--- _id: '14930' 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. 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thanks go to Christof Geiss, Bernard Leclerc and Jan Schröer for explaining their work but also for sharing some unpublished results with us.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. article_number: '20' article_processing_charge: No article_type: original author: - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Emmanuel full_name: Letellier, Emmanuel last_name: Letellier - first_name: Fernando full_name: Rodriguez-Villegas, Fernando last_name: Rodriguez-Villegas citation: ama: Hausel T, Letellier E, Rodriguez-Villegas F. Locally free representations of quivers over commutative Frobenius algebras. Selecta Mathematica. 2024;30(2). doi:10.1007/s00029-023-00914-2 apa: Hausel, T., Letellier, E., & Rodriguez-Villegas, F. (2024). Locally free representations of quivers over commutative Frobenius algebras. Selecta Mathematica. Springer Nature. https://doi.org/10.1007/s00029-023-00914-2 chicago: Hausel, Tamás, Emmanuel Letellier, and Fernando Rodriguez-Villegas. “Locally Free Representations of Quivers over Commutative Frobenius Algebras.” Selecta Mathematica. Springer Nature, 2024. https://doi.org/10.1007/s00029-023-00914-2. ieee: T. Hausel, E. Letellier, and F. Rodriguez-Villegas, “Locally free representations of quivers over commutative Frobenius algebras,” Selecta Mathematica, vol. 30, no. 2. Springer Nature, 2024. ista: Hausel T, Letellier E, Rodriguez-Villegas F. 2024. Locally free representations of quivers over commutative Frobenius algebras. Selecta Mathematica. 30(2), 20. mla: Hausel, Tamás, et al. “Locally Free Representations of Quivers over Commutative Frobenius Algebras.” Selecta Mathematica, vol. 30, no. 2, 20, Springer Nature, 2024, doi:10.1007/s00029-023-00914-2. short: T. Hausel, E. Letellier, F. Rodriguez-Villegas, Selecta Mathematica 30 (2024). date_created: 2024-02-04T23:00:53Z date_published: 2024-01-27T00:00:00Z date_updated: 2024-02-05T12:58:21Z day: '27' department: - _id: TaHa doi: 10.1007/s00029-023-00914-2 intvolume: ' 30' issue: '2' language: - iso: eng month: '01' oa_version: None publication: Selecta Mathematica publication_identifier: eissn: - 1420-9020 issn: - 1022-1824 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Locally free representations of quivers over commutative Frobenius algebras type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 30 year: '2024' ... --- _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: '10704' abstract: - lang: eng 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. 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). 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: Nigel full_name: Hitchin, Nigel last_name: Hitchin citation: ama: Hausel T, Hitchin N. Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. Inventiones Mathematicae. 2022;228:893-989. doi:10.1007/s00222-021-01093-7 apa: Hausel, T., & Hitchin, N. (2022). Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. Inventiones Mathematicae. Springer Nature. https://doi.org/10.1007/s00222-021-01093-7 chicago: Hausel, Tamás, and Nigel Hitchin. “Very Stable Higgs Bundles, Equivariant Multiplicity and Mirror Symmetry.” Inventiones Mathematicae. Springer Nature, 2022. https://doi.org/10.1007/s00222-021-01093-7. ieee: T. Hausel and N. Hitchin, “Very stable Higgs bundles, equivariant multiplicity and mirror symmetry,” Inventiones Mathematicae, vol. 228. Springer Nature, pp. 893–989, 2022. ista: Hausel T, Hitchin N. 2022. Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. Inventiones Mathematicae. 228, 893–989. mla: Hausel, Tamás, and Nigel Hitchin. “Very Stable Higgs Bundles, Equivariant Multiplicity and Mirror Symmetry.” Inventiones Mathematicae, vol. 228, Springer Nature, 2022, pp. 893–989, doi:10.1007/s00222-021-01093-7. short: T. Hausel, N. Hitchin, Inventiones Mathematicae 228 (2022) 893–989. date_created: 2022-01-30T23:01:34Z date_published: 2022-05-01T00:00:00Z date_updated: 2023-08-02T14:03:20Z day: '01' ddc: - '510' department: - _id: TaHa doi: 10.1007/s00222-021-01093-7 external_id: arxiv: - '2101.08583' isi: - '000745495400001' file: - access_level: open_access checksum: a382ba75acebc9adfb8fe56247cb410e content_type: application/pdf creator: dernst date_created: 2023-02-27T07:30:47Z date_updated: 2023-02-27T07:30:47Z file_id: '12687' file_name: 2022_InventionesMahtematicae_Hausel.pdf file_size: 1069538 relation: main_file success: 1 file_date_updated: 2023-02-27T07:30:47Z has_accepted_license: '1' intvolume: ' 228' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 893-989 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Inventiones Mathematicae publication_identifier: eissn: - 1432-1297 issn: - 0020-9910 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: link: - description: News on the ISTA Website relation: press_release url: https://ista.ac.at/en/news/the-tip-of-the-mathematical-iceberg/ scopus_import: '1' status: public title: Very stable Higgs bundles, equivariant multiplicity and mirror symmetry 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 228 year: '2022' ... --- _id: '15070' abstract: - lang: eng text: This workshop focused on interactions between the various perspectives on the moduli space of Higgs bundles over a Riemann surface. This subject draws on algebraic geometry, geometric topology, geometric analysis and mathematical physics, and the goal was to promote interactions between these various branches of the subject. The main current directions of research were well represented by the participants, and the talks included many from both senior and junior participants. article_processing_charge: No article_type: original author: - first_name: Lara full_name: Anderson, Lara last_name: Anderson - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Rafe full_name: Mazzeo, Rafe last_name: Mazzeo - first_name: Laura full_name: Schaposnik, Laura last_name: Schaposnik citation: ama: Anderson L, Hausel T, Mazzeo R, Schaposnik L. Geometry and physics of Higgs bundles. Oberwolfach Reports. 2020;16(2):1357-1417. doi:10.4171/owr/2019/23 apa: Anderson, L., Hausel, T., Mazzeo, R., & Schaposnik, L. (2020). Geometry and physics of Higgs bundles. Oberwolfach Reports. European Mathematical Society. https://doi.org/10.4171/owr/2019/23 chicago: Anderson, Lara, Tamás Hausel, Rafe Mazzeo, and Laura Schaposnik. “Geometry and Physics of Higgs Bundles.” Oberwolfach Reports. European Mathematical Society, 2020. https://doi.org/10.4171/owr/2019/23. ieee: L. Anderson, T. Hausel, R. Mazzeo, and L. Schaposnik, “Geometry and physics of Higgs bundles,” Oberwolfach Reports, vol. 16, no. 2. European Mathematical Society, pp. 1357–1417, 2020. ista: Anderson L, Hausel T, Mazzeo R, Schaposnik L. 2020. Geometry and physics of Higgs bundles. Oberwolfach Reports. 16(2), 1357–1417. mla: Anderson, Lara, et al. “Geometry and Physics of Higgs Bundles.” Oberwolfach Reports, vol. 16, no. 2, European Mathematical Society, 2020, pp. 1357–417, doi:10.4171/owr/2019/23. short: L. Anderson, T. Hausel, R. Mazzeo, L. Schaposnik, Oberwolfach Reports 16 (2020) 1357–1417. date_created: 2024-03-04T11:36:31Z date_published: 2020-06-04T00:00:00Z date_updated: 2024-03-11T09:20:34Z day: '04' department: - _id: TaHa doi: 10.4171/owr/2019/23 intvolume: ' 16' issue: '2' keyword: - Organic Chemistry - Biochemistry language: - iso: eng month: '06' oa_version: None page: 1357-1417 publication: Oberwolfach Reports publication_identifier: issn: - 1660-8933 publication_status: published publisher: European Mathematical Society quality_controlled: '1' status: public title: Geometry and physics of Higgs bundles type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 16 year: '2020' ... --- _id: '439' abstract: - lang: eng 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." article_processing_charge: No article_type: original author: - first_name: Tamas full_name: Hausel, Tamas id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Martin full_name: Mereb, Martin id: 43D735EE-F248-11E8-B48F-1D18A9856A87 last_name: Mereb - first_name: Michael full_name: Wong, Michael last_name: Wong citation: ama: Hausel T, Mereb M, Wong M. Arithmetic and representation theory of wild character varieties. Journal of the European Mathematical Society. 2019;21(10):2995-3052. doi:10.4171/JEMS/896 apa: Hausel, T., Mereb, M., & Wong, M. (2019). Arithmetic and representation theory of wild character varieties. Journal of the European Mathematical Society. European Mathematical Society. https://doi.org/10.4171/JEMS/896 chicago: Hausel, Tamás, Martin Mereb, and Michael Wong. “Arithmetic and Representation Theory of Wild Character Varieties.” Journal of the European Mathematical Society. European Mathematical Society, 2019. https://doi.org/10.4171/JEMS/896. ieee: T. Hausel, M. Mereb, and M. Wong, “Arithmetic and representation theory of wild character varieties,” Journal of the European Mathematical Society, vol. 21, no. 10. European Mathematical Society, pp. 2995–3052, 2019. 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. mla: Hausel, Tamás, et al. “Arithmetic and Representation Theory of Wild Character Varieties.” Journal of the European Mathematical Society, vol. 21, no. 10, European Mathematical Society, 2019, pp. 2995–3052, doi:10.4171/JEMS/896. short: T. Hausel, M. Mereb, M. Wong, Journal of the European Mathematical Society 21 (2019) 2995–3052. date_created: 2018-12-11T11:46:29Z date_published: 2019-10-01T00:00:00Z date_updated: 2023-08-24T14:24:49Z day: '01' department: - _id: TaHa doi: 10.4171/JEMS/896 ec_funded: 1 external_id: arxiv: - '1604.03382' isi: - '000480413600002' intvolume: ' 21' isi: 1 issue: '10' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1604.03382 month: '10' oa: 1 oa_version: Preprint page: 2995-3052 project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces publication: Journal of the European Mathematical Society publication_identifier: eissn: - 1435-9855 publication_status: published publisher: European Mathematical Society publist_id: '7384' quality_controlled: '1' scopus_import: '1' status: public title: Arithmetic and representation theory of wild character varieties type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 21 year: '2019' ... --- _id: '6525' 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. author: - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Anton full_name: Mellit, Anton id: 388D3134-F248-11E8-B48F-1D18A9856A87 last_name: Mellit - first_name: Du full_name: Pei, Du last_name: Pei citation: ama: 'Hausel T, Mellit A, Pei D. Mirror symmetry with branes by equivariant verlinde formulas. In: Geometry and Physics: Volume I. Oxford University Press; 2018:189-218. doi:10.1093/oso/9780198802013.003.0009' apa: 'Hausel, T., Mellit, A., & Pei, D. (2018). Mirror symmetry with branes by equivariant verlinde formulas. In Geometry and Physics: Volume I (pp. 189–218). Oxford University Press. https://doi.org/10.1093/oso/9780198802013.003.0009' chicago: 'Hausel, Tamás, Anton Mellit, and Du Pei. “Mirror Symmetry with Branes by Equivariant Verlinde Formulas.” In Geometry and Physics: Volume I, 189–218. Oxford University Press, 2018. https://doi.org/10.1093/oso/9780198802013.003.0009.' ieee: 'T. Hausel, A. Mellit, and D. Pei, “Mirror symmetry with branes by equivariant verlinde formulas,” 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.' mla: 'Hausel, Tamás, et al. “Mirror Symmetry with Branes by Equivariant Verlinde Formulas.” Geometry and Physics: Volume I, Oxford University Press, 2018, pp. 189–218, doi:10.1093/oso/9780198802013.003.0009.' short: 'T. Hausel, A. Mellit, D. Pei, in:, Geometry and Physics: Volume I, Oxford University Press, 2018, pp. 189–218.' date_created: 2019-06-06T12:42:01Z date_published: 2018-01-01T00:00:00Z date_updated: 2021-01-12T08:07:52Z day: '01' department: - _id: TaHa doi: 10.1093/oso/9780198802013.003.0009 language: - iso: eng month: '01' oa_version: None page: 189-218 publication: 'Geometry and Physics: Volume I' publication_identifier: isbn: - '9780198802013' - '9780191840500' publication_status: published publisher: Oxford University Press quality_controlled: '1' scopus_import: 1 status: public title: Mirror symmetry with branes by equivariant verlinde formulas type: book_chapter user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2018' ... --- _id: '1473' 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. author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Fernando full_name: Rodríguez Villegas, Fernando last_name: Rodríguez Villegas citation: ama: Hausel T, Rodríguez Villegas F. Cohomology of large semiprojective hyperkähler varieties. Asterisque. 2015;2015(370):113-156. apa: Hausel, T., & Rodríguez Villegas, F. (2015). Cohomology of large semiprojective hyperkähler varieties. Asterisque. Societe Mathematique de France. chicago: Hausel, Tamás, and Fernando Rodríguez Villegas. “Cohomology of Large Semiprojective Hyperkähler Varieties.” Asterisque. Societe Mathematique de France, 2015. ieee: T. Hausel and F. Rodríguez Villegas, “Cohomology of large semiprojective hyperkähler varieties,” Asterisque, 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. mla: Hausel, Tamás, and Fernando Rodríguez Villegas. “Cohomology of Large Semiprojective Hyperkähler Varieties.” Asterisque, vol. 2015, no. 370, Societe Mathematique de France, 2015, pp. 113–56. short: T. Hausel, F. Rodríguez Villegas, Asterisque 2015 (2015) 113–156. date_created: 2018-12-11T11:52:13Z date_published: 2015-01-01T00:00:00Z date_updated: 2021-01-12T06:50:59Z day: '01' extern: 1 intvolume: ' 2015' issue: '370' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1309.4914 month: '01' oa: 1 page: 113 - 156 publication: Asterisque publication_status: published publisher: Societe Mathematique de France publist_id: '5723' quality_controlled: 0 status: public title: Cohomology of large semiprojective hyperkähler varieties type: review volume: 2015 year: '2015' ... --- _id: '1442' abstract: - lang: eng 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. 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 ANR-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 - first_name: Emmanuel full_name: Letellier, Emmanuel last_name: Letellier - first_name: Fernando full_name: Rodríguez Villegas, Fernando last_name: Rodríguez Villegas citation: ama: Hausel T, Letellier E, Rodríguez Villegas F. Positivity for Kac polynomials and DT-invariants of quivers. Annals of Mathematics. 2013;177(3):1147-1168. doi:10.4007/annals.2013.177.3.8 apa: Hausel, T., Letellier, E., & Rodríguez Villegas, F. (2013). Positivity for Kac polynomials and DT-invariants of quivers. Annals of Mathematics. Princeton University Press. https://doi.org/10.4007/annals.2013.177.3.8 chicago: Hausel, Tamás, Emmanuel Letellier, and Fernando Rodríguez Villegas. “Positivity for Kac Polynomials and DT-Invariants of Quivers.” Annals of Mathematics. Princeton University Press, 2013. https://doi.org/10.4007/annals.2013.177.3.8. ieee: T. Hausel, E. Letellier, and F. Rodríguez Villegas, “Positivity for Kac polynomials and DT-invariants of quivers,” Annals of Mathematics, vol. 177, no. 3. Princeton University Press, pp. 1147–1168, 2013. 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. mla: Hausel, Tamás, et al. “Positivity for Kac Polynomials and DT-Invariants of Quivers.” Annals of Mathematics, vol. 177, no. 3, Princeton University Press, 2013, pp. 1147–68, doi:10.4007/annals.2013.177.3.8. short: T. Hausel, E. Letellier, F. Rodríguez Villegas, Annals of Mathematics 177 (2013) 1147–1168. date_created: 2018-12-11T11:52:02Z date_published: 2013-01-01T00:00:00Z date_updated: 2021-01-12T06:50:47Z day: '01' doi: 10.4007/annals.2013.177.3.8 extern: 1 intvolume: ' 177' issue: '3' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1204.2375 month: '01' oa: 1 page: 1147 - 1168 publication: Annals of Mathematics publication_status: published publisher: Princeton University Press publist_id: '5754' quality_controlled: 0 status: public title: Positivity for Kac polynomials and DT-invariants of quivers type: journal_article volume: 177 year: '2013' ... --- _id: '1443' abstract: - lang: eng 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.' alternative_title: - Advanced Lectures in Mathematics author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel citation: ama: 'Hausel T. Global topology of the Hitchin system. In: Handbook of Moduli: Volume II. Vol 25. International Press; 2013:29-70.' apa: 'Hausel, T. (2013). Global topology of the Hitchin system. In Handbook of Moduli: Volume II (Vol. 25, pp. 29–70). International Press.' chicago: 'Hausel, Tamás. “Global Topology of the Hitchin System.” In Handbook of Moduli: Volume II, 25:29–70. International Press, 2013.' ieee: 'T. Hausel, “Global topology of the Hitchin system,” in Handbook of Moduli: Volume II, vol. 25, International Press, 2013, pp. 29–70.' ista: 'Hausel T. 2013.Global topology of the Hitchin system. In: Handbook of Moduli: Volume II. Advanced Lectures in Mathematics, vol. 25, 29–70.' mla: 'Hausel, Tamás. “Global Topology of the Hitchin System.” Handbook of Moduli: Volume II, vol. 25, International Press, 2013, pp. 29–70.' short: 'T. Hausel, in:, Handbook of Moduli: Volume II, International Press, 2013, pp. 29–70.' date_created: 2018-12-11T11:52:03Z date_published: 2013-03-15T00:00:00Z date_updated: 2021-01-12T06:50:47Z day: '15' extern: 1 intvolume: ' 25' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1102.1717 month: '03' oa: 1 page: 29 - 70 publication: 'Handbook of Moduli: Volume II' publication_status: published publisher: International Press publist_id: '5753' quality_controlled: 0 status: public title: Global topology of the Hitchin system type: book_chapter volume: 25 year: '2013' ... --- _id: '1469' 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. 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. author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Emmanuel full_name: Letellier, Emmanuel last_name: Letellier - first_name: Fernando full_name: Rodríguez Villegas, Fernando last_name: Rodríguez Villegas citation: ama: Hausel T, Letellier E, Rodríguez Villegas F. Arithmetic harmonic analysis on character and quiver varieties II. Advances in Mathematics. 2013;234:85-128. doi:10.1016/j.aim.2012.10.009 apa: Hausel, T., Letellier, E., & Rodríguez Villegas, F. (2013). Arithmetic harmonic analysis on character and quiver varieties II. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2012.10.009 chicago: Hausel, Tamás, Emmanuel Letellier, and Fernando Rodríguez Villegas. “Arithmetic Harmonic Analysis on Character and Quiver Varieties II.” Advances in Mathematics. Academic Press, 2013. https://doi.org/10.1016/j.aim.2012.10.009. ieee: T. Hausel, E. Letellier, and F. Rodríguez Villegas, “Arithmetic harmonic analysis on character and quiver varieties II,” Advances in Mathematics, vol. 234. Academic Press, pp. 85–128, 2013. 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.” Advances in Mathematics, vol. 234, Academic Press, 2013, pp. 85–128, doi:10.1016/j.aim.2012.10.009. short: T. Hausel, E. Letellier, F. Rodríguez Villegas, Advances in Mathematics 234 (2013) 85–128. date_created: 2018-12-11T11:52:12Z date_published: 2013-02-15T00:00:00Z date_updated: 2021-01-12T06:50:57Z day: '15' doi: 10.1016/j.aim.2012.10.009 extern: 1 intvolume: ' 234' month: '02' page: 85 - 128 publication: Advances in Mathematics publication_status: published publisher: Academic Press publist_id: '5724' quality_controlled: 0 status: public title: Arithmetic harmonic analysis on character and quiver varieties II type: journal_article volume: 234 year: '2013' ... --- _id: '1470' abstract: - lang: eng 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. 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" author: - first_name: Mark full_name: De Cataldo, Mark A last_name: De Cataldo - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Luca full_name: Migliorini, Luca last_name: Migliorini citation: ama: De Cataldo M, Hausel T, Migliorini L. Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces. Journal of Singularities. 2013;7:23-38. doi:10.5427/jsing.2013.7c apa: 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. Worldwide Center of Mathematics. https://doi.org/10.5427/jsing.2013.7c chicago: De Cataldo, Mark, Tamás Hausel, and Luca Migliorini. “Exchange between Perverse and Weight Filtration for the Hilbert Schemes of Points of Two Surfaces.” Journal of Singularities. Worldwide Center of Mathematics, 2013. https://doi.org/10.5427/jsing.2013.7c. ieee: M. De Cataldo, T. Hausel, and L. Migliorini, “Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces,” Journal of Singularities, vol. 7. Worldwide Center of Mathematics, pp. 23–38, 2013. 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. mla: De Cataldo, Mark, et al. “Exchange between Perverse and Weight Filtration for the Hilbert Schemes of Points of Two Surfaces.” Journal of Singularities, vol. 7, Worldwide Center of Mathematics, 2013, pp. 23–38, doi:10.5427/jsing.2013.7c. short: M. De Cataldo, T. Hausel, L. Migliorini, Journal of Singularities 7 (2013) 23–38. date_created: 2018-12-11T11:52:12Z date_published: 2013-01-01T00:00:00Z date_updated: 2021-01-12T06:50:58Z day: '01' doi: 10.5427/jsing.2013.7c extern: 1 intvolume: ' 7' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1012.2583 month: '01' oa: 1 page: 23 - 38 publication: Journal of Singularities publication_status: published publisher: Worldwide Center of Mathematics publist_id: '5725' quality_controlled: 0 status: public title: Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces type: journal_article volume: 7 year: '2013' ... --- _id: '1472' 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. 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" author: - first_name: Mark full_name: De Cataldo, Mark A last_name: De Cataldo - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Luca full_name: Migliorini, Luca last_name: Migliorini citation: ama: 'De Cataldo M, Hausel T, Migliorini L. Topology of hitchin systems and Hodge theory of character varieties: The case A 1. Annals of Mathematics. 2012;175(3):1329-1407. doi:10.4007/annals.2012.175.3.7' apa: '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. Princeton University Press. https://doi.org/10.4007/annals.2012.175.3.7' chicago: 'De Cataldo, Mark, Tamás Hausel, and Luca Migliorini. “Topology of Hitchin Systems and Hodge Theory of Character Varieties: The Case A 1.” Annals of Mathematics. Princeton University Press, 2012. https://doi.org/10.4007/annals.2012.175.3.7.' ieee: 'M. De Cataldo, T. Hausel, and L. Migliorini, “Topology of hitchin systems and Hodge theory of character varieties: The case A 1,” Annals of Mathematics, vol. 175, no. 3. Princeton University Press, pp. 1329–1407, 2012.' 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.' mla: 'De Cataldo, Mark, et al. “Topology of Hitchin Systems and Hodge Theory of Character Varieties: The Case A 1.” Annals of Mathematics, vol. 175, no. 3, Princeton University Press, 2012, pp. 1329–407, doi:10.4007/annals.2012.175.3.7.' short: M. De Cataldo, T. Hausel, L. Migliorini, Annals of Mathematics 175 (2012) 1329–1407. date_created: 2018-12-11T11:52:13Z date_published: 2012-05-01T00:00:00Z date_updated: 2021-01-12T06:50:59Z day: '01' doi: 10.4007/annals.2012.175.3.7 extern: 1 intvolume: ' 175' issue: '3' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1004.1420 month: '05' oa: 1 page: 1329 - 1407 publication: Annals of Mathematics publication_status: published publisher: Princeton University Press publist_id: '5727' quality_controlled: 0 status: public title: 'Topology of hitchin systems and Hodge theory of character varieties: The case A 1' type: journal_article volume: 175 year: '2012' ... --- _id: '1471' 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.' author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Christian full_name: Pauly, Christian last_name: Pauly citation: ama: Hausel T, Pauly C. Prym varieties of spectral covers. Geometry and Topology. 2012;16(3):1609-1638. doi:10.2140/gt.2012.16.1609 apa: Hausel, T., & Pauly, C. (2012). Prym varieties of spectral covers. Geometry and Topology. University of Warwick. https://doi.org/10.2140/gt.2012.16.1609 chicago: Hausel, Tamás, and Christian Pauly. “Prym Varieties of Spectral Covers.” Geometry and Topology. University of Warwick, 2012. https://doi.org/10.2140/gt.2012.16.1609. ieee: T. Hausel and C. Pauly, “Prym varieties of spectral covers,” Geometry and Topology, 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. mla: Hausel, Tamás, and Christian Pauly. “Prym Varieties of Spectral Covers.” Geometry and Topology, vol. 16, no. 3, University of Warwick, 2012, pp. 1609–38, doi:10.2140/gt.2012.16.1609. short: T. Hausel, C. Pauly, Geometry and Topology 16 (2012) 1609–1638. date_created: 2018-12-11T11:52:13Z date_published: 2012-08-01T00:00:00Z date_updated: 2021-01-12T06:50:58Z day: '01' doi: 10.2140/gt.2012.16.1609 extern: 1 intvolume: ' 16' issue: '3' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1012.4748 month: '08' oa: 1 page: 1609 - 1638 publication: Geometry and Topology publication_status: published publisher: University of Warwick publist_id: '5726' quality_controlled: 0 status: public title: Prym varieties of spectral covers type: journal_article volume: 16 year: '2012' ... --- _id: '1467' abstract: - lang: eng 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). 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. Rodriguez-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. author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Emmanuel full_name: Letellier, Emmanuel last_name: Letellier - first_name: Fernando full_name: Rodríguez Villegas, Fernando last_name: Rodríguez Villegas citation: ama: Hausel T, Letellier E, Rodríguez Villegas F. Arithmetic harmonic analysis on character and quiver varieties. Duke Mathematical Journal. 2011;160(2):323-400. doi:10.1215/00127094-1444258 apa: Hausel, T., Letellier, E., & Rodríguez Villegas, F. (2011). Arithmetic harmonic analysis on character and quiver varieties. Duke Mathematical Journal. Duke University Press. https://doi.org/10.1215/00127094-1444258 chicago: Hausel, Tamás, Emmanuel Letellier, and Fernando Rodríguez Villegas. “Arithmetic Harmonic Analysis on Character and Quiver Varieties.” Duke Mathematical Journal. Duke University Press, 2011. https://doi.org/10.1215/00127094-1444258. ieee: T. Hausel, E. Letellier, and F. Rodríguez Villegas, “Arithmetic harmonic analysis on character and quiver varieties,” Duke Mathematical Journal, vol. 160, no. 2. Duke University Press, pp. 323–400, 2011. ista: Hausel T, Letellier E, Rodríguez Villegas F. 2011. Arithmetic harmonic analysis on character and quiver varieties. Duke Mathematical Journal. 160(2), 323–400. mla: Hausel, Tamás, et al. “Arithmetic Harmonic Analysis on Character and Quiver Varieties.” Duke Mathematical Journal, vol. 160, no. 2, Duke University Press, 2011, pp. 323–400, doi:10.1215/00127094-1444258. short: T. Hausel, E. Letellier, F. Rodríguez Villegas, Duke Mathematical Journal 160 (2011) 323–400. date_created: 2018-12-11T11:52:11Z date_published: 2011-01-01T00:00:00Z date_updated: 2021-01-12T06:50:56Z day: '01' doi: 10.1215/00127094-1444258 extern: 1 intvolume: ' 160' issue: '2' main_file_link: - open_access: '1' url: http://arxiv.org/abs/0810.2076 month: '01' oa: 1 page: 323 - 400 publication: Duke Mathematical Journal publication_status: published publisher: Duke University Press publist_id: '5728' quality_controlled: 0 status: public title: Arithmetic harmonic analysis on character and quiver varieties type: journal_article volume: 160 year: '2011' ... --- _id: '1466' abstract: - lang: eng 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]. author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Emmanuel full_name: Letellier, Emmanuel last_name: Letellier - first_name: Fernando full_name: Rodríguez Villegas, Fernando last_name: Rodríguez Villegas citation: ama: Hausel T, Letellier E, Rodríguez Villegas F. Topology of character varieties and representations of quivers. Comptes Rendus Mathematique. 2010;348(3-4):131-135. doi:10.1016/j.crma.2010.01.025 apa: Hausel, T., Letellier, E., & Rodríguez Villegas, F. (2010). Topology of character varieties and representations of quivers. Comptes Rendus Mathematique. Elsevier. https://doi.org/10.1016/j.crma.2010.01.025 chicago: Hausel, Tamás, Emmanuel Letellier, and Fernando Rodríguez Villegas. “Topology of Character Varieties and Representations of Quivers.” Comptes Rendus Mathematique. Elsevier, 2010. https://doi.org/10.1016/j.crma.2010.01.025. ieee: T. Hausel, E. Letellier, and F. Rodríguez Villegas, “Topology of character varieties and representations of quivers,” Comptes Rendus Mathematique, vol. 348, no. 3–4. Elsevier, pp. 131–135, 2010. 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.” Comptes Rendus Mathematique, vol. 348, no. 3–4, Elsevier, 2010, pp. 131–35, doi:10.1016/j.crma.2010.01.025. short: T. Hausel, E. Letellier, F. Rodríguez Villegas, Comptes Rendus Mathematique 348 (2010) 131–135. date_created: 2018-12-11T11:52:11Z date_published: 2010-02-01T00:00:00Z date_updated: 2021-01-12T06:50:56Z day: '01' doi: 10.1016/j.crma.2010.01.025 extern: 1 intvolume: ' 348' issue: 3-4 main_file_link: - open_access: '1' url: http://arxiv.org/abs/0905.3491 month: '02' oa: 1 page: 131 - 135 publication: Comptes Rendus Mathematique publication_status: published publisher: Elsevier publist_id: '5731' quality_controlled: 0 status: public title: Topology of character varieties and representations of quivers type: journal_article volume: 348 year: '2010' ... --- _id: '1465' abstract: - lang: eng 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. 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. author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel citation: ama: Hausel T. Kac’s conjecture from Nakajima quiver varieties. Inventiones Mathematicae. 2010;181(1):21-37. doi:10.1007/s00222-010-0241-3 apa: Hausel, T. (2010). Kac’s conjecture from Nakajima quiver varieties. Inventiones Mathematicae. Springer. https://doi.org/10.1007/s00222-010-0241-3 chicago: Hausel, Tamás. “Kac’s Conjecture from Nakajima Quiver Varieties.” Inventiones Mathematicae. Springer, 2010. https://doi.org/10.1007/s00222-010-0241-3. ieee: T. Hausel, “Kac’s conjecture from Nakajima quiver varieties,” Inventiones Mathematicae, vol. 181, no. 1. Springer, pp. 21–37, 2010. ista: Hausel T. 2010. Kac’s conjecture from Nakajima quiver varieties. Inventiones Mathematicae. 181(1), 21–37. mla: Hausel, Tamás. “Kac’s Conjecture from Nakajima Quiver Varieties.” Inventiones Mathematicae, vol. 181, no. 1, Springer, 2010, pp. 21–37, doi:10.1007/s00222-010-0241-3. short: T. Hausel, Inventiones Mathematicae 181 (2010) 21–37. date_created: 2018-12-11T11:52:11Z date_published: 2010-07-01T00:00:00Z date_updated: 2021-01-12T06:50:56Z day: '01' doi: 10.1007/s00222-010-0241-3 extern: 1 intvolume: ' 181' issue: '1' main_file_link: - open_access: '1' url: http://arxiv.org/abs/0811.1569 month: '07' oa: 1 page: 21 - 37 publication: Inventiones Mathematicae publication_status: published publisher: Springer publist_id: '5730' quality_controlled: 0 status: public title: Kac's conjecture from Nakajima quiver varieties type: journal_article volume: 181 year: '2010' ... --- _id: '1468' abstract: - lang: eng 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?' author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel citation: ama: 'Hausel T. S-Duality in HyperkäHler Hodge Theory. In: The Many Facets of Geometry: A Tribute to Nigel Hitchin. Oxford University Press; 2010. doi:10.1093/acprof:oso/9780199534920.003.0016' apa: 'Hausel, T. (2010). S-Duality in HyperkäHler Hodge Theory. In The Many Facets of Geometry: A Tribute to Nigel Hitchin. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199534920.003.0016' chicago: 'Hausel, Tamás. “S-Duality in HyperkäHler Hodge Theory.” In The Many Facets of Geometry: A Tribute to Nigel Hitchin. Oxford University Press, 2010. https://doi.org/10.1093/acprof:oso/9780199534920.003.0016.' ieee: 'T. Hausel, “S-Duality in HyperkäHler Hodge Theory,” in The Many Facets of Geometry: A Tribute to Nigel Hitchin, Oxford University Press, 2010.' ista: 'Hausel T. 2010.S-Duality in HyperkäHler Hodge Theory. In: The Many Facets of Geometry: A Tribute to Nigel Hitchin. .' mla: 'Hausel, Tamás. “S-Duality in HyperkäHler Hodge Theory.” The Many Facets of Geometry: A Tribute to Nigel Hitchin, Oxford University Press, 2010, doi:10.1093/acprof:oso/9780199534920.003.0016.' short: 'T. Hausel, in:, The Many Facets of Geometry: A Tribute to Nigel Hitchin, Oxford University Press, 2010.' date_created: 2018-12-11T11:52:12Z date_published: 2010-09-01T00:00:00Z date_updated: 2021-01-12T06:50:57Z day: '01' doi: 10.1093/acprof:oso/9780199534920.003.0016 extern: 1 main_file_link: - open_access: '1' url: http://arxiv.org/abs/0709.0504 month: '09' oa: 1 publication: 'The Many Facets of Geometry: A Tribute to Nigel Hitchin' publication_status: published publisher: Oxford University Press publist_id: '5729' quality_controlled: 0 status: public title: S-Duality in HyperkäHler Hodge Theory type: book_chapter year: '2010' ... --- _id: '1460' abstract: - lang: eng 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.' 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. author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Fernando full_name: Rodríguez Villegas, Fernando last_name: Rodríguez Villegas citation: ama: 'Hausel T, Rodríguez Villegas F. Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz. Inventiones Mathematicae. 2008;174(3):555-624. doi:10.1007/s00222-008-0142-x' apa: 'Hausel, T., & Rodríguez Villegas, F. (2008). Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz. Inventiones Mathematicae. Springer. https://doi.org/10.1007/s00222-008-0142-x' chicago: 'Hausel, Tamás, and Fernando Rodríguez Villegas. “Mixed Hodge Polynomials of Character Varieties: With an Appendix by Nicholas M. Katz.” Inventiones Mathematicae. Springer, 2008. https://doi.org/10.1007/s00222-008-0142-x.' ieee: 'T. Hausel and F. Rodríguez Villegas, “Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz,” Inventiones Mathematicae, vol. 174, no. 3. Springer, pp. 555–624, 2008.' 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.' mla: 'Hausel, Tamás, and Fernando Rodríguez Villegas. “Mixed Hodge Polynomials of Character Varieties: With an Appendix by Nicholas M. Katz.” Inventiones Mathematicae, vol. 174, no. 3, Springer, 2008, pp. 555–624, doi:10.1007/s00222-008-0142-x.' short: T. Hausel, F. Rodríguez Villegas, Inventiones Mathematicae 174 (2008) 555–624. date_created: 2018-12-11T11:52:09Z date_published: 2008-12-01T00:00:00Z date_updated: 2021-01-12T06:50:54Z day: '01' doi: 10.1007/s00222-008-0142-x extern: 1 intvolume: ' 174' issue: '3' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math/0612668 month: '12' oa: 1 page: 555 - 624 publication: Inventiones Mathematicae publication_status: published publisher: Springer publist_id: '5732' quality_controlled: 0 status: public title: 'Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz' type: journal_article volume: 174 year: '2008' ... --- _id: '1462' abstract: - lang: eng 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. 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. author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel citation: ama: Hausel T. Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform. PNAS. 2006;103(16):6120-6124. doi:10.1073/pnas.0601337103 apa: Hausel, T. (2006). Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.0601337103 chicago: Hausel, Tamás. “Betti Numbers of Holomorphic Symplectic Quotients via Arithmetic Fourier Transform.” PNAS. National Academy of Sciences, 2006. https://doi.org/10.1073/pnas.0601337103. ieee: T. Hausel, “Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform,” PNAS, vol. 103, no. 16. National Academy of Sciences, pp. 6120–6124, 2006. ista: Hausel T. 2006. Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform. PNAS. 103(16), 6120–6124. mla: Hausel, Tamás. “Betti Numbers of Holomorphic Symplectic Quotients via Arithmetic Fourier Transform.” PNAS, vol. 103, no. 16, National Academy of Sciences, 2006, pp. 6120–24, doi:10.1073/pnas.0601337103. short: T. Hausel, PNAS 103 (2006) 6120–6124. date_created: 2018-12-11T11:52:10Z date_published: 2006-04-18T00:00:00Z date_updated: 2021-01-12T06:50:55Z day: '18' doi: 10.1073/pnas.0601337103 extern: 1 intvolume: ' 103' issue: '16' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math/0511163 month: '04' oa: 1 page: 6120 - 6124 publication: PNAS publication_status: published publisher: National Academy of Sciences publist_id: '5734' quality_controlled: 0 status: public title: Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform type: journal_article volume: 103 year: '2006' ... --- _id: '1461' 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. 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. author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Edward full_name: Swartz, Edward last_name: Swartz citation: ama: Hausel T, Swartz E. Intersection forms of toric hyperkähler varieties. Proceedings of the American Mathematical Society. 2006;134(8):2403-2409. doi:10.1090/S0002-9939-06-08248-7 apa: Hausel, T., & Swartz, E. (2006). Intersection forms of toric hyperkähler varieties. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/S0002-9939-06-08248-7 chicago: Hausel, Tamás, and Edward Swartz. “Intersection Forms of Toric Hyperkähler Varieties.” Proceedings of the American Mathematical Society. American Mathematical Society, 2006. https://doi.org/10.1090/S0002-9939-06-08248-7. ieee: T. Hausel and E. Swartz, “Intersection forms of toric hyperkähler varieties,” Proceedings of the American Mathematical Society, vol. 134, no. 8. American Mathematical Society, pp. 2403–2409, 2006. ista: Hausel T, Swartz E. 2006. Intersection forms of toric hyperkähler varieties. Proceedings of the American Mathematical Society. 134(8), 2403–2409. mla: Hausel, Tamás, and Edward Swartz. “Intersection Forms of Toric Hyperkähler Varieties.” Proceedings of the American Mathematical Society, vol. 134, no. 8, American Mathematical Society, 2006, pp. 2403–09, doi:10.1090/S0002-9939-06-08248-7. short: T. Hausel, E. Swartz, Proceedings of the American Mathematical Society 134 (2006) 2403–2409. date_created: 2018-12-11T11:52:09Z date_published: 2006-08-01T00:00:00Z date_updated: 2021-01-12T06:50:54Z day: '01' doi: 10.1090/S0002-9939-06-08248-7 extern: 1 intvolume: ' 134' issue: '8' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math/0306369 month: '08' oa: 1 page: 2403 - 2409 publication: Proceedings of the American Mathematical Society publication_status: published publisher: American Mathematical Society publist_id: '5733' quality_controlled: 0 status: public title: Intersection forms of toric hyperkähler varieties type: journal_article volume: 134 year: '2006' ... --- _id: '1447' abstract: - lang: eng text: Building on a recent paper [8], here we argue that the combinatorics of matroids are intimately related to the geometry and topology of toric hyperkähler varieties. We show that just like toric varieties occupy a central role in Stanley’s proof for the necessity of McMullen’s conjecture (or g-inequalities) about the classification of face vectors of simplicial polytopes, the topology of toric hyperkähler varieties leads to new restrictions on face vectors of matroid complexes. Namely in this paper we will give two proofs that the injectivity part of the Hard Lefschetz theorem survives for toric hyperkähler varieties. We explain how this implies the g-inequalities for rationally representable matroids. We show how the geometrical intuition in the first proof, coupled with results of Chari [3], leads to a proof of the g-inequalities for general matroid complexes, which is a recent result of Swartz [20]. The geometrical idea in the second proof will show that a pure O-sequence should satisfy the g-inequalities, thus showing that our result is in fact a consequence of a long-standing conjecture of Stanley. acknowledgement: Financial support wa s provided by a Miller Research Fellowship at the University of California at Berkeley , and by NSF grants DMS- 0072675 and DMS-0305505. author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel citation: ama: Hausel T. Quaternionic geometry of matroids. Open Mathematics. 2005;3(1):26-38. doi:10.2478/BF02475653 apa: Hausel, T. (2005). Quaternionic geometry of matroids. Open Mathematics. Central European Science Journals. https://doi.org/10.2478/BF02475653 chicago: Hausel, Tamás. “Quaternionic Geometry of Matroids.” Open Mathematics. Central European Science Journals, 2005. https://doi.org/10.2478/BF02475653. ieee: T. Hausel, “Quaternionic geometry of matroids,” Open Mathematics, vol. 3, no. 1. Central European Science Journals, pp. 26–38, 2005. ista: Hausel T. 2005. Quaternionic geometry of matroids. Open Mathematics. 3(1), 26–38. mla: Hausel, Tamás. “Quaternionic Geometry of Matroids.” Open Mathematics, vol. 3, no. 1, Central European Science Journals, 2005, pp. 26–38, doi:10.2478/BF02475653. short: T. Hausel, Open Mathematics 3 (2005) 26–38. date_created: 2018-12-11T11:52:05Z date_published: 2005-03-01T00:00:00Z date_updated: 2021-01-12T06:50:49Z day: '01' doi: 10.2478/BF02475653 extern: 1 intvolume: ' 3' issue: '1' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math/0308146 month: '03' oa: 1 page: 26 - 38 publication: Open Mathematics publication_status: published publisher: Central European Science Journals publist_id: '5749' quality_controlled: 0 status: public title: Quaternionic geometry of matroids type: journal_article volume: 3 year: '2005' ... --- _id: '1444' abstract: - lang: eng 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. alternative_title: - Progress in Mathematics author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel citation: ama: 'Hausel T. Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve. In: Geometric Methods in Algebra and Number Theory. Vol 235. Springer; 2005:193-217. doi:10.1007/0-8176-4417-2_9' apa: 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 (Vol. 235, pp. 193–217). Springer. https://doi.org/10.1007/0-8176-4417-2_9 chicago: Hausel, Tamás. “Mirror Symmetry and Langlands Duality in the Non-Abelian Hodge Theory of a Curve.” In Geometric Methods in Algebra and Number Theory, 235:193–217. Springer, 2005. https://doi.org/10.1007/0-8176-4417-2_9. ieee: T. Hausel, “Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve,” in Geometric Methods in Algebra and Number Theory, vol. 235, Springer, 2005, pp. 193–217. 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.' mla: Hausel, Tamás. “Mirror Symmetry and Langlands Duality in the Non-Abelian Hodge Theory of a Curve.” Geometric Methods in Algebra and Number Theory, vol. 235, Springer, 2005, pp. 193–217, doi:10.1007/0-8176-4417-2_9. short: T. Hausel, in:, Geometric Methods in Algebra and Number Theory, Springer, 2005, pp. 193–217. date_created: 2018-12-11T11:52:03Z date_published: 2005-01-01T00:00:00Z date_updated: 2021-01-12T06:50:47Z day: '01' doi: 10.1007/0-8176-4417-2_9 extern: 1 intvolume: ' 235' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math/0406380 month: '01' oa: 1 page: 193 - 217 publication: Geometric Methods in Algebra and Number Theory publication_status: published publisher: Springer publist_id: '5752' quality_controlled: 0 status: public title: Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve type: book_chapter volume: 235 year: '2005' ... --- _id: '1463' abstract: - lang: eng text: We study an integration theory in circle equivariant cohomology in order to prove a theorem relating the cohomology ring of a hyperkähler quotient to the cohomology ring of the quotient by a maximal abelian subgroup, analogous to a theorem of Martin for symplectic quotients. We discuss applications of this theorem to quiver varieties, and compute as an example the ordinary and equivariant cohomology rings of a hyperpolygon space. acknowledgement: ' Financial support was provided in part by NSF Grants DMS-0072675 and DMS-0305505.' author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Nicholas full_name: Proudfoot, Nicholas J last_name: Proudfoot citation: ama: Hausel T, Proudfoot N. Abelianization for hyperkähler quotients. Topology. 2005;44(1):231-248. doi:10.1016/j.top.2004.04.002 apa: Hausel, T., & Proudfoot, N. (2005). Abelianization for hyperkähler quotients. Topology. Elsevier. https://doi.org/10.1016/j.top.2004.04.002 chicago: Hausel, Tamás, and Nicholas Proudfoot. “Abelianization for Hyperkähler Quotients.” Topology. Elsevier, 2005. https://doi.org/10.1016/j.top.2004.04.002. ieee: T. Hausel and N. Proudfoot, “Abelianization for hyperkähler quotients,” Topology, vol. 44, no. 1. Elsevier, pp. 231–248, 2005. ista: Hausel T, Proudfoot N. 2005. Abelianization for hyperkähler quotients. Topology. 44(1), 231–248. mla: Hausel, Tamás, and Nicholas Proudfoot. “Abelianization for Hyperkähler Quotients.” Topology, vol. 44, no. 1, Elsevier, 2005, pp. 231–48, doi:10.1016/j.top.2004.04.002. short: T. Hausel, N. Proudfoot, Topology 44 (2005) 231–248. date_created: 2018-12-11T11:52:10Z date_published: 2005-01-01T00:00:00Z date_updated: 2021-01-12T06:50:55Z day: '01' doi: 10.1016/j.top.2004.04.002 extern: 1 intvolume: ' 44' issue: '1' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math/0310141 month: '01' oa: 1 page: 231 - 248 publication: Topology publication_status: published publisher: Elsevier publist_id: '5735' quality_controlled: 0 status: public title: Abelianization for hyperkähler quotients type: journal_article volume: 44 year: '2005' ... --- _id: '1456' abstract: - lang: eng text: We study the space of L2 harmonic forms on complete manifolds with metrics of fibred boundary or fibred cusp type. These metrics generalize the geometric structures at infinity of several different well-known classes of metrics, including asymptotically locally Euclidean manifolds, the (known types of) gravitational instantons, and also Poincaré metrics on ℚ-rank 1 ends of locally symmetric spaces and on the complements of smooth divisors in Kähler manifolds. The answer in all cases is given in terms of intersection cohomology of a stratified compactification of the manifold. The L2 signature formula implied by our result is closely related to the one proved by Dai and more generally by Vaillant and identifies Dai's τ-invariant directly in terms of intersection cohomology of differing perversities. This work is also closely related to a recent paper of Carron and the forthcoming paper of Cheeger and Dai. We apply our results to a number of examples, gravitational instantons among them, arising in predictions about L2 harmonic forms in duality theories in string theory. acknowledgement: |- Hausel’s work supported by a Miller Research Fellowship at the University of California, Berkeley. Hunsicker’s work partially supported by Stanford University. Mazzeo’s work supported by National Science Foundation grant numbers DMS-991975 and DMS-0204730 and by the Mathematical Sciences Research Institute. author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Eugénie full_name: Hunsicker, Eugénie last_name: Hunsicker - first_name: Rafe full_name: Mazzeo, Rafe R last_name: Mazzeo citation: ama: Hausel T, Hunsicker E, Mazzeo R. Hodge cohomology of gravitational instantons. Duke Mathematical Journal. 2004;122(3):485-548. doi:10.1215/S0012-7094-04-12233-X apa: Hausel, T., Hunsicker, E., & Mazzeo, R. (2004). Hodge cohomology of gravitational instantons. Duke Mathematical Journal. Duke University Press. https://doi.org/10.1215/S0012-7094-04-12233-X chicago: Hausel, Tamás, Eugénie Hunsicker, and Rafe Mazzeo. “Hodge Cohomology of Gravitational Instantons.” Duke Mathematical Journal. Duke University Press, 2004. https://doi.org/10.1215/S0012-7094-04-12233-X. ieee: T. Hausel, E. Hunsicker, and R. Mazzeo, “Hodge cohomology of gravitational instantons,” Duke Mathematical Journal, vol. 122, no. 3. Duke University Press, pp. 485–548, 2004. ista: Hausel T, Hunsicker E, Mazzeo R. 2004. Hodge cohomology of gravitational instantons. Duke Mathematical Journal. 122(3), 485–548. mla: Hausel, Tamás, et al. “Hodge Cohomology of Gravitational Instantons.” Duke Mathematical Journal, vol. 122, no. 3, Duke University Press, 2004, pp. 485–548, doi:10.1215/S0012-7094-04-12233-X. short: T. Hausel, E. Hunsicker, R. Mazzeo, Duke Mathematical Journal 122 (2004) 485–548. date_created: 2018-12-11T11:52:08Z date_published: 2004-04-15T00:00:00Z date_updated: 2021-01-12T06:50:52Z day: '15' doi: 10.1215/S0012-7094-04-12233-X extern: 1 intvolume: ' 122' issue: '3' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math/0207169 month: '04' oa: 1 page: 485 - 548 publication: Duke Mathematical Journal publication_status: published publisher: Duke University Press publist_id: '5737' quality_controlled: 0 status: public title: Hodge cohomology of gravitational instantons type: journal_article volume: 122 year: '2004' ... --- _id: '1464' abstract: - lang: eng text: "The moduli space of stable vector bundles on a Riemann surface is smooth when the rank and degree are coprime, and is diffeomorphic to the space of unitary connections of central constant curvature. A classic result of Newstead and Atiyah and Bott asserts that its rational cohomology ring is generated by the universal classes, that is, by the Kunneth components of the Chern classes of the universal bundle.\n\nThis paper studies the larger, non-compact moduli space of Higgs bundles, as introduced by Hitchin and Simpson, with values in the canonical bundle K. This is diffeomorphic to the space of all connections of central constant curvature, whether unitary or not. The main result of the paper is that, in the rank 2 case, the rational cohomology ring of this space is again generated by universal classes.\n\nThe spaces of Higgs bundles with values in K(n) for n > 0 turn out to be essential to the story. Indeed, we show that their direct limit has the homotopy type of the classifying space of the gauge group, and hence has cohomology generated by universal classes. 2000 Mathematics Subject Classification 14H60 (primary), 14D20, 14H81, 32Q55, 58D27 (secondary). " author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Michael full_name: Thaddeus, Michael last_name: Thaddeus citation: ama: Hausel T, Thaddeus M. Generators for the cohomology ring of the moduli space of rank 2 higgs bundles. Proceedings of the London Mathematical Society. 2004;88(3):632-658. doi:10.1112/S0024611503014618 apa: Hausel, T., & Thaddeus, M. (2004). Generators for the cohomology ring of the moduli space of rank 2 higgs bundles. Proceedings of the London Mathematical Society. Oxford University Press. https://doi.org/10.1112/S0024611503014618 chicago: Hausel, Tamás, and Michael Thaddeus. “Generators for the Cohomology Ring of the Moduli Space of Rank 2 Higgs Bundles.” Proceedings of the London Mathematical Society. Oxford University Press, 2004. https://doi.org/10.1112/S0024611503014618. ieee: T. Hausel and M. Thaddeus, “Generators for the cohomology ring of the moduli space of rank 2 higgs bundles,” Proceedings of the London Mathematical Society, vol. 88, no. 3. Oxford University Press, pp. 632–658, 2004. ista: Hausel T, Thaddeus M. 2004. Generators for the cohomology ring of the moduli space of rank 2 higgs bundles. Proceedings of the London Mathematical Society. 88(3), 632–658. mla: Hausel, Tamás, and Michael Thaddeus. “Generators for the Cohomology Ring of the Moduli Space of Rank 2 Higgs Bundles.” Proceedings of the London Mathematical Society, vol. 88, no. 3, Oxford University Press, 2004, pp. 632–58, doi:10.1112/S0024611503014618. short: T. Hausel, M. Thaddeus, Proceedings of the London Mathematical Society 88 (2004) 632–658. date_created: 2018-12-11T11:52:10Z date_published: 2004-05-01T00:00:00Z date_updated: 2021-01-12T06:50:55Z day: '01' doi: 10.1112/S0024611503014618 extern: 1 intvolume: ' 88' issue: '3' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math/0003093 month: '05' oa: 1 page: 632 - 658 publication: Proceedings of the London Mathematical Society publication_status: published publisher: Oxford University Press publist_id: '5736' quality_controlled: 0 status: public title: Generators for the cohomology ring of the moduli space of rank 2 higgs bundles type: journal_article volume: 88 year: '2004' ... --- _id: '1457' abstract: - lang: eng text: 'Among the major mathematical approaches to mirror symmetry are those of Batyrev-Borisov and Stromdnger-Yau-Zaslow (SYZ). The first is explicit and amenable to computation but is not clearly related to the physical motivation; the second is the opposite. Furthermore, it is far from obvious that mirror partners in one sense will also be mirror partners in the other. This paper concerns a class of examples that can be shown to satisfy the requirements of SYZ, but whose Hodge numbers are also equal. This provides significant evidence in support of SYZ. Moreover, the examples are of great interest in their own right: they are spaces of flat SLr-connections on a smooth curve. The mirror is the corresponding space for the Langlands dual group PGLr. These examples therefore throw a bridge from mirror symmetry to the duality theory of Lie groups and, more broadly, to the geometric Langlands program.' author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Michael full_name: Thaddeus, Michael last_name: Thaddeus citation: ama: Hausel T, Thaddeus M. Mirror symmetry, langlands duality, and the Hitchin system. Inventiones Mathematicae. 2003;153(1):197-229. doi:10.1007/s00222-003-0286-7 apa: Hausel, T., & Thaddeus, M. (2003). Mirror symmetry, langlands duality, and the Hitchin system. Inventiones Mathematicae. Springer. https://doi.org/10.1007/s00222-003-0286-7 chicago: Hausel, Tamás, and Michael Thaddeus. “Mirror Symmetry, Langlands Duality, and the Hitchin System.” Inventiones Mathematicae. Springer, 2003. https://doi.org/10.1007/s00222-003-0286-7. ieee: T. Hausel and M. Thaddeus, “Mirror symmetry, langlands duality, and the Hitchin system,” Inventiones Mathematicae, vol. 153, no. 1. Springer, pp. 197–229, 2003. ista: Hausel T, Thaddeus M. 2003. Mirror symmetry, langlands duality, and the Hitchin system. Inventiones Mathematicae. 153(1), 197–229. mla: Hausel, Tamás, and Michael Thaddeus. “Mirror Symmetry, Langlands Duality, and the Hitchin System.” Inventiones Mathematicae, vol. 153, no. 1, Springer, 2003, pp. 197–229, doi:10.1007/s00222-003-0286-7. short: T. Hausel, M. Thaddeus, Inventiones Mathematicae 153 (2003) 197–229. date_created: 2018-12-11T11:52:08Z date_published: 2003-07-01T00:00:00Z date_updated: 2021-01-12T06:50:52Z day: '01' doi: 10.1007/s00222-003-0286-7 extern: 1 intvolume: ' 153' issue: '1' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math/0205236 month: '07' oa: 1 page: 197 - 229 publication: Inventiones Mathematicae publication_status: published publisher: Springer publist_id: '5738' quality_controlled: 0 status: public title: Mirror symmetry, langlands duality, and the Hitchin system type: journal_article volume: 153 year: '2003' ... --- _id: '1458' abstract: - lang: eng text: The moduli space of stable bundles of rank $2$ and degree $1$ on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian and Zagier provided a complete set of relations between these classes, expressed in terms of a recursion in the genus. This paper accomplishes the same thing for the noncompact moduli spaces of Higgs bundles, in the sense of Hitchin and Simpson. There are many more independent relations than for stable bundles, but in a sense the answer is simpler, since the formulas are completely explicit, not recursive. The results of Kirwan on equivariant cohomology for holomorphic circle actions are of key importance. acknowledgement: The first author was supported by NSF grant DMS-97-29992. The second author was supported by NSF grant DMS-98-08529. author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Michael full_name: Thaddeus, Michael last_name: Thaddeus citation: ama: Hausel T, Thaddeus M. Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles. Journal of the American Mathematical Society. 2003;16(2):303-329. doi:10.1090/S0894-0347-02-00417-4 apa: Hausel, T., & Thaddeus, M. (2003). Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles. Journal of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/S0894-0347-02-00417-4 chicago: Hausel, Tamás, and Michael Thaddeus. “Relations in the Cohomology Ring of the Moduli Space of Rank 2 Higgs Bundles.” Journal of the American Mathematical Society. American Mathematical Society, 2003. https://doi.org/10.1090/S0894-0347-02-00417-4. ieee: T. Hausel and M. Thaddeus, “Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles,” Journal of the American Mathematical Society, vol. 16, no. 2. American Mathematical Society, pp. 303–329, 2003. ista: Hausel T, Thaddeus M. 2003. Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles. Journal of the American Mathematical Society. 16(2), 303–329. mla: Hausel, Tamás, and Michael Thaddeus. “Relations in the Cohomology Ring of the Moduli Space of Rank 2 Higgs Bundles.” Journal of the American Mathematical Society, vol. 16, no. 2, American Mathematical Society, 2003, pp. 303–29, doi:10.1090/S0894-0347-02-00417-4. short: T. Hausel, M. Thaddeus, Journal of the American Mathematical Society 16 (2003) 303–329. date_created: 2018-12-11T11:52:08Z date_published: 2003-04-01T00:00:00Z date_updated: 2021-01-12T06:50:53Z day: '01' doi: 10.1090/S0894-0347-02-00417-4 extern: 1 intvolume: ' 16' issue: '2' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math/0003094 month: '04' oa: 1 page: 303 - 329 publication: Journal of the American Mathematical Society publication_status: published publisher: American Mathematical Society publist_id: '5739' quality_controlled: 0 status: public title: Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles type: journal_article volume: 16 year: '2003' ... --- _id: '1459' abstract: - lang: eng text: 'In this paper we explicitly calculate the analogue of the ''t Hooft SU (2) Yang-Mills instantons on Gibbons-Hawking multi-centered gravitational instantons, which come in two parallel families: the multi-Eguchi-Hanson, or Ak ALE gravitational instantons and the multi-Taub-NUT spaces, or Ak ALF gravitational instantons. We calculate their energy and find the reducible ones. Following Kronheimer we also exploit the U(1) invariance of our solutions and study the corresponding explicit singular SU (2) magnetic monopole solutions of the Bogomolny equations on flat ℝ3.' acknowledgement: We would like to acknowledge the financial support by Prof. P. Major (R ́ enyi Institute, Hungary) from his OTKA grant No. T26176 and of the Miller Institute for Basic Research in Science at UC Berkeley. author: - first_name: Gábor full_name: Etesi, Gábor last_name: Etesi - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel citation: ama: Etesi G, Hausel T. On Yang-Mills instantons over multi-centered gravitational instantons. Communications in Mathematical Physics. 2003;235(2):275-288. doi:10.1007/s00220-003-0806-8 apa: Etesi, G., & Hausel, T. (2003). On Yang-Mills instantons over multi-centered gravitational instantons. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-003-0806-8 chicago: Etesi, Gábor, and Tamás Hausel. “On Yang-Mills Instantons over Multi-Centered Gravitational Instantons.” Communications in Mathematical Physics. Springer, 2003. https://doi.org/10.1007/s00220-003-0806-8. ieee: G. Etesi and T. Hausel, “On Yang-Mills instantons over multi-centered gravitational instantons,” Communications in Mathematical Physics, vol. 235, no. 2. Springer, pp. 275–288, 2003. ista: Etesi G, Hausel T. 2003. On Yang-Mills instantons over multi-centered gravitational instantons. Communications in Mathematical Physics. 235(2), 275–288. mla: Etesi, Gábor, and Tamás Hausel. “On Yang-Mills Instantons over Multi-Centered Gravitational Instantons.” Communications in Mathematical Physics, vol. 235, no. 2, Springer, 2003, pp. 275–88, doi:10.1007/s00220-003-0806-8. short: G. Etesi, T. Hausel, Communications in Mathematical Physics 235 (2003) 275–288. date_created: 2018-12-11T11:52:09Z date_published: 2003-04-01T00:00:00Z date_updated: 2021-01-12T06:50:53Z day: '01' doi: 10.1007/s00220-003-0806-8 extern: 1 intvolume: ' 235' issue: '2' main_file_link: - open_access: '1' url: http://arxiv.org/abs/hep-th/0207196 month: '04' oa: 1 page: 275 - 288 publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '5740' quality_controlled: 0 status: public title: On Yang-Mills instantons over multi-centered gravitational instantons type: journal_article volume: 235 year: '2003' ... --- _id: '1451' abstract: - lang: eng text: Extending work of Bielawski-Dancer 3 and Konno 14, we develop a theory of toric hyperkähler varieties, which involves toric geometry, matroid theory and convex polyhedra. The framework is a detailed study of semi-projective toric varieties, meaning GIT quotients of affine spaces by torus actions, and specifically, of Lawrence toric varieties, meaning GIT quotients of even-dimensional affine spaces by symplectic torus actions. A toric hyperkähler variety is a complete intersection in a Lawrence toric variety. Both varieties are non-compact, and they share the same cohomology ring, namely, the Stanley-Reisner ring of a matroid modulo a linear system of parameters. Familiar applications of toric geometry to combinatorics, including the Hard Lefschetz Theorem and the volume polynomials of Khovanskii-Pukhlikov 11, are extended to the hyperkähler setting. When the matroid is graphic, our construction gives the toric quiver varieties, in the sense of Nakajima 17. acknowledgement: "Both authors were supported by the Miller Institute for Basic Research in Science, in the form of a Miller Research Fellowship (1999-2002) for the first author and a Miller Professorship (2000-2001) for the second author. The second author was also supported by the National Science\r\nFoundation (DMS-9970254)." article_processing_charge: No article_type: original author: - first_name: Tamas full_name: Hausel, Tamas id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Bernd full_name: Sturmfels, Bernd last_name: Sturmfels citation: ama: Hausel T, Sturmfels B. Toric hyperkähler varieties. Documenta Mathematica. 2002;7(1):495-534. doi:10.4171/DM/130 apa: Hausel, T., & Sturmfels, B. (2002). Toric hyperkähler varieties. Documenta Mathematica. Deutsche Mathematiker Vereinigung. https://doi.org/10.4171/DM/130 chicago: Hausel, Tamás, and Bernd Sturmfels. “Toric Hyperkähler Varieties.” Documenta Mathematica. Deutsche Mathematiker Vereinigung, 2002. https://doi.org/10.4171/DM/130. ieee: T. Hausel and B. Sturmfels, “Toric hyperkähler varieties,” Documenta Mathematica, vol. 7, no. 1. Deutsche Mathematiker Vereinigung, pp. 495–534, 2002. ista: Hausel T, Sturmfels B. 2002. Toric hyperkähler varieties. Documenta Mathematica. 7(1), 495–534. mla: Hausel, Tamás, and Bernd Sturmfels. “Toric Hyperkähler Varieties.” Documenta Mathematica, vol. 7, no. 1, Deutsche Mathematiker Vereinigung, 2002, pp. 495–534, doi:10.4171/DM/130. short: T. Hausel, B. Sturmfels, Documenta Mathematica 7 (2002) 495–534. date_created: 2018-12-11T11:52:06Z date_published: 2002-01-01T00:00:00Z date_updated: 2023-07-26T09:16:33Z day: '01' doi: 10.4171/DM/130 extern: '1' external_id: arxiv: - math/0203096 intvolume: ' 7' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://ems.press/journals/dm/articles/8965058 month: '01' oa: 1 oa_version: Published Version page: 495 - 534 publication: Documenta Mathematica publication_identifier: issn: - 1431-0635 publication_status: published publisher: Deutsche Mathematiker Vereinigung publist_id: '5741' quality_controlled: '1' scopus_import: '1' status: public title: Toric hyperkähler varieties type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 7 year: '2002' ... --- _id: '1452' abstract: - lang: eng text: 'In this Note we present pairs of hyperkähler orbifolds which satisfy two different versions of mirror symmetry. On the one hand, we show that their Hodge numbers (or more precisely, stringy E-polynomials) are equal. On the other hand, we show that they satisfy the prescription of Strominger, Yau, and Zaslow (which in the present case goes back to Bershadsky, Johansen, Sadov and Vafa): that a Calabi-Yau and its mirror should fiber over the same real manifold, with special Lagrangian fibers which are tori dual to each other. Our examples arise as moduli spaces of local systems on a curve with structure group SL(n); the mirror is the corresponding space with structure group PGL(n). The special Lagrangian tori come from an algebraically completely integrable Hamiltonian system: the Hitchin system.' acknowledgement: The authors are grateful for Nigel Hitchin for suggesting the similarity between [4] and [12] in 1996 and for Pierre Deligne for numerous useful comments article_processing_charge: No article_type: original author: - first_name: Tamas full_name: Hausel, Tamas id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Michael full_name: Thaddeus, Michael last_name: Thaddeus citation: ama: 'Hausel T, Thaddeus M. Examples of mirror partners arising from integrable systems. Comptes Rendus de l’Academie des Sciences - Series I: Mathematics. 2001;333(4):313-318. doi:10.1016/S0764-4442(01)02057-2' apa: 'Hausel, T., & Thaddeus, M. (2001). Examples of mirror partners arising from integrable systems. Comptes Rendus de l’Academie Des Sciences - Series I: Mathematics. Elsevier. https://doi.org/10.1016/S0764-4442(01)02057-2' chicago: 'Hausel, Tamás, and Michael Thaddeus. “Examples of Mirror Partners Arising from Integrable Systems.” Comptes Rendus de l’Academie Des Sciences - Series I: Mathematics. Elsevier, 2001. https://doi.org/10.1016/S0764-4442(01)02057-2.' ieee: 'T. Hausel and M. Thaddeus, “Examples of mirror partners arising from integrable systems,” Comptes Rendus de l’Academie des Sciences - Series I: Mathematics, vol. 333, no. 4. Elsevier, pp. 313–318, 2001.' ista: 'Hausel T, Thaddeus M. 2001. Examples of mirror partners arising from integrable systems. Comptes Rendus de l’Academie des Sciences - Series I: Mathematics. 333(4), 313–318.' mla: 'Hausel, Tamás, and Michael Thaddeus. “Examples of Mirror Partners Arising from Integrable Systems.” Comptes Rendus de l’Academie Des Sciences - Series I: Mathematics, vol. 333, no. 4, Elsevier, 2001, pp. 313–18, doi:10.1016/S0764-4442(01)02057-2.' short: 'T. Hausel, M. Thaddeus, Comptes Rendus de l’Academie Des Sciences - Series I: Mathematics 333 (2001) 313–318.' date_created: 2018-12-11T11:52:06Z date_published: 2001-08-15T00:00:00Z date_updated: 2023-05-31T09:57:48Z day: '15' doi: 10.1016/S0764-4442(01)02057-2 extern: '1' external_id: arxiv: - math/0106140 intvolume: ' 333' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/math/0106140 month: '08' oa: 1 oa_version: Preprint page: 313 - 318 publication: 'Comptes Rendus de l''Academie des Sciences - Series I: Mathematics' publication_identifier: issn: - 0764-4442 publication_status: published publisher: Elsevier publist_id: '5742' quality_controlled: '1' scopus_import: '1' status: public title: Examples of mirror partners arising from integrable systems type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 333 year: '2001' ... --- _id: '1453' abstract: - lang: eng text: In this Letter we exhibit a one-parameter family of new Taub-NUT instantons parameterized by a half-line. The endpoint of the half-line will be the reducible Yang-Mills instanton corresponding to the Eguchi-Hanson-Gibbons L2 harmonic 2-form, while at an inner point we recover the Pope-Yuille instanton constructed as a projection of the Levi-Civitá connection onto the positive su(2)+ ⊂ so(4) subalgebra. Our method imitates the Jackiw-Nohl-Rebbi construction originally designed for flat R4. That is we find a one-parameter family of harmonic functions on the Taub-NUT space with a point singularity, rescale the metric and project the obtained Levi-Civitá connection onto the other negative su(2)- ⊂ so(4) part. Our solutions will possess the full U(2) symmetry, and thus provide more solutions to the recently proposed U(2) symmetric ansatz of Kim and Yoon. acknowledgement: We would like to acknowledge the financial support provided by the Miller Institute of Basic Research in Science, the Japan Society for the Promotion of Science, grant No. P99736 and the partial support by OTKA grant No. T032478. article_processing_charge: No article_type: original author: - first_name: Gábor full_name: Etesi, Gábor last_name: Etesi - first_name: Tamas full_name: Hausel, Tamas id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel citation: ama: 'Etesi G, Hausel T. Geometric construction of new Yang-Mills instantons over Taub-NUT space. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics. 2001;514(1-2):189-199. doi:10.1016/S0370-2693(01)00821-8' apa: 'Etesi, G., & Hausel, T. (2001). Geometric construction of new Yang-Mills instantons over Taub-NUT space. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics. Elsevier. https://doi.org/10.1016/S0370-2693(01)00821-8' chicago: 'Etesi, Gábor, and Tamás Hausel. “Geometric Construction of New Yang-Mills Instantons over Taub-NUT Space.” Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics. Elsevier, 2001. https://doi.org/10.1016/S0370-2693(01)00821-8.' ieee: 'G. Etesi and T. Hausel, “Geometric construction of new Yang-Mills instantons over Taub-NUT space,” Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, vol. 514, no. 1–2. Elsevier, pp. 189–199, 2001.' ista: 'Etesi G, Hausel T. 2001. Geometric construction of new Yang-Mills instantons over Taub-NUT space. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics. 514(1–2), 189–199.' mla: 'Etesi, Gábor, and Tamás Hausel. “Geometric Construction of New Yang-Mills Instantons over Taub-NUT Space.” Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, vol. 514, no. 1–2, Elsevier, 2001, pp. 189–99, doi:10.1016/S0370-2693(01)00821-8.' short: 'G. Etesi, T. Hausel, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 514 (2001) 189–199.' date_created: 2018-12-11T11:52:07Z date_published: 2001-08-09T00:00:00Z date_updated: 2023-05-31T11:51:37Z day: '09' doi: 10.1016/S0370-2693(01)00821-8 extern: '1' external_id: arxiv: - hep-th/0105118 intvolume: ' 514' issue: 1-2 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/hep-th/0105118 month: '08' oa: 1 oa_version: Preprint page: 189 - 199 publication: 'Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics' publication_identifier: issn: - 0370-2693 publication_status: published publisher: Elsevier publist_id: '5743' quality_controlled: '1' scopus_import: '1' status: public title: Geometric construction of new Yang-Mills instantons over Taub-NUT space type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 514 year: '2001' ... --- _id: '1454' abstract: - lang: eng text: We address the problem of finding Abelian instantons of finite energy on the Euclidean Schwarzschild manifold. This amounts to construct self-dual L2 harmonic 2-forms on the space. Gibbons found a non-topological L2 harmonic form in the Taub-NUT metric, leading to Abelian instantons with continuous energy. We imitate his construction in the case of the Euclidean Schwarzschild manifold and find a non-topological self-dual L2 harmonic 2-form on it. We show how this gives rise to Abelian instantons and identify them with SU(2)-instantons of Pontryagin number 2n2 found by Charap and Duff in 1977. Using results of Dodziuk and Hitchin we also calculate the full L2 harmonic space for the Euclidean Schwarzschild manifold. acknowledgement: The work in this paper was done when Tamás Hausel visited the Yukawa Institute of Kyoto University in February 2000. We are grateful for Prof. G.W. Gibbons for insightful discussions and Prof. H. Kodama and the Yukawa Institute for the invitation and hospitality. article_processing_charge: No article_type: original author: - first_name: Gábor full_name: Etesi, Gábor last_name: Etesi - first_name: Tamas full_name: Hausel, Tamas id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel citation: ama: Etesi G, Hausel T. Geometric interpretation of Schwarzschild instantons. Journal of Geometry and Physics. 2001;37(1-2):126-136. doi:10.1016/S0393-0440(00)00040-1 apa: Etesi, G., & Hausel, T. (2001). Geometric interpretation of Schwarzschild instantons. Journal of Geometry and Physics. Elsevier. https://doi.org/10.1016/S0393-0440(00)00040-1 chicago: Etesi, Gábor, and Tamás Hausel. “Geometric Interpretation of Schwarzschild Instantons.” Journal of Geometry and Physics. Elsevier, 2001. https://doi.org/10.1016/S0393-0440(00)00040-1. ieee: G. Etesi and T. Hausel, “Geometric interpretation of Schwarzschild instantons,” Journal of Geometry and Physics, vol. 37, no. 1–2. Elsevier, pp. 126–136, 2001. ista: Etesi G, Hausel T. 2001. Geometric interpretation of Schwarzschild instantons. Journal of Geometry and Physics. 37(1–2), 126–136. mla: Etesi, Gábor, and Tamás Hausel. “Geometric Interpretation of Schwarzschild Instantons.” Journal of Geometry and Physics, vol. 37, no. 1–2, Elsevier, 2001, pp. 126–36, doi:10.1016/S0393-0440(00)00040-1. short: G. Etesi, T. Hausel, Journal of Geometry and Physics 37 (2001) 126–136. date_created: 2018-12-11T11:52:07Z date_published: 2001-01-01T00:00:00Z date_updated: 2023-05-31T12:08:45Z day: '01' doi: 10.1016/S0393-0440(00)00040-1 extern: '1' external_id: arxiv: - hep-th/0003239 intvolume: ' 37' issue: 1-2 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/hep-th/0003239 month: '01' oa: 1 oa_version: Preprint page: 126 - 136 publication: Journal of Geometry and Physics publication_identifier: issn: - 0393-0440 publication_status: published publisher: Elsevier publist_id: '5744' quality_controlled: '1' scopus_import: '1' status: public title: Geometric interpretation of Schwarzschild instantons type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 37 year: '2001' ... --- _id: '1455' abstract: - lang: eng text: First, a special case of Knaster's problem is proved implying that each symmetric convex body in ℝ3 admits an inscribed cube. It is deduced from a theorem in equivariant topology, which says that there is no S4 - equivariant map from SO(3) to S2, where S4 acts on SO(3) on the right as the rotation group of the cube, and on S2 on the right as the symmetry group of the regular tetrahedron. Some generalizations are also given. Second, it is shown how the above non-existence theorem yields Makeev's conjecture in ℝ3 that each set in ℝ3 of diameter 1 can be covered by a rhombic dodecahedron, which has distance 1 between its opposite faces. This reveals an unexpected connection between inscribing cubes into symmetric bodies and covering sets by rhombic dodecahedra. Finally, a possible application of our second theorem to the Borsuk problem in ℝ3 is pointed out. acknowledgement: The research of the first author was partially supported by Trinity College, Cambridge, and that of all the authors by grants 23444, T-030012 and A 046/96, respectively, from the Hungarian National Foundation for Scientific Research. article_processing_charge: No article_type: original author: - first_name: Tamas full_name: Hausel, Tamas id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Endre full_name: Makai, Endre last_name: Makai - first_name: András full_name: Szücs, András last_name: Szücs citation: ama: Hausel T, Makai E, Szücs A. Inscribing cubes and covering by rhombic dodecahedra via equivariant topology. Mathematika. 2000;47(1-2):371-397. doi:10.1112/S0025579300015965 apa: Hausel, T., Makai, E., & Szücs, A. (2000). Inscribing cubes and covering by rhombic dodecahedra via equivariant topology. Mathematika. University College London. https://doi.org/10.1112/S0025579300015965 chicago: Hausel, Tamás, Endre Makai, and András Szücs. “Inscribing Cubes and Covering by Rhombic Dodecahedra via Equivariant Topology.” Mathematika. University College London, 2000. https://doi.org/10.1112/S0025579300015965. ieee: T. Hausel, E. Makai, and A. Szücs, “Inscribing cubes and covering by rhombic dodecahedra via equivariant topology,” Mathematika, vol. 47, no. 1–2. University College London, pp. 371–397, 2000. ista: Hausel T, Makai E, Szücs A. 2000. Inscribing cubes and covering by rhombic dodecahedra via equivariant topology. Mathematika. 47(1–2), 371–397. mla: Hausel, Tamás, et al. “Inscribing Cubes and Covering by Rhombic Dodecahedra via Equivariant Topology.” Mathematika, vol. 47, no. 1–2, University College London, 2000, pp. 371–97, doi:10.1112/S0025579300015965. short: T. Hausel, E. Makai, A. Szücs, Mathematika 47 (2000) 371–397. date_created: 2018-12-11T11:52:07Z date_published: 2000-06-01T00:00:00Z date_updated: 2023-05-08T08:56:46Z day: '01' doi: 10.1112/S0025579300015965 extern: '1' external_id: arxiv: - math/9906066 intvolume: ' 47' issue: 1-2 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/math/9906066 month: '06' oa: 1 oa_version: Preprint page: 371 - 397 publication: Mathematika publication_identifier: issn: - 0025-5793 publication_status: published publisher: University College London publist_id: '5745' quality_controlled: '1' scopus_import: '1' status: public title: Inscribing cubes and covering by rhombic dodecahedra via equivariant topology type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 47 year: '2000' ... --- _id: '1450' abstract: - lang: eng text: In this paper we consider the topological side of a problem which is the analogue of Sen's S-duality testing conjecture for Hitchin's moduli space M of rank 2 stable Higgs bundles of fixed determinant of odd degree over a Riemann surface ∑. We prove that all intersection numbers in the compactly supported cohomology of M vanish, i.e. "there are no topological L2 harmonic forms on M". This result generalizes the well known vanishing of the Euler characteristic of the moduli space of rank 2 stable bundles N of fixed determinant of odd degree over ∑. Our proof shows that the vanishing of all intersection numbers of H* cpt(M) is given by relations analogous to the Mumford relations in the cohomology ring of N. acknowledgement: "First of all I would like to thank my supervisor Nigel Hitchin for suggesting Problem 1, and for his help and \r\n encouragement. I am grateful to Michael Thaddeus for his inspiring paper [Thai], enlightening communications and his constant interest in my work. I am also indebted to Manfred Lehn for the idea of the proof of Theorem 6.2. I have found\r\nconversations with Michael Atiyah, Frances Kirwan and Graeme Segal very stimulating. I thank the Mathematical Institute and St. Catherine's College, Oxford for their hospitality during the preparation of this work. Finally I thank Trinity College, Cambridge for financial support." article_processing_charge: No article_type: original author: - first_name: Tamas full_name: Hausel, Tamas id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel citation: ama: Hausel T. Vanishing of intersection numbers on the moduli space of Higgs bundles. Advances in Theoretical and Mathematical Physics. 1998;2(5):1011-1040. doi:10.4310/ATMP.1998.v2.n5.a3 apa: Hausel, T. (1998). Vanishing of intersection numbers on the moduli space of Higgs bundles. Advances in Theoretical and Mathematical Physics. International Press. https://doi.org/10.4310/ATMP.1998.v2.n5.a3 chicago: Hausel, Tamás. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.” Advances in Theoretical and Mathematical Physics. International Press, 1998. https://doi.org/10.4310/ATMP.1998.v2.n5.a3. ieee: T. Hausel, “Vanishing of intersection numbers on the moduli space of Higgs bundles,” Advances in Theoretical and Mathematical Physics, vol. 2, no. 5. International Press, pp. 1011–1040, 1998. ista: Hausel T. 1998. Vanishing of intersection numbers on the moduli space of Higgs bundles. Advances in Theoretical and Mathematical Physics. 2(5), 1011–1040. mla: Hausel, Tamás. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.” Advances in Theoretical and Mathematical Physics, vol. 2, no. 5, International Press, 1998, pp. 1011–40, doi:10.4310/ATMP.1998.v2.n5.a3. short: T. Hausel, Advances in Theoretical and Mathematical Physics 2 (1998) 1011–1040. date_created: 2018-12-11T11:52:06Z date_published: 1998-09-01T00:00:00Z date_updated: 2022-09-01T14:09:49Z day: '01' doi: 10.4310/ATMP.1998.v2.n5.a3 extern: '1' external_id: arxiv: - math/9805071 intvolume: ' 2' issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/math/9805071 month: '09' oa: 1 oa_version: Preprint page: 1011 - 1040 publication: Advances in Theoretical and Mathematical Physics publication_identifier: issn: - 1095-0761 publication_status: published publisher: International Press publist_id: '5747' quality_controlled: '1' scopus_import: '1' status: public title: Vanishing of intersection numbers on the moduli space of Higgs bundles type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 2 year: '1998' ... --- _id: '1449' abstract: - lang: eng text: In this paper we consider a canonical compactification of M, the moduli space of stable Higgs bundles with fixed determinant of odd degree over a Riemann surface Σ, producing a projective variety M̄ = M ∪ Z. We give a detailed study of the spaces M̄, Z and M. In doing so we reprove some assertions of Laumon and Thaddeus on the nilpotent cone. article_processing_charge: No article_type: original author: - first_name: Tamas full_name: Hausel, Tamas id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel citation: ama: Hausel T. Compactification of moduli of Higgs bundles. Journal fur die Reine und Angewandte Mathematik. 1998;1998(503):169-192. doi:10.1515/crll.1998.096 apa: Hausel, T. (1998). Compactification of moduli of Higgs bundles. Journal Fur Die Reine Und Angewandte Mathematik. Walter de Gruyter. https://doi.org/10.1515/crll.1998.096 chicago: Hausel, Tamás. “Compactification of Moduli of Higgs Bundles.” Journal Fur Die Reine Und Angewandte Mathematik. Walter de Gruyter, 1998. https://doi.org/10.1515/crll.1998.096. ieee: T. Hausel, “Compactification of moduli of Higgs bundles,” Journal fur die Reine und Angewandte Mathematik, vol. 1998, no. 503. Walter de Gruyter, pp. 169–192, 1998. ista: Hausel T. 1998. Compactification of moduli of Higgs bundles. Journal fur die Reine und Angewandte Mathematik. 1998(503), 169–192. mla: Hausel, Tamás. “Compactification of Moduli of Higgs Bundles.” Journal Fur Die Reine Und Angewandte Mathematik, vol. 1998, no. 503, Walter de Gruyter, 1998, pp. 169–92, doi:10.1515/crll.1998.096. short: T. Hausel, Journal Fur Die Reine Und Angewandte Mathematik 1998 (1998) 169–192. date_created: 2018-12-11T11:52:05Z date_published: 1998-10-01T00:00:00Z date_updated: 2022-09-01T13:51:07Z day: '01' doi: 10.1515/crll.1998.096 extern: '1' external_id: arxiv: - math/9804083 intvolume: ' 1998' issue: '503' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/math/9804083 month: '10' oa: 1 oa_version: Preprint page: 169 - 192 publication: Journal fur die Reine und Angewandte Mathematik publication_identifier: issn: - 1435-5345 publication_status: published publisher: Walter de Gruyter publist_id: '5746' quality_controlled: '1' scopus_import: '1' status: public title: Compactification of moduli of Higgs bundles type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 1998 year: '1998' ...