[{"intvolume":"       169","abstract":[{"lang":"eng","text":"An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface x1y21+⋯+x4y24=0 in ℙ3×ℙ3. This confirms the modified Manin conjecture for this variety, in which the removal of a thin set of rational points is allowed."}],"publication_identifier":{"issn":["0012-7094"]},"publication_status":"published","oa_version":"Preprint","title":"Density of rational points on a quadric bundle in ℙ3×ℙ3","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","last_name":"Browning","first_name":"Timothy D","orcid":"0000-0002-8314-0177"},{"last_name":"Heath Brown","full_name":"Heath Brown, Roger","first_name":"Roger"}],"day":"10","article_type":"original","date_created":"2018-12-11T11:45:02Z","volume":169,"language":[{"iso":"eng"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"16","citation":{"ieee":"T. D. Browning and R. Heath Brown, “Density of rational points on a quadric bundle in ℙ3×ℙ3,” <i>Duke Mathematical Journal</i>, vol. 169, no. 16. Duke University Press, pp. 3099–3165, 2020.","short":"T.D. Browning, R. Heath Brown, Duke Mathematical Journal 169 (2020) 3099–3165.","ama":"Browning TD, Heath Brown R. Density of rational points on a quadric bundle in ℙ3×ℙ3. <i>Duke Mathematical Journal</i>. 2020;169(16):3099-3165. doi:<a href=\"https://doi.org/10.1215/00127094-2020-0031\">10.1215/00127094-2020-0031</a>","apa":"Browning, T. D., &#38; Heath Brown, R. (2020). Density of rational points on a quadric bundle in ℙ3×ℙ3. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/00127094-2020-0031\">https://doi.org/10.1215/00127094-2020-0031</a>","mla":"Browning, Timothy D., and Roger Heath Brown. “Density of Rational Points on a Quadric Bundle in ℙ3×ℙ3.” <i>Duke Mathematical Journal</i>, vol. 169, no. 16, Duke University Press, 2020, pp. 3099–165, doi:<a href=\"https://doi.org/10.1215/00127094-2020-0031\">10.1215/00127094-2020-0031</a>.","chicago":"Browning, Timothy D, and Roger Heath Brown. “Density of Rational Points on a Quadric Bundle in ℙ3×ℙ3.” <i>Duke Mathematical Journal</i>. Duke University Press, 2020. <a href=\"https://doi.org/10.1215/00127094-2020-0031\">https://doi.org/10.1215/00127094-2020-0031</a>.","ista":"Browning TD, Heath Brown R. 2020. Density of rational points on a quadric bundle in ℙ3×ℙ3. Duke Mathematical Journal. 169(16), 3099–3165."},"month":"09","arxiv":1,"department":[{"_id":"TiBr"}],"page":"3099-3165","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1805.10715"}],"publisher":"Duke University Press","doi":"10.1215/00127094-2020-0031","article_processing_charge":"No","type":"journal_article","date_updated":"2023-10-17T12:51:10Z","_id":"179","publication":"Duke Mathematical Journal","status":"public","date_published":"2020-09-10T00:00:00Z","external_id":{"isi":["000582676300002"],"arxiv":["1805.10715"]},"year":"2020","isi":1},{"year":"2017","external_id":{"arxiv":["1603.08838"]},"date_published":"2017-12-08T00:00:00Z","status":"public","publication":"Duke Mathematical Journal","extern":"1","_id":"8423","date_updated":"2021-01-12T08:19:11Z","type":"journal_article","article_processing_charge":"No","doi":"10.1215/00127094-2017-0038","publisher":"Duke University Press","main_file_link":[{"url":"https://arxiv.org/abs/1603.08838","open_access":"1"}],"quality_controlled":"1","page":"175-209","arxiv":1,"month":"12","citation":{"short":"G. Huang, V. Kaloshin, A. Sorrentino, Duke Mathematical Journal 167 (2017) 175–209.","ieee":"G. Huang, V. Kaloshin, and A. Sorrentino, “On the marked length spectrum of generic strictly convex billiard tables,” <i>Duke Mathematical Journal</i>, vol. 167, no. 1. Duke University Press, pp. 175–209, 2017.","ama":"Huang G, Kaloshin V, Sorrentino A. On the marked length spectrum of generic strictly convex billiard tables. <i>Duke Mathematical Journal</i>. 2017;167(1):175-209. doi:<a href=\"https://doi.org/10.1215/00127094-2017-0038\">10.1215/00127094-2017-0038</a>","mla":"Huang, Guan, et al. “On the Marked Length Spectrum of Generic Strictly Convex Billiard Tables.” <i>Duke Mathematical Journal</i>, vol. 167, no. 1, Duke University Press, 2017, pp. 175–209, doi:<a href=\"https://doi.org/10.1215/00127094-2017-0038\">10.1215/00127094-2017-0038</a>.","apa":"Huang, G., Kaloshin, V., &#38; Sorrentino, A. (2017). On the marked length spectrum of generic strictly convex billiard tables. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/00127094-2017-0038\">https://doi.org/10.1215/00127094-2017-0038</a>","chicago":"Huang, Guan, Vadim Kaloshin, and Alfonso Sorrentino. “On the Marked Length Spectrum of Generic Strictly Convex Billiard Tables.” <i>Duke Mathematical Journal</i>. Duke University Press, 2017. <a href=\"https://doi.org/10.1215/00127094-2017-0038\">https://doi.org/10.1215/00127094-2017-0038</a>.","ista":"Huang G, Kaloshin V, Sorrentino A. 2017. On the marked length spectrum of generic strictly convex billiard tables. Duke Mathematical Journal. 167(1), 175–209."},"issue":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"language":[{"iso":"eng"}],"volume":167,"date_created":"2020-09-17T10:42:42Z","article_type":"original","day":"08","author":[{"last_name":"Huang","full_name":"Huang, Guan","first_name":"Guan"},{"first_name":"Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","last_name":"Kaloshin"},{"full_name":"Sorrentino, Alfonso","last_name":"Sorrentino","first_name":"Alfonso"}],"oa_version":"Preprint","title":"On the marked length spectrum of generic strictly convex billiard tables","publication_identifier":{"issn":["0012-7094"]},"publication_status":"published","intvolume":"       167","abstract":[{"text":"In this paper we show that for a generic strictly convex domain, one can recover the eigendata corresponding to Aubry–Mather periodic orbits of the induced billiard map from the (maximal) marked length spectrum of the domain.","lang":"eng"}]},{"title":"Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action","oa_version":"None","publisher":"Duke University Press","author":[{"full_name":"Galante, Joseph","last_name":"Galante","first_name":"Joseph"},{"orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"}],"doi":"10.1215/00127094-1415878","day":"04","article_processing_charge":"No","article_type":"original","type":"journal_article","date_created":"2020-09-18T10:47:41Z","date_updated":"2021-01-12T08:19:45Z","volume":159,"_id":"8505","abstract":[{"text":"The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. In this paper we utilize this principle along with Aubry-Mather theory to construct (Birkhoff) regions of instability for a certain three-body problem, given by a Hamiltonian system of 2 degrees of freedom. We believe that these methods can be applied to construct instability regions for a variety of Hamiltonian systems with 2 degrees of freedom. The Hamiltonian model we consider describes dynamics of a Sun-Jupiter-comet system, and under some simplifying assumptions, we show the existence of instabilities for the orbit of the comet. In particular, we show that a comet which starts close to an orbit in the shape of an ellipse of eccentricity e=0.66 can increase in eccentricity up to e=0.96. In the sequels to this paper, we extend the result to beyond e=1 and show the existence of ejection orbits. Such orbits are initially well within the range of our solar system. This might give an indication of why most objects rotating around the Sun in our solar system have relatively low eccentricity.","lang":"eng"}],"intvolume":"       159","page":"275-327","publication_identifier":{"issn":["0012-7094"]},"publication_status":"published","quality_controlled":"1","month":"08","year":"2011","keyword":["General Mathematics"],"publication":"Duke Mathematical Journal","language":[{"iso":"eng"}],"status":"public","extern":"1","date_published":"2011-08-04T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"2","citation":{"apa":"Galante, J., &#38; Kaloshin, V. (2011). Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/00127094-1415878\">https://doi.org/10.1215/00127094-1415878</a>","mla":"Galante, Joseph, and Vadim Kaloshin. “Destruction of Invariant Curves in the Restricted Circular Planar Three-Body Problem by Using Comparison of Action.” <i>Duke Mathematical Journal</i>, vol. 159, no. 2, Duke University Press, 2011, pp. 275–327, doi:<a href=\"https://doi.org/10.1215/00127094-1415878\">10.1215/00127094-1415878</a>.","chicago":"Galante, Joseph, and Vadim Kaloshin. “Destruction of Invariant Curves in the Restricted Circular Planar Three-Body Problem by Using Comparison of Action.” <i>Duke Mathematical Journal</i>. Duke University Press, 2011. <a href=\"https://doi.org/10.1215/00127094-1415878\">https://doi.org/10.1215/00127094-1415878</a>.","ista":"Galante J, Kaloshin V. 2011. Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action. Duke Mathematical Journal. 159(2), 275–327.","ieee":"J. Galante and V. Kaloshin, “Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action,” <i>Duke Mathematical Journal</i>, vol. 159, no. 2. Duke University Press, pp. 275–327, 2011.","short":"J. Galante, V. Kaloshin, Duke Mathematical Journal 159 (2011) 275–327.","ama":"Galante J, Kaloshin V. Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action. <i>Duke Mathematical Journal</i>. 2011;159(2):275-327. doi:<a href=\"https://doi.org/10.1215/00127094-1415878\">10.1215/00127094-1415878</a>"}},{"publisher":"Duke University Press","doi":"10.1215/S0012-7094-99-09604-7","article_processing_charge":"No","type":"journal_article","date_updated":"2023-02-20T07:34:48Z","_id":"2730","page":"127 - 173","quality_controlled":"1","year":"1999","publist_id":"4162","publication":"Duke Mathematical Journal","status":"public","extern":"1","acknowledgement":"The first author gratefully acknowledges financial support from the Eidgen6ssiche Technische Hochschule, Forschungsinstitut für Mathematik, Zürich, where this work was started. He is also grateful for the hospitality and support of Aarhus University during his visits there.","date_published":"1999-01-15T00:00:00Z","title":"Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate","oa_version":"None","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603"},{"full_name":"Solovej, Jan","last_name":"Solovej","first_name":"Jan"}],"scopus_import":"1","day":"15","article_type":"original","date_created":"2018-12-11T11:59:18Z","volume":96,"abstract":[{"text":"We give the leading order semiclassical asymptotics for the sum of the negative eigenvalues of the Pauli operator (in dimension two and three) with a strong non-homogeneous magnetic field. This result can be used to prove that the magnetic Thomas-Fermi theory gives the leading order ground state energy of large atoms. We develop a new localization scheme well suited to the anisotropic character of the strong magnetic field. We also use the basic Lieb-Thirring estimate obtained earlier (1996). (orig.) 19 refs.","lang":"eng"}],"intvolume":"        96","publication_identifier":{"issn":["0012-7094"]},"publication_status":"published","month":"01","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"1","citation":{"short":"L. Erdös, J. Solovej, Duke Mathematical Journal 96 (1999) 127–173.","ieee":"L. Erdös and J. Solovej, “Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate,” <i>Duke Mathematical Journal</i>, vol. 96, no. 1. Duke University Press, pp. 127–173, 1999.","ama":"Erdös L, Solovej J. Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate. <i>Duke Mathematical Journal</i>. 1999;96(1):127-173. doi:<a href=\"https://doi.org/10.1215/S0012-7094-99-09604-7\">10.1215/S0012-7094-99-09604-7</a>","mla":"Erdös, László, and Jan Solovej. “Semiclassical Eigenvalue Estimates for the Pauli Operator with Strong Nonhomogeneous Magnetic Fields, I: Nonasymptotic Lieb-Thirring-Type Estimate.” <i>Duke Mathematical Journal</i>, vol. 96, no. 1, Duke University Press, 1999, pp. 127–73, doi:<a href=\"https://doi.org/10.1215/S0012-7094-99-09604-7\">10.1215/S0012-7094-99-09604-7</a>.","apa":"Erdös, L., &#38; Solovej, J. (1999). Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/S0012-7094-99-09604-7\">https://doi.org/10.1215/S0012-7094-99-09604-7</a>","ista":"Erdös L, Solovej J. 1999. Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate. Duke Mathematical Journal. 96(1), 127–173.","chicago":"Erdös, László, and Jan Solovej. “Semiclassical Eigenvalue Estimates for the Pauli Operator with Strong Nonhomogeneous Magnetic Fields, I: Nonasymptotic Lieb-Thirring-Type Estimate.” <i>Duke Mathematical Journal</i>. Duke University Press, 1999. <a href=\"https://doi.org/10.1215/S0012-7094-99-09604-7\">https://doi.org/10.1215/S0012-7094-99-09604-7</a>."}},{"publication":"Duke Mathematical Journal","extern":"1","status":"public","date_published":"1994-11-01T00:00:00Z","acknowledgement":"Work supported by the NSF grant PHY90-19433 A02 and by the Alfred Sloan Foundation dissertation fellowship.","year":"1994","publist_id":"4183","page":"541 - 566","main_file_link":[{"url":"https://projecteuclid.org/journals/duke-mathematical-journal/volume-76/issue-2/Estimates-on-stochastic-oscillatory-integrals-and-on-the-heat-kernel/10.1215/S0012-7094-94-07619-9.short"}],"quality_controlled":"1","article_processing_charge":"No","doi":"10.1215/S0012-7094-94-07619-9","publisher":"Duke University Press","_id":"2713","date_updated":"2022-06-03T11:59:06Z","type":"journal_article","language":[{"iso":"eng"}],"citation":{"short":"L. Erdös, Duke Mathematical Journal 76 (1994) 541–566.","ieee":"L. Erdös, “Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator,” <i>Duke Mathematical Journal</i>, vol. 76, no. 2. Duke University Press, pp. 541–566, 1994.","ama":"Erdös L. Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator. <i>Duke Mathematical Journal</i>. 1994;76(2):541-566. doi:<a href=\"https://doi.org/10.1215/S0012-7094-94-07619-9\">10.1215/S0012-7094-94-07619-9</a>","mla":"Erdös, László. “Estimates on Stochastic Oscillatory Integrals and on the Heat Kernel of the Magnetic Schrödinger Operator.” <i>Duke Mathematical Journal</i>, vol. 76, no. 2, Duke University Press, 1994, pp. 541–66, doi:<a href=\"https://doi.org/10.1215/S0012-7094-94-07619-9\">10.1215/S0012-7094-94-07619-9</a>.","apa":"Erdös, L. (1994). Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/S0012-7094-94-07619-9\">https://doi.org/10.1215/S0012-7094-94-07619-9</a>","chicago":"Erdös, László. “Estimates on Stochastic Oscillatory Integrals and on the Heat Kernel of the Magnetic Schrödinger Operator.” <i>Duke Mathematical Journal</i>. Duke University Press, 1994. <a href=\"https://doi.org/10.1215/S0012-7094-94-07619-9\">https://doi.org/10.1215/S0012-7094-94-07619-9</a>.","ista":"Erdös L. 1994. Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator. Duke Mathematical Journal. 76(2), 541–566."},"issue":"2","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","month":"11","intvolume":"        76","publication_status":"published","publication_identifier":{"issn":["0012-7094"]},"scopus_import":"1","day":"01","author":[{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László"}],"title":"Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator","oa_version":"None","volume":76,"date_created":"2018-12-11T11:59:13Z","article_type":"original"}]