selecta Mathematica</i>. 2024;30(2). doi:<a href=\"https://doi.org/10.1007/s00029-023-00914-2\">10.1007/s00029-023-00914-2</a>","ieee":"T. Hausel, E. Letellier, and F. Rodriguez-Villegas, “Locally free representations of quivers over commutative Frobenius algebras,” <i>Selecta Mathematica</i>, vol. 30, no. 2. Springer Nature, 2024.","short":"T. Hausel, E. Letellier, F. Rodriguez-Villegas, Selecta Mathematica 30 (2024)."},"issue":"2","language":[{"iso":"eng"}]},{"isi":1,"year":"2023","external_id":{"arxiv":["1807.04057"],"isi":["001049312700001"]},"ec_funded":1,"date_published":"2023-10-01T00:00:00Z","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).","project":[{"_id":"25E549F4-B435-11E9-9278-68D0E5697425","grant_number":"320593","name":"Arithmetic and physics of Higgs moduli spaces","call_identifier":"FP7"},{"_id":"25E6C798-B435-11E9-9278-68D0E5697425","name":"Arithmetic quantization of character and quiver varities","grant_number":"153627"}],"status":"public","publication":"Proceedings of the London Mathematical Society","date_updated":"2024-01-30T12:56:10Z","_id":"14244","type":"journal_article","doi":"10.1112/plms.12555","article_processing_charge":"Yes (via OA deal)","publisher":"Wiley","quality_controlled":"1","page":"958-1027","ddc":["510"],"department":[{"_id":"TaHa"}],"file":[{"relation":"main_file","checksum":"2af4d2d6a8ae42f7d3fba0188e79ae82","success":1,"file_name":"2023_ProcLondonMathSoc_Hausel.pdf","access_level":"open_access","content_type":"application/pdf","file_id":"14910","date_created":"2024-01-30T12:56:00Z","file_size":651335,"creator":"dernst","date_updated":"2024-01-30T12:56:00Z"}],"month":"10","arxiv":1,"issue":"4","citation":{"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.","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>","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.","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>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"language":[{"iso":"eng"}],"volume":127,"article_type":"original","date_created":"2023-08-27T22:01:18Z","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","last_name":"Wyss","full_name":"Wyss, Dimitri"}],"day":"01","scopus_import":"1","title":"Arithmetic and metric aspects of open de Rham spaces","oa_version":"Published Version","publication_identifier":{"eissn":["1460-244X"],"issn":["0024-6115"]},"publication_status":"published","file_date_updated":"2024-01-30T12:56:00Z","has_accepted_license":"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"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"intvolume":"       127"},{"publication_identifier":{"issn":["0020-9910"],"eissn":["1432-1297"]},"publication_status":"published","file_date_updated":"2023-02-27T07:30:47Z","abstract":[{"text":"We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it implies a precise formula for the multiplicity of the very stable components of the global nilpotent cone and its relationship to mirror symmetry. The main ingredients are the Bialynicki-Birula theory of C∗-actions on semiprojective varieties, C∗ characters of indices of C∗-equivariant coherent sheaves, Hecke transformation for Higgs bundles, relative Fourier–Mukai transform along the Hitchin fibration, hyperholomorphic structures on universal bundles and cominuscule Higgs bundles.","lang":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"intvolume":"       228","has_accepted_license":"1","article_type":"original","date_created":"2022-01-30T23:01:34Z","volume":228,"oa_version":"Published Version","title":"Very stable Higgs bundles, equivariant multiplicity and mirror symmetry","author":[{"first_name":"Tamás","full_name":"Hausel, Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel"},{"last_name":"Hitchin","full_name":"Hitchin, Nigel","first_name":"Nigel"}],"day":"01","scopus_import":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"short":"T. Hausel, N. Hitchin, Inventiones Mathematicae 228 (2022) 893–989.","ieee":"T. Hausel and N. Hitchin, “Very stable Higgs bundles, equivariant multiplicity and mirror symmetry,” <i>Inventiones Mathematicae</i>, vol. 228. Springer Nature, pp. 893–989, 2022.","ama":"Hausel T, Hitchin N. Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. <i>Inventiones Mathematicae</i>. 2022;228:893-989. doi:<a href=\"https://doi.org/10.1007/s00222-021-01093-7\">10.1007/s00222-021-01093-7</a>","mla":"Hausel, Tamás, and Nigel Hitchin. “Very Stable Higgs Bundles, Equivariant Multiplicity and Mirror Symmetry.” <i>Inventiones Mathematicae</i>, vol. 228, Springer Nature, 2022, pp. 893–989, doi:<a href=\"https://doi.org/10.1007/s00222-021-01093-7\">10.1007/s00222-021-01093-7</a>.","apa":"Hausel, T., &#38; Hitchin, N. (2022). Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-021-01093-7\">https://doi.org/10.1007/s00222-021-01093-7</a>","chicago":"Hausel, Tamás, and Nigel Hitchin. “Very Stable Higgs Bundles, Equivariant Multiplicity and Mirror Symmetry.” <i>Inventiones Mathematicae</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00222-021-01093-7\">https://doi.org/10.1007/s00222-021-01093-7</a>.","ista":"Hausel T, Hitchin N. 2022. Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. Inventiones Mathematicae. 228, 893–989."},"language":[{"iso":"eng"}],"oa":1,"file":[{"file_name":"2022_InventionesMahtematicae_Hausel.pdf","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"a382ba75acebc9adfb8fe56247cb410e","file_size":1069538,"date_created":"2023-02-27T07:30:47Z","date_updated":"2023-02-27T07:30:47Z","creator":"dernst","file_id":"12687"}],"department":[{"_id":"TaHa"}],"arxiv":1,"month":"05","quality_controlled":"1","ddc":["510"],"page":"893-989","type":"journal_article","date_updated":"2023-08-02T14:03:20Z","_id":"10704","publisher":"Springer Nature","doi":"10.1007/s00222-021-01093-7","article_processing_charge":"Yes (via OA deal)","acknowledgement":"We would like to thank Brian Collier, Davide Gaiotto, Peter Gothen, Jochen Heinloth, Daniel Huybrechts, Quoc Ho, Joel Kamnitzer, Gérard Laumon, Luca Migliorini, Alexander Minets, Brent Pym, Peng Shan, Carlos Simpson, András Szenes, Fernando R. Villegas, Richard Wentworth, Edward Witten and Kōta Yoshioka for interesting comments and discussions. Most of all we are grateful for a long list of very helpful comments by the referee. We would also like to thank the organizers of the Summer School on Higgs bundles in Hamburg in September 2018, where the authors and Richard Wentworth were giving lectures and where the work in this paper started by considering the mirror of the Lagrangian upward flows W+E investigated in [17]. The second author wishes to thank EPSRC and ICMAT for support. Open access funding provided by Institute of Science and Technology (IST Austria).","date_published":"2022-05-01T00:00:00Z","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"publication":"Inventiones Mathematicae","status":"public","external_id":{"arxiv":["2101.08583"],"isi":["000745495400001"]},"related_material":{"link":[{"url":"https://ista.ac.at/en/news/the-tip-of-the-mathematical-iceberg/","description":"News on the ISTA Website","relation":"press_release"}]},"year":"2022","isi":1},{"citation":{"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.","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>.","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.","short":"T. Hausel, M. Mereb, M. Wong, Journal of the European Mathematical Society 21 (2019) 2995–3052.","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>"},"issue":"10","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"TaHa"}],"month":"10","arxiv":1,"publication_identifier":{"eissn":["1435-9855"]},"publication_status":"published","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"}],"intvolume":"        21","volume":21,"date_created":"2018-12-11T11:46:29Z","article_type":"original","day":"01","scopus_import":"1","author":[{"first_name":"Tamas","last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Hausel, Tamas"},{"first_name":"Martin","id":"43D735EE-F248-11E8-B48F-1D18A9856A87","full_name":"Mereb, Martin","last_name":"Mereb"},{"first_name":"Michael","full_name":"Wong, Michael","last_name":"Wong"}],"title":"Arithmetic and representation theory of wild character varieties","oa_version":"Preprint","ec_funded":1,"date_published":"2019-10-01T00:00:00Z","publication":"Journal of the European Mathematical Society","status":"public","project":[{"_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces","grant_number":"320593","call_identifier":"FP7"}],"publist_id":"7384","year":"2019","isi":1,"external_id":{"isi":["000480413600002"],"arxiv":["1604.03382"]},"main_file_link":[{"url":"https://arxiv.org/abs/1604.03382","open_access":"1"}],"quality_controlled":"1","page":"2995-3052","_id":"439","date_updated":"2023-08-24T14:24:49Z","type":"journal_article","article_processing_charge":"No","doi":"10.4171/JEMS/896","publisher":"European Mathematical Society"},{"date_created":"2019-06-06T12:42:01Z","type":"book_chapter","_id":"6525","date_updated":"2021-01-12T08:07:52Z","title":"Mirror symmetry with branes by equivariant verlinde formulas","oa_version":"None","publisher":"Oxford University Press","scopus_import":1,"day":"01","author":[{"first_name":"Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Hausel, Tamás","last_name":"Hausel"},{"last_name":"Mellit","id":"388D3134-F248-11E8-B48F-1D18A9856A87","full_name":"Mellit, Anton","first_name":"Anton"},{"full_name":"Pei, Du","last_name":"Pei","first_name":"Du"}],"doi":"10.1093/oso/9780198802013.003.0009","publication_status":"published","publication_identifier":{"isbn":["9780198802013","9780191840500"]},"quality_controlled":"1","abstract":[{"lang":"eng","text":"This chapter finds an agreement of equivariant indices of semi-classical homomorphisms between pairwise mirror branes in the GL2 Higgs moduli space on a Riemann surface. On one side of the agreement, components of the Lagrangian brane of U(1,1) Higgs bundles, whose mirror was proposed by Hitchin to be certain even exterior powers of the hyperholomorphic Dirac bundle on the SL2 Higgs moduli space, are present. The agreement arises from a mysterious functional equation. This gives strong computational evidence for Hitchin’s proposal."}],"page":"189-218","department":[{"_id":"TaHa"}],"month":"01","year":"2018","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_published":"2018-01-01T00:00:00Z","citation":{"ama":"Hausel T, Mellit A, Pei D. Mirror symmetry with branes by equivariant verlinde formulas. In: <i>Geometry and Physics: Volume I</i>. Oxford University Press; 2018:189-218. doi:<a href=\"https://doi.org/10.1093/oso/9780198802013.003.0009\">10.1093/oso/9780198802013.003.0009</a>","ieee":"T. Hausel, A. Mellit, and D. Pei, “Mirror symmetry with branes by equivariant verlinde formulas,” in <i>Geometry and Physics: Volume I</i>, Oxford University Press, 2018, pp. 189–218.","short":"T. Hausel, A. Mellit, D. Pei, in:, Geometry and Physics: Volume I, Oxford University Press, 2018, pp. 189–218.","ista":"Hausel T, Mellit A, Pei D. 2018.Mirror symmetry with branes by equivariant verlinde formulas. In: Geometry and Physics: Volume I. , 189–218.","chicago":"Hausel, Tamás, Anton Mellit, and Du Pei. “Mirror Symmetry with Branes by Equivariant Verlinde Formulas.” In <i>Geometry and Physics: Volume I</i>, 189–218. Oxford University Press, 2018. <a href=\"https://doi.org/10.1093/oso/9780198802013.003.0009\">https://doi.org/10.1093/oso/9780198802013.003.0009</a>.","apa":"Hausel, T., Mellit, A., &#38; Pei, D. (2018). Mirror symmetry with branes by equivariant verlinde formulas. In <i>Geometry and Physics: Volume I</i> (pp. 189–218). Oxford University Press. <a href=\"https://doi.org/10.1093/oso/9780198802013.003.0009\">https://doi.org/10.1093/oso/9780198802013.003.0009</a>","mla":"Hausel, Tamás, et al. “Mirror Symmetry with Branes by Equivariant Verlinde Formulas.” <i>Geometry and Physics: Volume I</i>, Oxford University Press, 2018, pp. 189–218, doi:<a href=\"https://doi.org/10.1093/oso/9780198802013.003.0009\">10.1093/oso/9780198802013.003.0009</a>."},"language":[{"iso":"eng"}],"publication":"Geometry and Physics: Volume I","status":"public"},{"oa":1,"status":"public","publication":"Asterisque","extern":1,"issue":"370","citation":{"ama":"Hausel T, Rodríguez Villegas F. Cohomology of large semiprojective hyperkähler varieties. <i>Asterisque</i>. 2015;2015(370):113-156.","short":"T. Hausel, F. Rodríguez Villegas, Asterisque 2015 (2015) 113–156.","ieee":"T. Hausel and F. Rodríguez Villegas, “Cohomology of large semiprojective hyperkähler varieties,” <i>Asterisque</i>, vol. 2015, no. 370. Societe Mathematique de France, pp. 113–156, 2015.","ista":"Hausel T, Rodríguez Villegas F. 2015. Cohomology of large semiprojective hyperkähler varieties. Asterisque. 2015(370), 113–156.","chicago":"Hausel, Tamás, and Fernando Rodríguez Villegas. “Cohomology of Large Semiprojective Hyperkähler Varieties.” <i>Asterisque</i>. Societe Mathematique de France, 2015.","mla":"Hausel, Tamás, and Fernando Rodríguez Villegas. “Cohomology of Large Semiprojective Hyperkähler Varieties.” <i>Asterisque</i>, vol. 2015, no. 370, Societe Mathematique de France, 2015, pp. 113–56.","apa":"Hausel, T., &#38; Rodríguez Villegas, F. (2015). Cohomology of large semiprojective hyperkähler varieties. <i>Asterisque</i>. Societe Mathematique de France."},"date_published":"2015-01-01T00:00:00Z","year":"2015","month":"01","publist_id":"5723","page":"113 - 156","abstract":[{"lang":"eng","text":"In this paper we survey geometric and arithmetic techniques to study the cohomology of semiprojective hyperkähler manifolds including toric hyperkähler varieties, Nakajima quiver varieties and moduli spaces of Higgs bundles on Riemann surfaces. The resulting formulae for their Poincaré polynomials are combinatorial and representation theoretical in nature. In particular we will look at their Betti numbers and will establish some results and state some expectations on their asymptotic shape."}],"intvolume":"      2015","main_file_link":[{"url":"http://arxiv.org/abs/1309.4914","open_access":"1"}],"quality_controlled":0,"publication_status":"published","author":[{"first_name":"Tamas","full_name":"Tamas Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel"},{"first_name":"Fernando","last_name":"Rodríguez Villegas","full_name":"Rodríguez Villegas, Fernando"}],"day":"01","publisher":"Societe Mathematique de France","title":"Cohomology of large semiprojective hyperkähler varieties","date_updated":"2021-01-12T06:50:59Z","volume":2015,"_id":"1473","type":"review","date_created":"2018-12-11T11:52:13Z"},{"doi":"10.4007/annals.2013.177.3.8","author":[{"last_name":"Hausel","full_name":"Tamas Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamas"},{"last_name":"Letellier","full_name":"Letellier, Emmanuel","first_name":"Emmanuel"},{"first_name":"Fernando","full_name":"Rodríguez Villegas, Fernando","last_name":"Rodríguez Villegas"}],"day":"01","title":"Positivity for Kac polynomials and DT-invariants of quivers","publisher":"Princeton University Press","date_updated":"2021-01-12T06:50:47Z","_id":"1442","volume":177,"type":"journal_article","date_created":"2018-12-11T11:52:02Z","page":"1147 - 1168","abstract":[{"text":"We give a cohomological interpretation of both the Kac polynomial and the refined Donaldson-Thomas-invariants of quivers. This interpretation yields a proof of a conjecture of Kac from 1982 and gives a new perspective on recent work of Kontsevich-Soibelman. Thisis achieved by computing, via an arithmetic Fourier transform, the dimensions of the isotypical components of the cohomology of associated Nakajima quiver varieties under the action of a Weyl group. The generating function of the corresponding Poincare polynomials is an extension of Hua's formula for Kac polynomials of quivers involving Hall-Littlewood symmetric functions. The resulting formulae contain a wide range of information on the geometry of the quiver varieties.","lang":"eng"}],"intvolume":"       177","main_file_link":[{"url":"http://arxiv.org/abs/1204.2375","open_access":"1"}],"quality_controlled":0,"publication_status":"published","year":"2013","month":"01","publist_id":"5754","oa":1,"status":"public","extern":1,"publication":"Annals of Mathematics","issue":"3","citation":{"ama":"Hausel T, Letellier E, Rodríguez Villegas F. Positivity for Kac polynomials and DT-invariants of quivers. <i>Annals of Mathematics</i>. 2013;177(3):1147-1168. doi:<a href=\"https://doi.org/10.4007/annals.2013.177.3.8\">10.4007/annals.2013.177.3.8</a>","ieee":"T. Hausel, E. Letellier, and F. Rodríguez Villegas, “Positivity for Kac polynomials and DT-invariants of quivers,” <i>Annals of Mathematics</i>, vol. 177, no. 3. Princeton University Press, pp. 1147–1168, 2013.","short":"T. Hausel, E. Letellier, F. Rodríguez Villegas, Annals of Mathematics 177 (2013) 1147–1168.","ista":"Hausel T, Letellier E, Rodríguez Villegas F. 2013. Positivity for Kac polynomials and DT-invariants of quivers. Annals of Mathematics. 177(3), 1147–1168.","chicago":"Hausel, Tamás, Emmanuel Letellier, and Fernando Rodríguez Villegas. “Positivity for Kac Polynomials and DT-Invariants of Quivers.” <i>Annals of Mathematics</i>. Princeton University Press, 2013. <a href=\"https://doi.org/10.4007/annals.2013.177.3.8\">https://doi.org/10.4007/annals.2013.177.3.8</a>.","apa":"Hausel, T., Letellier, E., &#38; Rodríguez Villegas, F. (2013). Positivity for Kac polynomials and DT-invariants of quivers. <i>Annals of Mathematics</i>. Princeton University Press. <a href=\"https://doi.org/10.4007/annals.2013.177.3.8\">https://doi.org/10.4007/annals.2013.177.3.8</a>","mla":"Hausel, Tamás, et al. “Positivity for Kac Polynomials and DT-Invariants of Quivers.” <i>Annals of Mathematics</i>, vol. 177, no. 3, Princeton University Press, 2013, pp. 1147–68, doi:<a href=\"https://doi.org/10.4007/annals.2013.177.3.8\">10.4007/annals.2013.177.3.8</a>."},"date_published":"2013-01-01T00:00:00Z","acknowledgement":"The first author thanks the Royal Society for funding his research 2005-2012 in the form of a Royal Society University Research Fellowship as well as the Mathematical Institute and Wadham College in Oxford for a very productive environment. The second author is supported by Agence Nationale de la Recherche grant\nANR-09-JCJC-0102-01. The third author is supported by the NSF grant DMS-1101484 and a Research Scholarship from the Clay Mathematical Institute."},{"author":[{"first_name":"Tamas","full_name":"Tamas Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel"}],"alternative_title":["Advanced Lectures in Mathematics"],"day":"15","title":"Global topology of the Hitchin system","publisher":"International Press","date_updated":"2021-01-12T06:50:47Z","_id":"1443","volume":25,"type":"book_chapter","date_created":"2018-12-11T11:52:03Z","page":"29 - 70","intvolume":"        25","abstract":[{"text":"Here we survey several results and conjectures on the cohomology of the total space of the Hitchin system: the moduli space of semi-stable rank n and degree d Higgs bundles on a complex algebraic curve C. The picture emerging is a dynamic mixture of ideas originating in theoretical physics such as gauge theory and mirror symmetry, Weil conjectures in arithmetic algebraic geometry, representation theory of finite groups of Lie type and Langlands duality in number theory.","lang":"eng"}],"main_file_link":[{"url":"http://arxiv.org/abs/1102.1717","open_access":"1"}],"publication_status":"published","quality_controlled":0,"year":"2013","month":"03","publist_id":"5753","oa":1,"status":"public","publication":"Handbook of Moduli: Volume II","extern":1,"citation":{"mla":"Hausel, Tamás. “Global Topology of the Hitchin System.” <i>Handbook of Moduli: Volume II</i>, vol. 25, International Press, 2013, pp. 29–70.","apa":"Hausel, T. (2013). Global topology of the Hitchin system. In <i>Handbook of Moduli: Volume II</i> (Vol. 25, pp. 29–70). International Press.","chicago":"Hausel, Tamás. “Global Topology of the Hitchin System.” In <i>Handbook of Moduli: Volume II</i>, 25:29–70. International Press, 2013.","ista":"Hausel T. 2013.Global topology of the Hitchin system. In: Handbook of Moduli: Volume II. Advanced Lectures in Mathematics, vol. 25, 29–70.","short":"T. Hausel, in:, Handbook of Moduli: Volume II, International Press, 2013, pp. 29–70.","ieee":"T. Hausel, “Global topology of the Hitchin system,” in <i>Handbook of Moduli: Volume II</i>, vol. 25, International Press, 2013, pp. 29–70.","ama":"Hausel T. Global topology of the Hitchin system. In: <i>Handbook of Moduli: Volume II</i>. Vol 25. International Press; 2013:29-70."},"date_published":"2013-03-15T00:00:00Z"},{"extern":1,"status":"public","publication":"Advances in Mathematics","date_published":"2013-02-15T00:00:00Z","acknowledgement":"During the preparation of this paper TH was supported by a Royal Society University Research Fellowship at the University of Oxford. EL was supported by ANR-09-JCJC-0102-01. FRV was supported by NSF grant DMS-0200605, an FRA from the University of Texas at Austin, EPSRC grant EP/G027110/1, Visiting Fellowships at All Souls and Wadham Colleges in Oxford and a Research Scholarship from the Clay Mathematical Institute.","citation":{"chicago":"Hausel, Tamás, Emmanuel Letellier, and Fernando Rodríguez Villegas. “Arithmetic Harmonic Analysis on Character and Quiver Varieties II.” <i>Advances in Mathematics</i>. Academic Press, 2013. <a href=\"https://doi.org/10.1016/j.aim.2012.10.009\">https://doi.org/10.1016/j.aim.2012.10.009</a>.","ista":"Hausel T, Letellier E, Rodríguez Villegas F. 2013. Arithmetic harmonic analysis on character and quiver varieties II. Advances in Mathematics. 234, 85–128.","mla":"Hausel, Tamás, et al. “Arithmetic Harmonic Analysis on Character and Quiver Varieties II.” <i>Advances in Mathematics</i>, vol. 234, Academic Press, 2013, pp. 85–128, doi:<a href=\"https://doi.org/10.1016/j.aim.2012.10.009\">10.1016/j.aim.2012.10.009</a>.","apa":"Hausel, T., Letellier, E., &#38; Rodríguez Villegas, F. (2013). Arithmetic harmonic analysis on character and quiver varieties II. <i>Advances in Mathematics</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.aim.2012.10.009\">https://doi.org/10.1016/j.aim.2012.10.009</a>","ama":"Hausel T, Letellier E, Rodríguez Villegas F. Arithmetic harmonic analysis on character and quiver varieties II. <i>Advances in Mathematics</i>. 2013;234:85-128. doi:<a href=\"https://doi.org/10.1016/j.aim.2012.10.009\">10.1016/j.aim.2012.10.009</a>","short":"T. Hausel, E. Letellier, F. Rodríguez Villegas, Advances in Mathematics 234 (2013) 85–128.","ieee":"T. Hausel, E. Letellier, and F. Rodríguez Villegas, “Arithmetic harmonic analysis on character and quiver varieties II,” <i>Advances in Mathematics</i>, vol. 234. Academic Press, pp. 85–128, 2013."},"month":"02","year":"2013","publist_id":"5724","intvolume":"       234","abstract":[{"lang":"eng","text":"We study connections between the topology of generic character varieties of fundamental groups of punctured Riemann surfaces, Macdonald polynomials, quiver representations, Hilbert schemes on Cx × Cx, modular forms and multiplicities in tensor products of irreducible characters of finite general linear groups."}],"page":"85 - 128","publication_status":"published","quality_controlled":0,"publisher":"Academic Press","title":"Arithmetic harmonic analysis on character and quiver varieties II","day":"15","doi":"10.1016/j.aim.2012.10.009","author":[{"first_name":"Tamas","last_name":"Hausel","full_name":"Tamas Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Letellier","full_name":"Letellier, Emmanuel","first_name":"Emmanuel"},{"last_name":"Rodríguez Villegas","full_name":"Rodríguez Villegas, Fernando","first_name":"Fernando"}],"date_created":"2018-12-11T11:52:12Z","type":"journal_article","volume":234,"_id":"1469","date_updated":"2021-01-12T06:50:57Z"},{"page":"23 - 38","intvolume":"         7","abstract":[{"text":"We show that a natural isomorphism between the rational cohomology groups of the two zero-dimensional Hilbert schemes of n-points of two surfaces, the affine plane minus the axes and the cotangent bundle of an elliptic curve, exchanges the weight filtration on the first set of cohomology groups with the perverse Leray filtration associated with a natural fibration on the second set of cohomology groups. We discuss some associated hard Lefschetz phenomena.","lang":"eng"}],"main_file_link":[{"url":"http://arxiv.org/abs/1012.2583","open_access":"1"}],"publication_status":"published","quality_controlled":0,"doi":"10.5427/jsing.2013.7c","author":[{"first_name":"Mark","full_name":"De Cataldo, Mark A","last_name":"De Cataldo"},{"last_name":"Hausel","full_name":"Tamas Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamas"},{"first_name":"Luca","full_name":"Migliorini, Luca","last_name":"Migliorini"}],"day":"01","publisher":"Worldwide Center of Mathematics","title":"Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces","date_updated":"2021-01-12T06:50:58Z","volume":7,"_id":"1470","type":"journal_article","date_created":"2018-12-11T11:52:12Z","oa":1,"extern":1,"status":"public","publication":"Journal of Singularities","citation":{"ista":"De Cataldo M, Hausel T, Migliorini L. 2013. Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces. Journal of Singularities. 7, 23–38.","chicago":"De Cataldo, Mark, Tamás Hausel, and Luca Migliorini. “Exchange between Perverse and Weight Filtration for the Hilbert Schemes of Points of Two Surfaces.” <i>Journal of Singularities</i>. Worldwide Center of Mathematics, 2013. <a href=\"https://doi.org/10.5427/jsing.2013.7c\">https://doi.org/10.5427/jsing.2013.7c</a>.","mla":"De Cataldo, Mark, et al. “Exchange between Perverse and Weight Filtration for the Hilbert Schemes of Points of Two Surfaces.” <i>Journal of Singularities</i>, vol. 7, Worldwide Center of Mathematics, 2013, pp. 23–38, doi:<a href=\"https://doi.org/10.5427/jsing.2013.7c\">10.5427/jsing.2013.7c</a>.","apa":"De Cataldo, M., Hausel, T., &#38; Migliorini, L. (2013). Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces. <i>Journal of Singularities</i>. Worldwide Center of Mathematics. <a href=\"https://doi.org/10.5427/jsing.2013.7c\">https://doi.org/10.5427/jsing.2013.7c</a>","ama":"De Cataldo M, Hausel T, Migliorini L. Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces. <i>Journal of Singularities</i>. 2013;7:23-38. doi:<a href=\"https://doi.org/10.5427/jsing.2013.7c\">10.5427/jsing.2013.7c</a>","short":"M. De Cataldo, T. Hausel, L. Migliorini, Journal of Singularities 7 (2013) 23–38.","ieee":"M. De Cataldo, T. Hausel, and L. Migliorini, “Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces,” <i>Journal of Singularities</i>, vol. 7. Worldwide Center of Mathematics, pp. 23–38, 2013."},"acknowledgement":"Mark Andrea A. de Cataldo was partially supported by N.S.A. and N.S.F. Tamás Hausel was supported by a Royal Society University Research Fellowship. Luca Migliorini was partially supported by PRIN 2007 project \"Spazi di moduli e teoria di Lie\"","date_published":"2013-01-01T00:00:00Z","year":"2013","month":"01","publist_id":"5725"},{"oa":1,"status":"public","extern":1,"publication":"Geometry and Topology","citation":{"ama":"Hausel T, Pauly C. Prym varieties of spectral covers. <i>Geometry and Topology</i>. 2012;16(3):1609-1638. doi:<a href=\"https://doi.org/10.2140/gt.2012.16.1609\">10.2140/gt.2012.16.1609</a>","short":"T. Hausel, C. Pauly, Geometry and Topology 16 (2012) 1609–1638.","ieee":"T. Hausel and C. Pauly, “Prym varieties of spectral covers,” <i>Geometry and Topology</i>, vol. 16, no. 3. University of Warwick, pp. 1609–1638, 2012.","ista":"Hausel T, Pauly C. 2012. Prym varieties of spectral covers. Geometry and Topology. 16(3), 1609–1638.","chicago":"Hausel, Tamás, and Christian Pauly. “Prym Varieties of Spectral Covers.” <i>Geometry and Topology</i>. University of Warwick, 2012. <a href=\"https://doi.org/10.2140/gt.2012.16.1609\">https://doi.org/10.2140/gt.2012.16.1609</a>.","mla":"Hausel, Tamás, and Christian Pauly. “Prym Varieties of Spectral Covers.” <i>Geometry and Topology</i>, vol. 16, no. 3, University of Warwick, 2012, pp. 1609–38, doi:<a href=\"https://doi.org/10.2140/gt.2012.16.1609\">10.2140/gt.2012.16.1609</a>.","apa":"Hausel, T., &#38; Pauly, C. (2012). Prym varieties of spectral covers. <i>Geometry and Topology</i>. University of Warwick. <a href=\"https://doi.org/10.2140/gt.2012.16.1609\">https://doi.org/10.2140/gt.2012.16.1609</a>"},"issue":"3","date_published":"2012-08-01T00:00:00Z","year":"2012","month":"08","publist_id":"5726","page":"1609 - 1638","intvolume":"        16","abstract":[{"lang":"eng","text":"Given a possibly reducible and non-reduced spectral cover π: X → C over a smooth projective complex curve C we determine the group of connected components of the Prym variety Prym(X/C). As an immediate application we show that the finite group of n-torsion points of the Jacobian of C acts trivially on the cohomology of the twisted SL n-Higgs moduli space up to the degree which is predicted by topological mirror symmetry. In particular this yields a new proof of a result of Harder-Narasimhan, showing that this finite group acts trivially on the cohomology of the twisted SL n stable bundle moduli space."}],"main_file_link":[{"url":"http://arxiv.org/abs/1012.4748","open_access":"1"}],"publication_status":"published","quality_controlled":0,"day":"01","doi":"10.2140/gt.2012.16.1609","author":[{"first_name":"Tamas","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Tamas Hausel","last_name":"Hausel"},{"first_name":"Christian","full_name":"Pauly, Christian","last_name":"Pauly"}],"publisher":"University of Warwick","title":"Prym varieties of spectral covers","volume":16,"_id":"1471","date_updated":"2021-01-12T06:50:58Z","date_created":"2018-12-11T11:52:13Z","type":"journal_article"},{"publist_id":"5727","year":"2012","month":"05","issue":"3","citation":{"ieee":"M. De Cataldo, T. Hausel, and L. Migliorini, “Topology of hitchin systems and Hodge theory of character varieties: The case A 1,” <i>Annals of Mathematics</i>, vol. 175, no. 3. Princeton University Press, pp. 1329–1407, 2012.","short":"M. De Cataldo, T. Hausel, L. Migliorini, Annals of Mathematics 175 (2012) 1329–1407.","ama":"De Cataldo M, Hausel T, Migliorini L. Topology of hitchin systems and Hodge theory of character varieties: The case A 1. <i>Annals of Mathematics</i>. 2012;175(3):1329-1407. doi:<a href=\"https://doi.org/10.4007/annals.2012.175.3.7\">10.4007/annals.2012.175.3.7</a>","apa":"De Cataldo, M., Hausel, T., &#38; Migliorini, L. (2012). Topology of hitchin systems and Hodge theory of character varieties: The case A 1. <i>Annals of Mathematics</i>. Princeton University Press. <a href=\"https://doi.org/10.4007/annals.2012.175.3.7\">https://doi.org/10.4007/annals.2012.175.3.7</a>","mla":"De Cataldo, Mark, et al. “Topology of Hitchin Systems and Hodge Theory of Character Varieties: The Case A 1.” <i>Annals of Mathematics</i>, vol. 175, no. 3, Princeton University Press, 2012, pp. 1329–407, doi:<a href=\"https://doi.org/10.4007/annals.2012.175.3.7\">10.4007/annals.2012.175.3.7</a>.","chicago":"De Cataldo, Mark, Tamás Hausel, and Luca Migliorini. “Topology of Hitchin Systems and Hodge Theory of Character Varieties: The Case A 1.” <i>Annals of Mathematics</i>. Princeton University Press, 2012. <a href=\"https://doi.org/10.4007/annals.2012.175.3.7\">https://doi.org/10.4007/annals.2012.175.3.7</a>.","ista":"De Cataldo M, Hausel T, Migliorini L. 2012. Topology of hitchin systems and Hodge theory of character varieties: The case A 1. Annals of Mathematics. 175(3), 1329–1407."},"acknowledgement":"Mark Andrea A. de Cataldo was partially supported by N.S.A. and N.S.F. Tamás Hausel was supported by a Royal Society University Research Fellowship. Luca Migliorini was partially supported by PRIN 2007 project \"Spazi di moduli e teoria di Lie\"","date_published":"2012-05-01T00:00:00Z","oa":1,"publication":"Annals of Mathematics","status":"public","extern":1,"date_updated":"2021-01-12T06:50:59Z","volume":175,"_id":"1472","type":"journal_article","date_created":"2018-12-11T11:52:13Z","author":[{"first_name":"Mark","last_name":"De Cataldo","full_name":"De Cataldo, Mark A"},{"first_name":"Tamas","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Tamas Hausel","last_name":"Hausel"},{"last_name":"Migliorini","full_name":"Migliorini, Luca","first_name":"Luca"}],"doi":"10.4007/annals.2012.175.3.7","day":"01","title":"Topology of hitchin systems and Hodge theory of character varieties: The case A 1","publisher":"Princeton University Press","main_file_link":[{"url":"http://arxiv.org/abs/1004.1420","open_access":"1"}],"quality_controlled":0,"publication_status":"published","page":"1329 - 1407","intvolume":"       175","abstract":[{"lang":"eng","text":"For G = GL 2, PGL 2, SL 2 we prove that the perverse filtration associated with the Hitchin map on the rational cohomology of the moduli space of twisted G-Higgs bundles on a compact Riemann surface C agrees with the weight filtration on the rational cohomology of the twisted G character variety of C when the cohomologies are identified via non-Abelian Hodge theory. The proof is accomplished by means of a study of the topology of the Hitchin map over the locus of integral spectral curves."}]},{"status":"public","publication":"Duke Mathematical Journal","extern":1,"oa":1,"acknowledgement":"Hausel’s work was supported by National Science Foundation grants DMS-0305505 and DMS-0604775, by an Alfred Sloan Fellowship, and by a Royal Society University Research Fellowship. Letellier’s work supported by Agence Nationale de la Recherche grant ANR-09-JCJC-0102-01.\nRodriguez-Villegas’s work supported by National Science Foundation grant DMS-0200605, by an FRA from the University of Texas at Austin, by EPSRC grant EP/G027110/1, by visiting fellowships at All Souls and Wadham Colleges in Oxford, and by a Research Scholarship from the Clay Mathematical Institute.","date_published":"2011-01-01T00:00:00Z","citation":{"ieee":"T. Hausel, E. Letellier, and F. Rodríguez Villegas, “Arithmetic harmonic analysis on character and quiver varieties,” <i>Duke Mathematical Journal</i>, vol. 160, no. 2. Duke University Press, pp. 323–400, 2011.","short":"T. Hausel, E. Letellier, F. Rodríguez Villegas, Duke Mathematical Journal 160 (2011) 323–400.","ama":"Hausel T, Letellier E, Rodríguez Villegas F. Arithmetic harmonic analysis on character and quiver varieties. <i>Duke Mathematical Journal</i>. 2011;160(2):323-400. doi:<a href=\"https://doi.org/10.1215/00127094-1444258\">10.1215/00127094-1444258</a>","apa":"Hausel, T., Letellier, E., &#38; Rodríguez Villegas, F. (2011). Arithmetic harmonic analysis on character and quiver varieties. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/00127094-1444258\">https://doi.org/10.1215/00127094-1444258</a>","mla":"Hausel, Tamás, et al. “Arithmetic Harmonic Analysis on Character and Quiver Varieties.” <i>Duke Mathematical Journal</i>, vol. 160, no. 2, Duke University Press, 2011, pp. 323–400, doi:<a href=\"https://doi.org/10.1215/00127094-1444258\">10.1215/00127094-1444258</a>.","ista":"Hausel T, Letellier E, Rodríguez Villegas F. 2011. Arithmetic harmonic analysis on character and quiver varieties. Duke Mathematical Journal. 160(2), 323–400.","chicago":"Hausel, Tamás, Emmanuel Letellier, and Fernando Rodríguez Villegas. “Arithmetic Harmonic Analysis on Character and Quiver Varieties.” <i>Duke Mathematical Journal</i>. Duke University Press, 2011. <a href=\"https://doi.org/10.1215/00127094-1444258\">https://doi.org/10.1215/00127094-1444258</a>."},"issue":"2","month":"01","year":"2011","publist_id":"5728","intvolume":"       160","abstract":[{"text":"We propose a general conjecture for the mixed Hodge polynomial of the generic character varieties of representations of the fundamental group of a Riemann surface of genus g to GLn(C) with fixed generic semisimple conjugacy classes at k punctures. This conjecture generalizes the Cauchy identity for Macdonald polynomials and is a common generalization of two formulas that we prove in this paper. The first is a formula for the E-polynomial of these character varieties which we obtain using the character table of GLn(Fq). We use this formula to compute the Euler characteristic of character varieties. The second formula gives the Poincaré polynomial of certain associated quiver varieties which we obtain using the character table of gln(Fq). In the last main result we prove that the Poincaré polynomials of the quiver varieties equal certain multiplicities in the tensor product of irreducible characters of GLn(Fq). As a consequence we find a curious connection between Kac-Moody algebras associated with comet-shaped, and typically wild, quivers and the representation theory of GLn(Fq).","lang":"eng"}],"page":"323 - 400","publication_status":"published","quality_controlled":0,"main_file_link":[{"url":"http://arxiv.org/abs/0810.2076","open_access":"1"}],"title":"Arithmetic harmonic analysis on character and quiver varieties","publisher":"Duke University Press","day":"01","doi":"10.1215/00127094-1444258","author":[{"id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Tamas Hausel","last_name":"Hausel","first_name":"Tamas"},{"first_name":"Emmanuel","full_name":"Letellier, Emmanuel","last_name":"Letellier"},{"full_name":"Rodríguez Villegas, Fernando","last_name":"Rodríguez Villegas","first_name":"Fernando"}],"date_created":"2018-12-11T11:52:11Z","type":"journal_article","_id":"1467","volume":160,"date_updated":"2021-01-12T06:50:56Z"},{"date_created":"2018-12-11T11:52:11Z","type":"journal_article","_id":"1465","volume":181,"date_updated":"2021-01-12T06:50:56Z","title":"Kac's conjecture from Nakajima quiver varieties","publisher":"Springer","day":"01","doi":"10.1007/s00222-010-0241-3","author":[{"first_name":"Tamas","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Tamas Hausel","last_name":"Hausel"}],"publication_status":"published","quality_controlled":0,"main_file_link":[{"url":"http://arxiv.org/abs/0811.1569","open_access":"1"}],"intvolume":"       181","abstract":[{"text":"We prove a generating function formula for the Betti numbers of Nakajima quiver varieties. We prove that it is a q-deformation of the Weyl-Kac character formula. In particular this implies that the constant term of the polynomial counting the number of absolutely indecomposable representations of a quiver equals the multiplicity of a certain weight in the corresponding Kac-Moody algebra, which was conjectured by Kac in 1982.","lang":"eng"}],"page":"21 - 37","publist_id":"5730","month":"07","year":"2010","date_published":"2010-07-01T00:00:00Z","acknowledgement":"This work has been supported by a Royal Society University Research Fellowship, NSF grants DMS-0305505 and DMS-0604775 and an Alfred Sloan Fellowship 2005-2007.","citation":{"ieee":"T. Hausel, “Kac’s conjecture from Nakajima quiver varieties,” <i>Inventiones Mathematicae</i>, vol. 181, no. 1. Springer, pp. 21–37, 2010.","short":"T. Hausel, Inventiones Mathematicae 181 (2010) 21–37.","ama":"Hausel T. Kac’s conjecture from Nakajima quiver varieties. <i>Inventiones Mathematicae</i>. 2010;181(1):21-37. doi:<a href=\"https://doi.org/10.1007/s00222-010-0241-3\">10.1007/s00222-010-0241-3</a>","apa":"Hausel, T. (2010). Kac’s conjecture from Nakajima quiver varieties. <i>Inventiones Mathematicae</i>. Springer. <a href=\"https://doi.org/10.1007/s00222-010-0241-3\">https://doi.org/10.1007/s00222-010-0241-3</a>","mla":"Hausel, Tamás. “Kac’s Conjecture from Nakajima Quiver Varieties.” <i>Inventiones Mathematicae</i>, vol. 181, no. 1, Springer, 2010, pp. 21–37, doi:<a href=\"https://doi.org/10.1007/s00222-010-0241-3\">10.1007/s00222-010-0241-3</a>.","chicago":"Hausel, Tamás. “Kac’s Conjecture from Nakajima Quiver Varieties.” <i>Inventiones Mathematicae</i>. Springer, 2010. <a href=\"https://doi.org/10.1007/s00222-010-0241-3\">https://doi.org/10.1007/s00222-010-0241-3</a>.","ista":"Hausel T. 2010. Kac’s conjecture from Nakajima quiver varieties. Inventiones Mathematicae. 181(1), 21–37."},"issue":"1","extern":1,"publication":"Inventiones Mathematicae","status":"public","oa":1},{"type":"journal_article","date_created":"2018-12-11T11:52:11Z","date_updated":"2021-01-12T06:50:56Z","_id":"1466","volume":348,"publisher":"Elsevier","title":"Topology of character varieties and representations of quivers","doi":"10.1016/j.crma.2010.01.025","author":[{"first_name":"Tamas","last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Tamas Hausel"},{"full_name":"Letellier, Emmanuel","last_name":"Letellier","first_name":"Emmanuel"},{"first_name":"Fernando","last_name":"Rodríguez Villegas","full_name":"Rodríguez Villegas, Fernando"}],"day":"01","publication_status":"published","quality_controlled":0,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0905.3491"}],"intvolume":"       348","abstract":[{"text":"In Hausel et al. (2008) [10] we presented a conjecture generalizing the Cauchy formula for Macdonald polynomial. This conjecture encodes the mixed Hodge polynomials of the character varieties of representations of the fundamental group of a punctured Riemann surface of genus g. We proved several results which support this conjecture. Here we announce new results which are consequences of those in Hausel et al. (2008) [10].","lang":"eng"}],"page":"131 - 135","publist_id":"5731","month":"02","year":"2010","date_published":"2010-02-01T00:00:00Z","issue":"3-4","citation":{"chicago":"Hausel, Tamás, Emmanuel Letellier, and Fernando Rodríguez Villegas. “Topology of Character Varieties and Representations of Quivers.” <i>Comptes Rendus Mathematique</i>. Elsevier, 2010. <a href=\"https://doi.org/10.1016/j.crma.2010.01.025\">https://doi.org/10.1016/j.crma.2010.01.025</a>.","ista":"Hausel T, Letellier E, Rodríguez Villegas F. 2010. Topology of character varieties and representations of quivers. Comptes Rendus Mathematique. 348(3–4), 131–135.","mla":"Hausel, Tamás, et al. “Topology of Character Varieties and Representations of Quivers.” <i>Comptes Rendus Mathematique</i>, vol. 348, no. 3–4, Elsevier, 2010, pp. 131–35, doi:<a href=\"https://doi.org/10.1016/j.crma.2010.01.025\">10.1016/j.crma.2010.01.025</a>.","apa":"Hausel, T., Letellier, E., &#38; Rodríguez Villegas, F. (2010). Topology of character varieties and representations of quivers. <i>Comptes Rendus Mathematique</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.crma.2010.01.025\">https://doi.org/10.1016/j.crma.2010.01.025</a>","ama":"Hausel T, Letellier E, Rodríguez Villegas F. Topology of character varieties and representations of quivers. <i>Comptes Rendus Mathematique</i>. 2010;348(3-4):131-135. doi:<a href=\"https://doi.org/10.1016/j.crma.2010.01.025\">10.1016/j.crma.2010.01.025</a>","short":"T. Hausel, E. Letellier, F. Rodríguez Villegas, Comptes Rendus Mathematique 348 (2010) 131–135.","ieee":"T. Hausel, E. Letellier, and F. Rodríguez Villegas, “Topology of character varieties and representations of quivers,” <i>Comptes Rendus Mathematique</i>, vol. 348, no. 3–4. Elsevier, pp. 131–135, 2010."},"publication":"Comptes Rendus Mathematique","status":"public","extern":1,"oa":1},{"title":"S-Duality in HyperkäHler Hodge Theory","publisher":"Oxford University Press","doi":"10.1093/acprof:oso/9780199534920.003.0016","author":[{"first_name":"Tamas","full_name":"Tamas Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel"}],"day":"01","type":"book_chapter","date_created":"2018-12-11T11:52:12Z","date_updated":"2021-01-12T06:50:57Z","_id":"1468","abstract":[{"text":"This chapter surveys the motivations, related results, and progress made towards the following problem, raised by Hitchin in 1995: What is the space of L2 harmonic forms on the moduli space of Higgs bundles on a Riemann surface?","lang":"eng"}],"quality_controlled":0,"publication_status":"published","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0709.0504"}],"month":"09","year":"2010","publist_id":"5729","publication":"The Many Facets of Geometry: A Tribute to Nigel Hitchin","status":"public","extern":1,"oa":1,"date_published":"2010-09-01T00:00:00Z","citation":{"ieee":"T. Hausel, “S-Duality in HyperkäHler Hodge Theory,” in <i>The Many Facets of Geometry: A Tribute to Nigel Hitchin</i>, Oxford University Press, 2010.","short":"T. Hausel, in:, The Many Facets of Geometry: A Tribute to Nigel Hitchin, Oxford University Press, 2010.","ama":"Hausel T. S-Duality in HyperkäHler Hodge Theory. In: <i>The Many Facets of Geometry: A Tribute to Nigel Hitchin</i>. Oxford University Press; 2010. doi:<a href=\"https://doi.org/10.1093/acprof:oso/9780199534920.003.0016\">10.1093/acprof:oso/9780199534920.003.0016</a>","apa":"Hausel, T. (2010). S-Duality in HyperkäHler Hodge Theory. In <i>The Many Facets of Geometry: A Tribute to Nigel Hitchin</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/acprof:oso/9780199534920.003.0016\">https://doi.org/10.1093/acprof:oso/9780199534920.003.0016</a>","mla":"Hausel, Tamás. “S-Duality in HyperkäHler Hodge Theory.” <i>The Many Facets of Geometry: A Tribute to Nigel Hitchin</i>, Oxford University Press, 2010, doi:<a href=\"https://doi.org/10.1093/acprof:oso/9780199534920.003.0016\">10.1093/acprof:oso/9780199534920.003.0016</a>.","chicago":"Hausel, Tamás. “S-Duality in HyperkäHler Hodge Theory.” In <i>The Many Facets of Geometry: A Tribute to Nigel Hitchin</i>. Oxford University Press, 2010. <a href=\"https://doi.org/10.1093/acprof:oso/9780199534920.003.0016\">https://doi.org/10.1093/acprof:oso/9780199534920.003.0016</a>.","ista":"Hausel T. 2010.S-Duality in HyperkäHler Hodge Theory. In: The Many Facets of Geometry: A Tribute to Nigel Hitchin. ."}},{"main_file_link":[{"url":"http://arxiv.org/abs/math/0612668","open_access":"1"}],"publication_status":"published","quality_controlled":0,"page":"555 - 624","abstract":[{"text":"We calculate the E-polynomials of certain twisted GL(n,ℂ)-character varieties Mn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n, q) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL(n,ℂ)-character variety. The calculation also leads to several conjectures about the cohomology of Mn: an explicit conjecture for its mixed Hodge polynomial; a conjectured curious hard Lefschetz theorem and a conjecture relating the pure part to absolutely indecomposable representations of a certain quiver. We prove these conjectures for n=2.","lang":"eng"}],"intvolume":"       174","date_updated":"2021-01-12T06:50:54Z","_id":"1460","volume":174,"type":"journal_article","date_created":"2018-12-11T11:52:09Z","doi":"10.1007/s00222-008-0142-x","author":[{"last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Tamas Hausel","first_name":"Tamas"},{"last_name":"Rodríguez Villegas","full_name":"Rodríguez Villegas, Fernando","first_name":"Fernando"}],"day":"01","publisher":"Springer","title":"Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz","issue":"3","citation":{"ista":"Hausel T, Rodríguez Villegas F. 2008. Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz. Inventiones Mathematicae. 174(3), 555–624.","chicago":"Hausel, Tamás, and Fernando Rodríguez Villegas. “Mixed Hodge Polynomials of Character Varieties: With an Appendix by Nicholas M. Katz.” <i>Inventiones Mathematicae</i>. Springer, 2008. <a href=\"https://doi.org/10.1007/s00222-008-0142-x\">https://doi.org/10.1007/s00222-008-0142-x</a>.","mla":"Hausel, Tamás, and Fernando Rodríguez Villegas. “Mixed Hodge Polynomials of Character Varieties: With an Appendix by Nicholas M. Katz.” <i>Inventiones Mathematicae</i>, vol. 174, no. 3, Springer, 2008, pp. 555–624, doi:<a href=\"https://doi.org/10.1007/s00222-008-0142-x\">10.1007/s00222-008-0142-x</a>.","apa":"Hausel, T., &#38; Rodríguez Villegas, F. (2008). Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz. <i>Inventiones Mathematicae</i>. Springer. <a href=\"https://doi.org/10.1007/s00222-008-0142-x\">https://doi.org/10.1007/s00222-008-0142-x</a>","ama":"Hausel T, Rodríguez Villegas F. Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz. <i>Inventiones Mathematicae</i>. 2008;174(3):555-624. doi:<a href=\"https://doi.org/10.1007/s00222-008-0142-x\">10.1007/s00222-008-0142-x</a>","short":"T. Hausel, F. Rodríguez Villegas, Inventiones Mathematicae 174 (2008) 555–624.","ieee":"T. Hausel and F. Rodríguez Villegas, “Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz,” <i>Inventiones Mathematicae</i>, vol. 174, no. 3. Springer, pp. 555–624, 2008."},"date_published":"2008-12-01T00:00:00Z","acknowledgement":"The first author was supported by NSF grants DMS-0305505 and DMS- 0604775 an Alfred Sloan Fellowship and a Royal Society University Research Fellowship. The second author was supported by an NSF grant DMS-0200605.","oa":1,"publication":"Inventiones Mathematicae","status":"public","extern":1,"publist_id":"5732","year":"2008","month":"12"},{"publisher":"American Mathematical Society","title":"Intersection forms of toric hyperkähler varieties","author":[{"last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Tamas Hausel","first_name":"Tamas"},{"full_name":"Swartz, Edward","last_name":"Swartz","first_name":"Edward"}],"doi":"10.1090/S0002-9939-06-08248-7","day":"01","type":"journal_article","date_created":"2018-12-11T11:52:09Z","date_updated":"2021-01-12T06:50:54Z","_id":"1461","volume":134,"intvolume":"       134","abstract":[{"lang":"eng","text":"This note proves combinatorially that the intersection pairing on the middle-dimensional compactly supported cohomology of a toric hyperkähler variety is always definite, providing a large number of non-trivial L 2 harmonic forms for toric hyperkähler metrics on these varieties. This is motivated by a result of Hitchin about the definiteness of the pairing of L 2 harmonic forms on complete hyperkähler manifolds of linear growth."}],"page":"2403 - 2409","quality_controlled":0,"publication_status":"published","main_file_link":[{"url":"http://arxiv.org/abs/math/0306369","open_access":"1"}],"month":"08","year":"2006","publist_id":"5733","extern":1,"publication":"Proceedings of the American Mathematical Society","status":"public","oa":1,"acknowledgement":"The first author was partly supported by NSF grant DMS-0072675. The second author was partly supported by a VIGRE postdoc under NSF grant number 9983660 to Cornell University.","date_published":"2006-08-01T00:00:00Z","issue":"8","citation":{"short":"T. Hausel, E. Swartz, Proceedings of the American Mathematical Society 134 (2006) 2403–2409.","ieee":"T. Hausel and E. Swartz, “Intersection forms of toric hyperkähler varieties,” <i>Proceedings of the American Mathematical Society</i>, vol. 134, no. 8. American Mathematical Society, pp. 2403–2409, 2006.","ama":"Hausel T, Swartz E. Intersection forms of toric hyperkähler varieties. <i>Proceedings of the American Mathematical Society</i>. 2006;134(8):2403-2409. doi:<a href=\"https://doi.org/10.1090/S0002-9939-06-08248-7\">10.1090/S0002-9939-06-08248-7</a>","mla":"Hausel, Tamás, and Edward Swartz. “Intersection Forms of Toric Hyperkähler Varieties.” <i>Proceedings of the American Mathematical Society</i>, vol. 134, no. 8, American Mathematical Society, 2006, pp. 2403–09, doi:<a href=\"https://doi.org/10.1090/S0002-9939-06-08248-7\">10.1090/S0002-9939-06-08248-7</a>.","apa":"Hausel, T., &#38; Swartz, E. (2006). Intersection forms of toric hyperkähler varieties. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/S0002-9939-06-08248-7\">https://doi.org/10.1090/S0002-9939-06-08248-7</a>","ista":"Hausel T, Swartz E. 2006. Intersection forms of toric hyperkähler varieties. Proceedings of the American Mathematical Society. 134(8), 2403–2409.","chicago":"Hausel, Tamás, and Edward Swartz. “Intersection Forms of Toric Hyperkähler Varieties.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2006. <a href=\"https://doi.org/10.1090/S0002-9939-06-08248-7\">https://doi.org/10.1090/S0002-9939-06-08248-7</a>."}},{"page":"6120 - 6124","intvolume":"       103","abstract":[{"text":"A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This technique in turn gives information on Betti numbers of holomorphic symplectic quotients. As a consequence, simple unified proofs are obtained for formulas of Poincaré polynomials of toric hyperkähler varieties (recovering results of Bielawski-Dancer and Hausel-Sturmfels), Poincaré polynomials of Hubert schemes of points and twisted Atiyah-Drinfeld-Hitchin-Manin (ADHM) spaces of instantons on ℂ2 (recovering results of Nakajima-Yoshioka), and Poincaré polynomials of all Nakajima quiver varieties. As an application, a proof of a conjecture of Kac on the number of absolutely indecomposable representations of a quiver is announced.","lang":"eng"}],"main_file_link":[{"url":"http://arxiv.org/abs/math/0511163","open_access":"1"}],"quality_controlled":0,"publication_status":"published","day":"18","author":[{"first_name":"Tamas","last_name":"Hausel","full_name":"Tamas Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87"}],"doi":"10.1073/pnas.0601337103","title":"Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform","publisher":"National Academy of Sciences","_id":"1462","volume":103,"date_updated":"2021-01-12T06:50:55Z","date_created":"2018-12-11T11:52:10Z","type":"journal_article","oa":1,"publication":"PNAS","status":"public","extern":1,"citation":{"ista":"Hausel T. 2006. Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform. PNAS. 103(16), 6120–6124.","chicago":"Hausel, Tamás. “Betti Numbers of Holomorphic Symplectic Quotients via Arithmetic Fourier Transform.” <i>PNAS</i>. National Academy of Sciences, 2006. <a href=\"https://doi.org/10.1073/pnas.0601337103\">https://doi.org/10.1073/pnas.0601337103</a>.","apa":"Hausel, T. (2006). Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform. <i>PNAS</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.0601337103\">https://doi.org/10.1073/pnas.0601337103</a>","mla":"Hausel, Tamás. “Betti Numbers of Holomorphic Symplectic Quotients via Arithmetic Fourier Transform.” <i>PNAS</i>, vol. 103, no. 16, National Academy of Sciences, 2006, pp. 6120–24, doi:<a href=\"https://doi.org/10.1073/pnas.0601337103\">10.1073/pnas.0601337103</a>.","ama":"Hausel T. Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform. <i>PNAS</i>. 2006;103(16):6120-6124. doi:<a href=\"https://doi.org/10.1073/pnas.0601337103\">10.1073/pnas.0601337103</a>","ieee":"T. Hausel, “Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform,” <i>PNAS</i>, vol. 103, no. 16. National Academy of Sciences, pp. 6120–6124, 2006.","short":"T. Hausel, PNAS 103 (2006) 6120–6124."},"issue":"16","acknowledgement":"This work was supported by a Royal Society University Research Fellowship, National Science Foundation Grant DMS-0305505, an Alfred P. Sloan Research Fellowship, and a Summer Research Assignment of the University of Texas at Austin.","date_published":"2006-04-18T00:00:00Z","year":"2006","month":"04","publist_id":"5734"},{"quality_controlled":0,"publication_status":"published","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math/0406380"}],"intvolume":"       235","abstract":[{"text":"The paper surveys the mirror symmetry conjectures of Hausel-Thaddeus and Hausel-Rodriguez-Villegas concerning the equality of certain Hodge numbers of SL(n, ℂ) vs. PGL(n, ℂ) flat connections and character varieties for curves, respectively. Several new results and conjectures and their relations to works of Hitchin, Gothen, Garsia-Haiman and Earl-Kirwan are explained. These use the representation theory of finite groups of Lie-type via the arithmetic of character varieties and lead to an unexpected conjecture for a Hard Lefschetz theorem for their cohomology.","lang":"eng"}],"page":"193 - 217","type":"book_chapter","date_created":"2018-12-11T11:52:03Z","date_updated":"2021-01-12T06:50:47Z","_id":"1444","volume":235,"title":"Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve","publisher":"Springer","author":[{"first_name":"Tamas","last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Tamas Hausel"}],"doi":"10.1007/0-8176-4417-2_9","alternative_title":["Progress in Mathematics"],"day":"01","date_published":"2005-01-01T00:00:00Z","citation":{"chicago":"Hausel, Tamás. “Mirror Symmetry and Langlands Duality in the Non-Abelian Hodge Theory of a Curve.” In <i>Geometric Methods in Algebra and Number Theory</i>, 235:193–217. Springer, 2005. <a href=\"https://doi.org/10.1007/0-8176-4417-2_9\">https://doi.org/10.1007/0-8176-4417-2_9</a>.","ista":"Hausel T. 2005.Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve. In: Geometric Methods in Algebra and Number Theory. Progress in Mathematics, vol. 235, 193–217.","apa":"Hausel, T. (2005). Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve. In <i>Geometric Methods in Algebra and Number Theory</i> (Vol. 235, pp. 193–217). Springer. <a href=\"https://doi.org/10.1007/0-8176-4417-2_9\">https://doi.org/10.1007/0-8176-4417-2_9</a>","mla":"Hausel, Tamás. “Mirror Symmetry and Langlands Duality in the Non-Abelian Hodge Theory of a Curve.” <i>Geometric Methods in Algebra and Number Theory</i>, vol. 235, Springer, 2005, pp. 193–217, doi:<a href=\"https://doi.org/10.1007/0-8176-4417-2_9\">10.1007/0-8176-4417-2_9</a>.","ama":"Hausel T. Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve. In: <i>Geometric Methods in Algebra and Number Theory</i>. Vol 235. Springer; 2005:193-217. doi:<a href=\"https://doi.org/10.1007/0-8176-4417-2_9\">10.1007/0-8176-4417-2_9</a>","ieee":"T. Hausel, “Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve,” in <i>Geometric Methods in Algebra and Number Theory</i>, vol. 235, Springer, 2005, pp. 193–217.","short":"T. Hausel, in:, Geometric Methods in Algebra and Number Theory, Springer, 2005, pp. 193–217."},"extern":1,"publication":"Geometric Methods in Algebra and Number Theory","status":"public","oa":1,"publist_id":"5752","month":"01","year":"2005"}]