[{"publication_identifier":{"issn":["1095-0761"],"eissn":["1095-0753"]},"publication":"Advances in Theoretical and Mathematical Physics","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","OA_type":"green","OA_place":"repository","date_published":"2024-10-30T00:00:00Z","ec_funded":1,"title":"Out-of-time-ordered correlators for Wigner matrices","oa_version":"Preprint","quality_controlled":"1","type":"journal_article","date_created":"2024-12-15T23:01:51Z","day":"30","scopus_import":"1","article_type":"original","arxiv":1,"corr_author":"1","citation":{"ieee":"G. Cipolloni, L. Erdös, and S. J. Henheik, “Out-of-time-ordered correlators for Wigner matrices,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 28, no. 6. International Press of Boston, pp. 2025–2083, 2024.","ista":"Cipolloni G, Erdös L, Henheik SJ. 2024. Out-of-time-ordered correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics. 28(6), 2025–2083.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, Advances in Theoretical and Mathematical Physics 28 (2024) 2025–2083.","apa":"Cipolloni, G., Erdös, L., &#38; Henheik, S. J. (2024). Out-of-time-ordered correlators for Wigner matrices. <i>Advances in Theoretical and Mathematical Physics</i>. International Press of Boston. <a href=\"https://doi.org/10.4310/ATMP.241031013250\">https://doi.org/10.4310/ATMP.241031013250</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Out-of-Time-Ordered Correlators for Wigner Matrices.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press of Boston, 2024. <a href=\"https://doi.org/10.4310/ATMP.241031013250\">https://doi.org/10.4310/ATMP.241031013250</a>.","mla":"Cipolloni, Giorgio, et al. “Out-of-Time-Ordered Correlators for Wigner Matrices.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 28, no. 6, International Press of Boston, 2024, pp. 2025–83, doi:<a href=\"https://doi.org/10.4310/ATMP.241031013250\">10.4310/ATMP.241031013250</a>.","ama":"Cipolloni G, Erdös L, Henheik SJ. Out-of-time-ordered correlators for Wigner matrices. <i>Advances in Theoretical and Mathematical Physics</i>. 2024;28(6):2025-2083. doi:<a href=\"https://doi.org/10.4310/ATMP.241031013250\">10.4310/ATMP.241031013250</a>"},"project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"}]},"acknowledgement":"LE and JH were supported by the ERC Advanced Grant łRMTBeyondž No. 101020331","issue":"6","_id":"18656","oa":1,"intvolume":"        28","language":[{"iso":"eng"}],"das_tickbox":"1","external_id":{"arxiv":["2402.17609"]},"article_processing_charge":"No","abstract":[{"lang":"eng","text":"We consider the time evolution of the out-of-time-ordered correlator (OTOC) of two general observables \r\n and \r\n in a mean field chaotic quantum system described by a random Wigner matrix as its Hamiltonian. We rigorously identify three time regimes separated by the physically relevant scrambling and relaxation times. The main feature of our analysis is that we express the error terms in the optimal Schatten (tracial) norms of the observables, allowing us to track the exact dependence of the errors on their rank. In particular, for significantly overlapping observables with low rank the OTOC is shown to exhibit a significant local maximum at the scrambling time, a feature that may not have been noticed in the physics literature before. Our main tool is a novel multi-resolvent local law with Schatten norms that unifies and improves previous local laws involving either the much cruder operator norm (cf. [10]) or the Hilbert-Schmidt norm (cf. [11])."}],"department":[{"_id":"LaEr"}],"doi":"10.4310/ATMP.241031013250","author":[{"last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","last_name":"Henheik","full_name":"Henheik, Sven Joscha"}],"page":"2025-2083","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2402.17609"}],"fulldoi":"https://doi.org/10.4310/ATMP.241031013250","publisher":"International Press of Boston","month":"10","year":"2024","volume":28,"date_updated":"2026-07-29T13:18:17Z"},{"ec_funded":1,"oa_version":"Submitted Version","title":"Bogoliubov correction to the mean-field dynamics of interacting bosons","date_published":"2017-01-01T00:00:00Z","quality_controlled":"1","publication_identifier":{"issn":["1095-0761"]},"publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Advances in Theoretical and Mathematical Physics","status":"public","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"call_identifier":"FWF","_id":"25C878CE-B435-11E9-9278-68D0E5697425","grant_number":"P27533_N27","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems"}],"citation":{"apa":"Nam, P., &#38; Napiórkowski, M. M. (2017). Bogoliubov correction to the mean-field dynamics of interacting bosons. <i>Advances in Theoretical and Mathematical Physics</i>. International Press of Boston. <a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a4\">https://doi.org/10.4310/ATMP.2017.v21.n3.a4</a>","short":"P. Nam, M.M. Napiórkowski, Advances in Theoretical and Mathematical Physics 21 (2017) 683–738.","ista":"Nam P, Napiórkowski MM. 2017. Bogoliubov correction to the mean-field dynamics of interacting bosons. Advances in Theoretical and Mathematical Physics. 21(3), 683–738.","ieee":"P. Nam and M. M. Napiórkowski, “Bogoliubov correction to the mean-field dynamics of interacting bosons,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 21, no. 3. International Press of Boston, pp. 683–738, 2017.","ama":"Nam P, Napiórkowski MM. Bogoliubov correction to the mean-field dynamics of interacting bosons. <i>Advances in Theoretical and Mathematical Physics</i>. 2017;21(3):683-738. doi:<a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a4\">10.4310/ATMP.2017.v21.n3.a4</a>","mla":"Nam, Phan, and Marcin M. Napiórkowski. “Bogoliubov Correction to the Mean-Field Dynamics of Interacting Bosons.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 21, no. 3, International Press of Boston, 2017, pp. 683–738, doi:<a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a4\">10.4310/ATMP.2017.v21.n3.a4</a>.","chicago":"Nam, Phan, and Marcin M Napiórkowski. “Bogoliubov Correction to the Mean-Field Dynamics of Interacting Bosons.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press of Boston, 2017. <a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a4\">https://doi.org/10.4310/ATMP.2017.v21.n3.a4</a>."},"type":"journal_article","isi":1,"date_created":"2018-12-11T11:46:43Z","day":"01","scopus_import":"1","arxiv":1,"doi":"10.4310/ATMP.2017.v21.n3.a4","article_processing_charge":"No","department":[{"_id":"RoSe"}],"abstract":[{"text":"We consider the dynamics of a large quantum system of N identical bosons in 3D interacting via a two-body potential of the form N3β-1w(Nβ(x - y)). For fixed 0 = β &lt; 1/3 and large N, we obtain a norm approximation to the many-body evolution in the Nparticle Hilbert space. The leading order behaviour of the dynamics is determined by Hartree theory while the second order is given by Bogoliubov theory.","lang":"eng"}],"author":[{"last_name":"Nam","id":"404092F4-F248-11E8-B48F-1D18A9856A87","first_name":"Phan","full_name":"Nam, Phan"},{"last_name":"Napiórkowski","first_name":"Marcin M","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","full_name":"Napiórkowski, Marcin M"}],"page":"683 - 738","_id":"484","issue":"3","language":[{"iso":"eng"}],"das_tickbox":"1","external_id":{"isi":["000409382300004"],"arxiv":["1509.04631"]},"publist_id":"7336","oa":1,"intvolume":"        21","date_updated":"2026-07-06T13:34:16Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1509.04631"}],"publisher":"International Press of Boston","year":"2017","month":"01","volume":21,"fulldoi":"https://doi.org/10.4310/ATMP.2017.v21.n3.a4"},{"date_updated":"2026-07-06T13:35:08Z","month":"08","publisher":"International Press of Boston","year":"2017","volume":21,"fulldoi":"https://doi.org/10.4310/ATMP.2017.v21.n3.a5","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1602.02312"}],"author":[{"full_name":"Bourgade, Paul","last_name":"Bourgade","first_name":"Paul"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"full_name":"Yau, Horng","first_name":"Horng","last_name":"Yau"},{"last_name":"Yin","first_name":"Jun","full_name":"Yin, Jun"}],"page":"739 - 800","doi":"10.4310/ATMP.2017.v21.n3.a5","article_processing_charge":"No","department":[{"_id":"LaEr"}],"abstract":[{"lang":"eng","text":"We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices."}],"language":[{"iso":"eng"}],"das_tickbox":"1","external_id":{"arxiv":["1602.02312"],"isi":["000409382300005"]},"publist_id":"7337","oa":1,"intvolume":"        21","_id":"483","issue":"3","project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"citation":{"ista":"Bourgade P, Erdös L, Yau H, Yin J. 2017. Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. 21(3), 739–800.","ieee":"P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random band matrices,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 21, no. 3. International Press of Boston, pp. 739–800, 2017.","apa":"Bourgade, P., Erdös, L., Yau, H., &#38; Yin, J. (2017). Universality for a class of random band matrices. <i>Advances in Theoretical and Mathematical Physics</i>. International Press of Boston. <a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a5\">https://doi.org/10.4310/ATMP.2017.v21.n3.a5</a>","short":"P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical Physics 21 (2017) 739–800.","mla":"Bourgade, Paul, et al. “Universality for a Class of Random Band Matrices.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 21, no. 3, International Press of Boston, 2017, pp. 739–800, doi:<a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a5\">10.4310/ATMP.2017.v21.n3.a5</a>.","chicago":"Bourgade, Paul, László Erdös, Horng Yau, and Jun Yin. “Universality for a Class of Random Band Matrices.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press of Boston, 2017. <a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a5\">https://doi.org/10.4310/ATMP.2017.v21.n3.a5</a>.","ama":"Bourgade P, Erdös L, Yau H, Yin J. Universality for a class of random band matrices. <i>Advances in Theoretical and Mathematical Physics</i>. 2017;21(3):739-800. doi:<a href=\"https://doi.org/10.4310/ATMP.2017.v21.n3.a5\">10.4310/ATMP.2017.v21.n3.a5</a>"},"isi":1,"scopus_import":"1","date_created":"2018-12-11T11:46:43Z","day":"25","arxiv":1,"type":"journal_article","quality_controlled":"1","ec_funded":1,"title":"Universality for a class of random band matrices","oa_version":"Submitted Version","date_published":"2017-08-25T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Advances in Theoretical and Mathematical Physics","publication_status":"published","status":"public","publication_identifier":{"issn":["1095-0761"]}},{"acknowledgement":"We are grateful to Elliott Lieb for helpful discussions. C.H. was supported by a Marie Curie Fellowship of the European Community programme “Improving Human Research Potential and the Socioeconomic Knowledge Base” under contract number HPMFCT-2000-00660 and by the Deutsche Forschungsgemeinschaft, and acknowledges kind hospitality at Princeton University, where part of this work was done. R.S. was supported by the Austrian Science Fund in the form of an Erwin Schrödinger Fellowship.\r\n","citation":{"apa":"Hainzl, C., &#38; Seiringer, R. (2002). Mass renormalization and energy level shift in non-relativistic QED. <i>Advances in Theoretical and Mathematical Physics</i>. International Press. <a href=\"https://doi.org/10.4310/ATMP.2002.v6.n5.a3\">https://doi.org/10.4310/ATMP.2002.v6.n5.a3</a>","short":"C. Hainzl, R. Seiringer, Advances in Theoretical and Mathematical Physics 6 (2002) 847–871.","ista":"Hainzl C, Seiringer R. 2002. Mass renormalization and energy level shift in non-relativistic QED. Advances in Theoretical and Mathematical Physics. 6(5), 847–871.","ieee":"C. Hainzl and R. Seiringer, “Mass renormalization and energy level shift in non-relativistic QED,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 6, no. 5. International Press, pp. 847–871, 2002.","ama":"Hainzl C, Seiringer R. Mass renormalization and energy level shift in non-relativistic QED. <i>Advances in Theoretical and Mathematical Physics</i>. 2002;6(5):847-871. doi:<a href=\"https://doi.org/10.4310/ATMP.2002.v6.n5.a3\">10.4310/ATMP.2002.v6.n5.a3</a>","mla":"Hainzl, Christian, and Robert Seiringer. “Mass Renormalization and Energy Level Shift in Non-Relativistic QED.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 6, no. 5, International Press, 2002, pp. 847–71, doi:<a href=\"https://doi.org/10.4310/ATMP.2002.v6.n5.a3\">10.4310/ATMP.2002.v6.n5.a3</a>.","chicago":"Hainzl, Christian, and Robert Seiringer. “Mass Renormalization and Energy Level Shift in Non-Relativistic QED.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press, 2002. <a href=\"https://doi.org/10.4310/ATMP.2002.v6.n5.a3\">https://doi.org/10.4310/ATMP.2002.v6.n5.a3</a>."},"article_type":"original","arxiv":1,"scopus_import":"1","day":"01","date_created":"2018-12-11T11:57:09Z","type":"journal_article","quality_controlled":"1","date_published":"2002-09-01T00:00:00Z","oa_version":"Published Version","title":"Mass renormalization and energy level shift in non-relativistic QED","status":"public","publication":"Advances in Theoretical and Mathematical Physics","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","publication_identifier":{"issn":["1095-0761"]},"date_updated":"2023-07-26T08:29:28Z","fulldoi":"https://doi.org/10.4310/ATMP.2002.v6.n5.a3","volume":6,"publisher":"International Press","month":"09","year":"2002","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0205044"}],"page":"847 - 871","author":[{"full_name":"Hainzl, Christian","first_name":"Christian","last_name":"Hainzl"},{"last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert"}],"abstract":[{"lang":"eng","text":"Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we calculate the binding energy of an electron in the field of a nucleus of charge Z and in presence of the quantized radiation field. We consider the case of small coupling constant α, but fixed Zα and ultraviolet cut-off Λ. We prove that after renormalizing the mass the binding energy has, to leading order in α, a finite limit as Λ goes to infinity; i.e., the cut-off can be removed. The expression for the ground state energy shift thus obtained agrees with Bethe's formula for small values of Zα, but shows a different behavior for bigger values."}],"article_processing_charge":"No","doi":"10.4310/ATMP.2002.v6.n5.a3","extern":"1","intvolume":"         6","oa":1,"publist_id":"4574","external_id":{"arxiv":["math-ph/0205044v3"]},"language":[{"iso":"eng"}],"_id":"2350","issue":"5"},{"abstract":[{"text":"We consider the time evolution of N bosonic particles interacting via a mean field Coulomb potential. Suppose the initial state is a product wavefunction. We show that at any finite time the correlation functions factorize in the limit N → ∞. Furthermore, the limiting one particle density matrix satisfies the nonlinear Hartree equation. The key ingredients are the uniqueness of the BBGKY hierarchy for the correlation functions and a new apriori estimate for the many-body Schrödinger equations.","lang":"eng"}],"article_processing_charge":"No","extern":"1","doi":"10.48550/arXiv.math-ph/0111042","page":"1169 - 1205","author":[{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Yau, Horng","last_name":"Yau","first_name":"Horng"}],"issue":"6","_id":"2736","intvolume":"         5","oa":1,"publist_id":"4156","external_id":{"arxiv":["math-ph/0111042"]},"language":[{"iso":"eng"}],"date_updated":"2023-05-16T12:12:41Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0111042"}],"fulldoi":"https://doi.org/10.48550/arXiv.math-ph/0111042","volume":5,"publisher":"International Press","month":"11","year":"2001","date_published":"2001-11-01T00:00:00Z","title":"Derivation of the nonlinear Schrödinger equation from a many body Coulomb system","oa_version":"Published Version","quality_controlled":"1","publication_identifier":{"issn":["1095-0761"]},"status":"public","publication_status":"published","publication":"Advances in Theoretical and Mathematical Physics","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"mla":"Erdös, László, and Horng Yau. “Derivation of the Nonlinear Schrödinger Equation from a Many Body Coulomb System.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 5, no. 6, International Press, 2001, pp. 1169–205, doi:<a href=\"https://doi.org/10.48550/arXiv.math-ph/0111042\">10.48550/arXiv.math-ph/0111042</a>.","chicago":"Erdös, László, and Horng Yau. “Derivation of the Nonlinear Schrödinger Equation from a Many Body Coulomb System.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press, 2001. <a href=\"https://doi.org/10.48550/arXiv.math-ph/0111042\">https://doi.org/10.48550/arXiv.math-ph/0111042</a>.","ama":"Erdös L, Yau H. Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. <i>Advances in Theoretical and Mathematical Physics</i>. 2001;5(6):1169-1205. doi:<a href=\"https://doi.org/10.48550/arXiv.math-ph/0111042\">10.48550/arXiv.math-ph/0111042</a>","ista":"Erdös L, Yau H. 2001. Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. Advances in Theoretical and Mathematical Physics. 5(6), 1169–1205.","ieee":"L. Erdös and H. Yau, “Derivation of the nonlinear Schrödinger equation from a many body Coulomb system,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 5, no. 6. International Press, pp. 1169–1205, 2001.","apa":"Erdös, L., &#38; Yau, H. (2001). Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. <i>Advances in Theoretical and Mathematical Physics</i>. International Press. <a href=\"https://doi.org/10.48550/arXiv.math-ph/0111042\">https://doi.org/10.48550/arXiv.math-ph/0111042</a>","short":"L. Erdös, H. Yau, Advances in Theoretical and Mathematical Physics 5 (2001) 1169–1205."},"type":"journal_article","arxiv":1,"article_type":"original","date_created":"2018-12-11T11:59:20Z","day":"01","scopus_import":"1"},{"_id":"1450","issue":"5","external_id":{"arxiv":["math/9805071"]},"language":[{"iso":"eng"}],"intvolume":"         2","oa":1,"publist_id":"5747","doi":"10.4310/ATMP.1998.v2.n5.a3","extern":"1","abstract":[{"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. &quot;there are no topological L2 harmonic forms on M&quot;. 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.","lang":"eng"}],"article_processing_charge":"No","page":"1011 - 1040","author":[{"last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamas","full_name":"Hausel, Tamas"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math/9805071"}],"volume":2,"publisher":"International Press","month":"09","year":"1998","fulldoi":"https://doi.org/10.4310/ATMP.1998.v2.n5.a3","date_updated":"2022-09-01T14:09:49Z","publication_identifier":{"issn":["1095-0761"]},"status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","publication":"Advances in Theoretical and Mathematical Physics","oa_version":"Preprint","title":"Vanishing of intersection numbers on the moduli space of Higgs bundles","date_published":"1998-09-01T00:00:00Z","quality_controlled":"1","type":"journal_article","arxiv":1,"article_type":"original","scopus_import":"1","day":"01","date_created":"2018-12-11T11:52:06Z","citation":{"mla":"Hausel, Tamás. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 2, no. 5, International Press, 1998, pp. 1011–40, doi:<a href=\"https://doi.org/10.4310/ATMP.1998.v2.n5.a3\">10.4310/ATMP.1998.v2.n5.a3</a>.","chicago":"Hausel, Tamás. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press, 1998. <a href=\"https://doi.org/10.4310/ATMP.1998.v2.n5.a3\">https://doi.org/10.4310/ATMP.1998.v2.n5.a3</a>.","ama":"Hausel T. Vanishing of intersection numbers on the moduli space of Higgs bundles. <i>Advances in Theoretical and Mathematical Physics</i>. 1998;2(5):1011-1040. doi:<a href=\"https://doi.org/10.4310/ATMP.1998.v2.n5.a3\">10.4310/ATMP.1998.v2.n5.a3</a>","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.","ieee":"T. Hausel, “Vanishing of intersection numbers on the moduli space of Higgs bundles,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 2, no. 5. International Press, pp. 1011–1040, 1998.","apa":"Hausel, T. (1998). Vanishing of intersection numbers on the moduli space of Higgs bundles. <i>Advances in Theoretical and Mathematical Physics</i>. International Press. <a href=\"https://doi.org/10.4310/ATMP.1998.v2.n5.a3\">https://doi.org/10.4310/ATMP.1998.v2.n5.a3</a>","short":"T. Hausel, Advances in Theoretical and Mathematical Physics 2 (1998) 1011–1040."},"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."}]