[{"acknowledgement":"Sah and Sawhney were supported by NSF Graduate Research Fellowship Program DGE1745302. Sah was supported by the PD Soros Fellowship. Simkin was supported by the Center of Mathematical Sciences and Applications at Harvard University.","type":"journal_article","volume":200,"OA_place":"repository","status":"public","publication_identifier":{"issn":["0003-486X"],"eissn":["1939-8980"]},"language":[{"iso":"eng"}],"year":"2024","oa":1,"issue":"3","doi":"10.4007/annals.2024.200.3.4","page":"1059-1156","month":"11","isi":1,"arxiv":1,"intvolume":"       200","department":[{"_id":"MaKw"}],"article_type":"original","scopus_import":"1","_id":"18559","oa_version":"Preprint","article_processing_charge":"No","day":"01","quality_controlled":"1","citation":{"chicago":"Kwan, Matthew Alan, Ashwin Sah, Mehtaab Sawhney, and Michael Simkin. “High-Girth Steiner Triple Systems.” <i>Annals of Mathematics</i>. Princeton University, 2024. <a href=\"https://doi.org/10.4007/annals.2024.200.3.4\">https://doi.org/10.4007/annals.2024.200.3.4</a>.","ama":"Kwan MA, Sah A, Sawhney M, Simkin M. High-girth Steiner triple systems. <i>Annals of Mathematics</i>. 2024;200(3):1059-1156. doi:<a href=\"https://doi.org/10.4007/annals.2024.200.3.4\">10.4007/annals.2024.200.3.4</a>","apa":"Kwan, M. A., Sah, A., Sawhney, M., &#38; Simkin, M. (2024). High-girth Steiner triple systems. <i>Annals of Mathematics</i>. Princeton University. <a href=\"https://doi.org/10.4007/annals.2024.200.3.4\">https://doi.org/10.4007/annals.2024.200.3.4</a>","ieee":"M. A. Kwan, A. Sah, M. Sawhney, and M. Simkin, “High-girth Steiner triple systems,” <i>Annals of Mathematics</i>, vol. 200, no. 3. Princeton University, pp. 1059–1156, 2024.","short":"M.A. Kwan, A. Sah, M. Sawhney, M. Simkin, Annals of Mathematics 200 (2024) 1059–1156.","mla":"Kwan, Matthew Alan, et al. “High-Girth Steiner Triple Systems.” <i>Annals of Mathematics</i>, vol. 200, no. 3, Princeton University, 2024, pp. 1059–156, doi:<a href=\"https://doi.org/10.4007/annals.2024.200.3.4\">10.4007/annals.2024.200.3.4</a>.","ista":"Kwan MA, Sah A, Sawhney M, Simkin M. 2024. High-girth Steiner triple systems. Annals of Mathematics. 200(3), 1059–1156."},"publisher":"Princeton University","publication":"Annals of Mathematics","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","corr_author":"1","OA_type":"green","date_published":"2024-11-01T00:00:00Z","date_created":"2024-11-17T23:01:48Z","external_id":{"isi":["001366233800004"],"arxiv":["2201.04554"]},"title":"High-girth Steiner triple systems","author":[{"full_name":"Kwan, Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","orcid":"0000-0002-4003-7567","last_name":"Kwan","first_name":"Matthew Alan"},{"last_name":"Sah","first_name":"Ashwin","full_name":"Sah, Ashwin"},{"full_name":"Sawhney, Mehtaab","last_name":"Sawhney","first_name":"Mehtaab"},{"last_name":"Simkin","first_name":"Michael","full_name":"Simkin, Michael"}],"abstract":[{"lang":"eng","text":"We prove a 1973 conjecture due to Erdős on the existence of Steiner triple systems with arbitrarily high girth."}],"date_updated":"2025-09-08T14:40:55Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2201.04554","open_access":"1"}]},{"page":"1115-1203","related_material":{"link":[{"url":"https://ist.ac.at/en/news/when-is-necessary-sufficient/","relation":"press_release","description":"News on IST Homepage"}]},"doi":"10.4007/annals.2023.197.3.3","issue":"3","language":[{"iso":"eng"}],"oa":1,"year":"2023","arxiv":1,"isi":1,"month":"05","type":"journal_article","status":"public","publication_identifier":{"issn":["0003-486X"]},"volume":197,"corr_author":"1","date_published":"2023-05-01T00:00:00Z","publication":"Annals of Mathematics","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous for smooth Fano hypersurfaces of dimension at least 3 over any number field. Moreover, for such varieties it follows from a general conjecture of Colliot-Thélène that the Brauer--Manin obstruction to the Hasse principle should be the only one, so that the Hasse principle is expected to hold. Working over the field of rational numbers and ordering Fano hypersurfaces of fixed degree and dimension by height, we prove that almost every such hypersurface satisfies the Hasse principle provided that the dimension is at least 3. This proves a conjecture of Poonen and Voloch in every case except for cubic surfaces.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2006.02356"}],"date_updated":"2024-10-21T06:01:30Z","title":"The Hasse principle for random Fano hypersurfaces","author":[{"full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177"},{"full_name":"Boudec, Pierre Le","last_name":"Boudec","first_name":"Pierre Le"},{"full_name":"Sawin, Will","first_name":"Will","last_name":"Sawin"}],"date_created":"2020-10-19T14:28:50Z","external_id":{"arxiv":["2006.02356"],"isi":["000966611000003"]},"article_processing_charge":"No","oa_version":"Preprint","_id":"8682","day":"01","department":[{"_id":"TiBr"}],"intvolume":"       197","scopus_import":"1","article_type":"original","publisher":"Princeton University","quality_controlled":"1","citation":{"apa":"Browning, T. D., Boudec, P. L., &#38; Sawin, W. (2023). The Hasse principle for random Fano hypersurfaces. <i>Annals of Mathematics</i>. Princeton University. <a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">https://doi.org/10.4007/annals.2023.197.3.3</a>","ama":"Browning TD, Boudec PL, Sawin W. The Hasse principle for random Fano hypersurfaces. <i>Annals of Mathematics</i>. 2023;197(3):1115-1203. doi:<a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">10.4007/annals.2023.197.3.3</a>","chicago":"Browning, Timothy D, Pierre Le Boudec, and Will Sawin. “The Hasse Principle for Random Fano Hypersurfaces.” <i>Annals of Mathematics</i>. Princeton University, 2023. <a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">https://doi.org/10.4007/annals.2023.197.3.3</a>.","ista":"Browning TD, Boudec PL, Sawin W. 2023. The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. 197(3), 1115–1203.","ieee":"T. D. Browning, P. L. Boudec, and W. Sawin, “The Hasse principle for random Fano hypersurfaces,” <i>Annals of Mathematics</i>, vol. 197, no. 3. Princeton University, pp. 1115–1203, 2023.","mla":"Browning, Timothy D., et al. “The Hasse Principle for Random Fano Hypersurfaces.” <i>Annals of Mathematics</i>, vol. 197, no. 3, Princeton University, 2023, pp. 1115–203, doi:<a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">10.4007/annals.2023.197.3.3</a>.","short":"T.D. Browning, P.L. Boudec, W. Sawin, Annals of Mathematics 197 (2023) 1115–1203."}},{"arxiv":1,"month":"07","doi":"10.4007/annals.2018.188.1.6","issue":"1","page":"315-380","year":"2018","oa":1,"extern":"1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0003-486X"]},"status":"public","volume":188,"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"type":"journal_article","date_updated":"2021-01-12T08:19:10Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.09194"}],"abstract":[{"text":"The classical Birkhoff conjecture claims that the boundary of a strictly convex integrable billiard table is necessarily an ellipse (or a circle as a special case). In this article we prove a complete local version of this conjecture: a small integrable perturbation of an ellipse must be an ellipse. This extends and completes the result in Avila-De Simoi-Kaloshin, where nearly circular domains were considered. One of the crucial ideas in the proof is to extend action-angle coordinates for elliptic billiards into complex domains (with respect to the angle), and to thoroughly analyze the nature of their complex singularities. As an application, we are able to prove some spectral rigidity results for elliptic domains.","lang":"eng"}],"date_created":"2020-09-17T10:42:22Z","external_id":{"arxiv":["1612.09194"]},"title":"On the local Birkhoff conjecture for convex billiards","author":[{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","last_name":"Kaloshin","first_name":"Vadim"},{"first_name":"Alfonso","last_name":"Sorrentino","full_name":"Sorrentino, Alfonso"}],"date_published":"2018-07-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","publication":"Annals of Mathematics","publisher":"Annals of Mathematics, Princeton U","citation":{"ieee":"V. Kaloshin and A. Sorrentino, “On the local Birkhoff conjecture for convex billiards,” <i>Annals of Mathematics</i>, vol. 188, no. 1. Annals of Mathematics, Princeton U, pp. 315–380, 2018.","short":"V. Kaloshin, A. Sorrentino, Annals of Mathematics 188 (2018) 315–380.","mla":"Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture for Convex Billiards.” <i>Annals of Mathematics</i>, vol. 188, no. 1, Annals of Mathematics, Princeton U, 2018, pp. 315–80, doi:<a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">10.4007/annals.2018.188.1.6</a>.","ista":"Kaloshin V, Sorrentino A. 2018. On the local Birkhoff conjecture for convex billiards. Annals of Mathematics. 188(1), 315–380.","chicago":"Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture for Convex Billiards.” <i>Annals of Mathematics</i>. Annals of Mathematics, Princeton U, 2018. <a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">https://doi.org/10.4007/annals.2018.188.1.6</a>.","ama":"Kaloshin V, Sorrentino A. On the local Birkhoff conjecture for convex billiards. <i>Annals of Mathematics</i>. 2018;188(1):315-380. doi:<a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">10.4007/annals.2018.188.1.6</a>","apa":"Kaloshin, V., &#38; Sorrentino, A. (2018). On the local Birkhoff conjecture for convex billiards. <i>Annals of Mathematics</i>. Annals of Mathematics, Princeton U. <a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">https://doi.org/10.4007/annals.2018.188.1.6</a>"},"quality_controlled":"1","day":"01","_id":"8421","oa_version":"Preprint","article_processing_charge":"No","article_type":"original","intvolume":"       188"},{"type":"journal_article","volume":186,"publication_identifier":{"issn":["0003-486X"]},"status":"public","year":"2017","oa":1,"extern":"1","language":[{"iso":"eng"}],"doi":"10.4007/annals.2017.186.1.7","issue":"1","page":"277-314","month":"07","arxiv":1,"article_type":"original","intvolume":"       186","day":"01","_id":"8427","oa_version":"Preprint","article_processing_charge":"No","citation":{"ieee":"J. De Simoi, V. Kaloshin, and Q. Wei, “Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle,” <i>Annals of Mathematics</i>, vol. 186, no. 1. Annals of Mathematics, pp. 277–314, 2017.","mla":"De Simoi, Jacopo, et al. “Dynamical Spectral Rigidity among Z2-Symmetric Strictly Convex Domains Close to a Circle.” <i>Annals of Mathematics</i>, vol. 186, no. 1, Annals of Mathematics, 2017, pp. 277–314, doi:<a href=\"https://doi.org/10.4007/annals.2017.186.1.7\">10.4007/annals.2017.186.1.7</a>.","short":"J. De Simoi, V. Kaloshin, Q. Wei, Annals of Mathematics 186 (2017) 277–314.","ista":"De Simoi J, Kaloshin V, Wei Q. 2017. Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle. Annals of Mathematics. 186(1), 277–314.","chicago":"De Simoi, Jacopo, Vadim Kaloshin, and Qiaoling Wei. “Dynamical Spectral Rigidity among Z2-Symmetric Strictly Convex Domains Close to a Circle.” <i>Annals of Mathematics</i>. Annals of Mathematics, 2017. <a href=\"https://doi.org/10.4007/annals.2017.186.1.7\">https://doi.org/10.4007/annals.2017.186.1.7</a>.","ama":"De Simoi J, Kaloshin V, Wei Q. Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle. <i>Annals of Mathematics</i>. 2017;186(1):277-314. doi:<a href=\"https://doi.org/10.4007/annals.2017.186.1.7\">10.4007/annals.2017.186.1.7</a>","apa":"De Simoi, J., Kaloshin, V., &#38; Wei, Q. (2017). Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle. <i>Annals of Mathematics</i>. Annals of Mathematics. <a href=\"https://doi.org/10.4007/annals.2017.186.1.7\">https://doi.org/10.4007/annals.2017.186.1.7</a>"},"quality_controlled":"1","publisher":"Annals of Mathematics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","publication":"Annals of Mathematics","date_published":"2017-07-01T00:00:00Z","date_created":"2020-09-17T10:46:42Z","external_id":{"arxiv":["1606.00230"]},"title":"Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle","author":[{"full_name":"De Simoi, Jacopo","first_name":"Jacopo","last_name":"De Simoi"},{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin"},{"full_name":"Wei, Qiaoling","last_name":"Wei","first_name":"Qiaoling"}],"date_updated":"2021-01-12T08:19:12Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1606.00230"}],"abstract":[{"lang":"eng","text":"We show that any sufficiently (finitely) smooth ℤ₂-symmetric strictly convex domain sufficiently close to a circle is dynamically spectrally rigid; i.e., all deformations among domains in the same class that preserve the length of all periodic orbits of the associated billiard flow must necessarily be isometric deformations. This gives a partial answer to a question of P. Sarnak."}]},{"article_type":"original","intvolume":"       184","day":"01","_id":"8496","type":"journal_article","oa_version":"None","article_processing_charge":"No","volume":184,"citation":{"apa":"Avila, A., De Simoi, J., &#38; Kaloshin, V. (2016). An integrable deformation of an ellipse of small eccentricity is an ellipse. <i>Annals of Mathematics</i>. Princeton University Press. <a href=\"https://doi.org/10.4007/annals.2016.184.2.5\">https://doi.org/10.4007/annals.2016.184.2.5</a>","ama":"Avila A, De Simoi J, Kaloshin V. An integrable deformation of an ellipse of small eccentricity is an ellipse. <i>Annals of Mathematics</i>. 2016;184(2):527-558. doi:<a href=\"https://doi.org/10.4007/annals.2016.184.2.5\">10.4007/annals.2016.184.2.5</a>","chicago":"Avila, Artur, Jacopo De Simoi, and Vadim Kaloshin. “An Integrable Deformation of an Ellipse of Small Eccentricity Is an Ellipse.” <i>Annals of Mathematics</i>. Princeton University Press, 2016. <a href=\"https://doi.org/10.4007/annals.2016.184.2.5\">https://doi.org/10.4007/annals.2016.184.2.5</a>.","ista":"Avila A, De Simoi J, Kaloshin V. 2016. An integrable deformation of an ellipse of small eccentricity is an ellipse. Annals of Mathematics. 184(2), 527–558.","short":"A. Avila, J. De Simoi, V. Kaloshin, Annals of Mathematics 184 (2016) 527–558.","mla":"Avila, Artur, et al. “An Integrable Deformation of an Ellipse of Small Eccentricity Is an Ellipse.” <i>Annals of Mathematics</i>, vol. 184, no. 2, Princeton University Press, 2016, pp. 527–58, doi:<a href=\"https://doi.org/10.4007/annals.2016.184.2.5\">10.4007/annals.2016.184.2.5</a>.","ieee":"A. Avila, J. De Simoi, and V. Kaloshin, “An integrable deformation of an ellipse of small eccentricity is an ellipse,” <i>Annals of Mathematics</i>, vol. 184, no. 2. Princeton University Press, pp. 527–558, 2016."},"quality_controlled":"1","publication_identifier":{"issn":["0003-486X"]},"status":"public","publisher":"Princeton University Press","year":"2016","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","publication_status":"published","publication":"Annals of Mathematics","language":[{"iso":"eng"}],"date_published":"2016-09-01T00:00:00Z","doi":"10.4007/annals.2016.184.2.5","issue":"2","page":"527-558","month":"09","date_created":"2020-09-18T10:46:22Z","title":"An integrable deformation of an ellipse of small eccentricity is an ellipse","author":[{"last_name":"Avila","first_name":"Artur","full_name":"Avila, Artur"},{"full_name":"De Simoi, Jacopo","first_name":"Jacopo","last_name":"De Simoi"},{"orcid":"0000-0002-6051-2628","last_name":"Kaloshin","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"}],"date_updated":"2021-01-12T08:19:40Z"},{"year":"2012","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","extern":"1","language":[{"iso":"eng"}],"publication":"Annals of Mathematics","date_published":"2012-07-01T00:00:00Z","doi":"10.4007/annals.2012.176.1.10","issue":"1","page":"535-588","month":"07","date_created":"2020-09-18T10:47:24Z","title":"Finiteness of central configurations of five bodies in the plane","author":[{"full_name":"Albouy, Alain","first_name":"Alain","last_name":"Albouy"},{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin"}],"date_updated":"2021-01-12T08:19:44Z","abstract":[{"lang":"eng","text":"We prove there are finitely many isometry classes of planar central configurations (also called relative equilibria) in the Newtonian 5-body problem, except perhaps if the 5-tuple of positive masses belongs to a given codimension 2 subvariety of the mass space."}],"article_type":"original","intvolume":"       176","day":"01","_id":"8503","type":"journal_article","article_processing_charge":"No","oa_version":"None","volume":176,"citation":{"ama":"Albouy A, Kaloshin V. Finiteness of central configurations of five bodies in the plane. <i>Annals of Mathematics</i>. 2012;176(1):535-588. doi:<a href=\"https://doi.org/10.4007/annals.2012.176.1.10\">10.4007/annals.2012.176.1.10</a>","apa":"Albouy, A., &#38; Kaloshin, V. (2012). Finiteness of central configurations of five bodies in the plane. <i>Annals of Mathematics</i>. Princeton University Press. <a href=\"https://doi.org/10.4007/annals.2012.176.1.10\">https://doi.org/10.4007/annals.2012.176.1.10</a>","chicago":"Albouy, Alain, and Vadim Kaloshin. “Finiteness of Central Configurations of Five Bodies in the Plane.” <i>Annals of Mathematics</i>. Princeton University Press, 2012. <a href=\"https://doi.org/10.4007/annals.2012.176.1.10\">https://doi.org/10.4007/annals.2012.176.1.10</a>.","ista":"Albouy A, Kaloshin V. 2012. Finiteness of central configurations of five bodies in the plane. Annals of Mathematics. 176(1), 535–588.","ieee":"A. Albouy and V. Kaloshin, “Finiteness of central configurations of five bodies in the plane,” <i>Annals of Mathematics</i>, vol. 176, no. 1. Princeton University Press, pp. 535–588, 2012.","short":"A. Albouy, V. Kaloshin, Annals of Mathematics 176 (2012) 535–588.","mla":"Albouy, Alain, and Vadim Kaloshin. “Finiteness of Central Configurations of Five Bodies in the Plane.” <i>Annals of Mathematics</i>, vol. 176, no. 1, Princeton University Press, 2012, pp. 535–88, doi:<a href=\"https://doi.org/10.4007/annals.2012.176.1.10\">10.4007/annals.2012.176.1.10</a>."},"quality_controlled":"1","publication_identifier":{"issn":["0003-486X"]},"status":"public","publisher":"Princeton University Press"},{"language":[{"iso":"eng"}],"publication":"Annals of Mathematics","year":"2007","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","publication_status":"published","issue":"1","doi":"10.4007/annals.2007.165.89","page":"89-170","date_published":"2007-01-01T00:00:00Z","date_created":"2020-09-18T10:48:33Z","title":"Stretched exponential estimates on growth of the number of periodic points for prevalent diffeomorphisms I","author":[{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin"},{"full_name":"Hunt, Brian","first_name":"Brian","last_name":"Hunt"}],"month":"01","abstract":[{"text":"For diffeomorphisms of smooth compact finite-dimensional manifolds, we consider the problem of how fast the number of periodic points with period n grows as a function of n. In many familiar cases (e.g., Anosov systems) the growth is exponential, but arbitrarily fast growth is possible; in fact, the first author has shown that arbitrarily fast growth is topologically (Baire) generic for C2 or smoother diffeomorphisms. In the present work we show that, by contrast, for a measure-theoretic notion of genericity we call “prevalence”, the growth is not much faster than exponential. Specifically, we show that for each ρ,δ>0, there is a prevalent set of C1+ρ (or smoother) diffeomorphisms for which the number of periodic n points is bounded above by exp(Cn1+δ) for some C independent of n. We also obtain a related bound on the decay of hyperbolicity of the periodic points as a function of n, and obtain the same results for 1-dimensional endomorphisms. The contrast between topologically generic and measure-theoretically generic behavior for the growth of the number of periodic points and the decay of their hyperbolicity show this to be a subtle and complex phenomenon, reminiscent of KAM theory. Here in Part I we state our results and describe the methods we use. We complete most of the proof in the 1-dimensional C2-smooth case and outline the remaining steps, deferred to Part II, that are needed to establish the general case.\r\n\r\nThe novel feature of the approach we develop in this paper is the introduction of Newton Interpolation Polynomials as a tool for perturbing trajectories of iterated maps.","lang":"eng"}],"date_updated":"2021-01-12T08:19:48Z","intvolume":"       165","article_type":"original","_id":"8512","type":"journal_article","article_processing_charge":"No","oa_version":"None","day":"01","volume":165,"quality_controlled":"1","citation":{"apa":"Kaloshin, V., &#38; Hunt, B. (2007). Stretched exponential estimates on growth of the number of periodic points for prevalent diffeomorphisms I. <i>Annals of Mathematics</i>. Princeton University Press. <a href=\"https://doi.org/10.4007/annals.2007.165.89\">https://doi.org/10.4007/annals.2007.165.89</a>","ama":"Kaloshin V, Hunt B. Stretched exponential estimates on growth of the number of periodic points for prevalent diffeomorphisms I. <i>Annals of Mathematics</i>. 2007;165(1):89-170. doi:<a href=\"https://doi.org/10.4007/annals.2007.165.89\">10.4007/annals.2007.165.89</a>","chicago":"Kaloshin, Vadim, and Brian Hunt. “Stretched Exponential Estimates on Growth of the Number of Periodic Points for Prevalent Diffeomorphisms I.” <i>Annals of Mathematics</i>. Princeton University Press, 2007. <a href=\"https://doi.org/10.4007/annals.2007.165.89\">https://doi.org/10.4007/annals.2007.165.89</a>.","ista":"Kaloshin V, Hunt B. 2007. Stretched exponential estimates on growth of the number of periodic points for prevalent diffeomorphisms I. Annals of Mathematics. 165(1), 89–170.","short":"V. Kaloshin, B. Hunt, Annals of Mathematics 165 (2007) 89–170.","mla":"Kaloshin, Vadim, and Brian Hunt. “Stretched Exponential Estimates on Growth of the Number of Periodic Points for Prevalent Diffeomorphisms I.” <i>Annals of Mathematics</i>, vol. 165, no. 1, Princeton University Press, 2007, pp. 89–170, doi:<a href=\"https://doi.org/10.4007/annals.2007.165.89\">10.4007/annals.2007.165.89</a>.","ieee":"V. Kaloshin and B. Hunt, “Stretched exponential estimates on growth of the number of periodic points for prevalent diffeomorphisms I,” <i>Annals of Mathematics</i>, vol. 165, no. 1. Princeton University Press, pp. 89–170, 2007."},"status":"public","publisher":"Princeton University Press","publication_identifier":{"issn":["0003-486X"]}},{"publication_status":"published","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","publication":"Annals of Mathematics","date_published":"2003-11-01T00:00:00Z","OA_type":"free access","author":[{"full_name":"Lieb, Élliott","first_name":"Élliott","last_name":"Lieb"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","first_name":"Robert"},{"first_name":"Jakob","last_name":"Yngvason","full_name":"Yngvason, Jakob"}],"title":"Poincaré inequalities in punctured domains","external_id":{"arxiv":["0205088"]},"date_created":"2018-12-11T11:57:11Z","main_file_link":[{"url":"http://arxiv.org/abs/math/0205088","open_access":"1"}],"date_updated":"2026-05-28T08:25:42Z","abstract":[{"lang":"eng","text":"The classic Poincaré inequality bounds the L q-norm of a function f in a bounded domain Ω ⊂ ℝ n in terms of some L p-norm of its gradient in Ω. We generalize this in two ways: In the first generalization we remove a set Τ from Ω and concentrate our attention on Λ = Ω \\ Τ. This new domain might not even be connected and hence no Poincaré inequality can generally hold for it, or if it does hold it might have a very bad constant. This is so even if the volume of Τ is arbitrarily small. A Poincaré inequality does hold, however, if one makes the additional assumption that f has a finite L p gradient norm on the whole of Ω, not just on Λ. The important point is that the Poincaré inequality thus obtained bounds the L q-norm of f in terms of the L p gradient norm on Λ (not Ω) plus an additional term that goes to zero as the volume of Τ goes to zero. This error term depends on Τ only through its volume. Apart from this additive error term, the constant in the inequality remains that of the 'nice' domain Ω. In the second generalization we are given a vector field A and replace ∇ by ∇ + iA(x) (geometrically, a connection on a U(1) bundle). Unlike the A = 0 case, the infimum of ∥(∇ + iA)f∥ p over all f with a given ∥f∥ q is in general not zero. This permits an improvement of the inequality by the addition of a term whose sharp value we derive. We describe some open problems that arise from these generalizations."}],"article_type":"original","scopus_import":"1","intvolume":"       158","day":"01","oa_version":"Published Version","article_processing_charge":"No","_id":"2357","quality_controlled":"1","citation":{"short":"É. Lieb, R. Seiringer, J. Yngvason, Annals of Mathematics 158 (2003) 1067–1080.","mla":"Lieb, Élliott, et al. “Poincaré Inequalities in Punctured Domains.” <i>Annals of Mathematics</i>, vol. 158, no. 3, Princeton University Press, 2003, pp. 1067–80, doi:<a href=\"https://doi.org/10.4007/annals.2003.158.1067 \">10.4007/annals.2003.158.1067 </a>.","ieee":"É. Lieb, R. Seiringer, and J. Yngvason, “Poincaré inequalities in punctured domains,” <i>Annals of Mathematics</i>, vol. 158, no. 3. Princeton University Press, pp. 1067–1080, 2003.","ista":"Lieb É, Seiringer R, Yngvason J. 2003. Poincaré inequalities in punctured domains. Annals of Mathematics. 158(3), 1067–1080.","chicago":"Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “Poincaré Inequalities in Punctured Domains.” <i>Annals of Mathematics</i>. Princeton University Press, 2003. <a href=\"https://doi.org/10.4007/annals.2003.158.1067 \">https://doi.org/10.4007/annals.2003.158.1067 </a>.","apa":"Lieb, É., Seiringer, R., &#38; Yngvason, J. (2003). Poincaré inequalities in punctured domains. <i>Annals of Mathematics</i>. Princeton University Press. <a href=\"https://doi.org/10.4007/annals.2003.158.1067 \">https://doi.org/10.4007/annals.2003.158.1067 </a>","ama":"Lieb É, Seiringer R, Yngvason J. Poincaré inequalities in punctured domains. <i>Annals of Mathematics</i>. 2003;158(3):1067-1080. doi:<a href=\"https://doi.org/10.4007/annals.2003.158.1067 \">10.4007/annals.2003.158.1067 </a>"},"publisher":"Princeton University Press","publist_id":"4570","extern":"1","oa":1,"year":"2003","language":[{"iso":"eng"}],"page":"1067 - 1080","issue":"3","doi":"10.4007/annals.2003.158.1067 ","month":"11","arxiv":1,"type":"journal_article","OA_place":"publisher","volume":158,"publication_identifier":{"issn":["0003-486X"],"eissn":["1939-8980"]},"status":"public"},{"date_updated":"2021-01-12T08:19:53Z","month":"09","title":"An extension of the Artin-Mazur theorem","author":[{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","first_name":"Vadim","last_name":"Kaloshin","orcid":"0000-0002-6051-2628"}],"date_created":"2020-09-18T10:50:28Z","date_published":"1999-09-01T00:00:00Z","page":"729-741","doi":"10.2307/121093","issue":"2","publication_status":"published","extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"1999","language":[{"iso":"eng"}],"publication":"The Annals of Mathematics","publication_identifier":{"issn":["0003-486X"]},"publisher":"JSTOR","status":"public","quality_controlled":"1","citation":{"ista":"Kaloshin V. 1999. An extension of the Artin-Mazur theorem. The Annals of Mathematics. 150(2), 729–741.","ieee":"V. Kaloshin, “An extension of the Artin-Mazur theorem,” <i>The Annals of Mathematics</i>, vol. 150, no. 2. JSTOR, pp. 729–741, 1999.","mla":"Kaloshin, Vadim. “An Extension of the Artin-Mazur Theorem.” <i>The Annals of Mathematics</i>, vol. 150, no. 2, JSTOR, 1999, pp. 729–41, doi:<a href=\"https://doi.org/10.2307/121093\">10.2307/121093</a>.","short":"V. Kaloshin, The Annals of Mathematics 150 (1999) 729–741.","ama":"Kaloshin V. An extension of the Artin-Mazur theorem. <i>The Annals of Mathematics</i>. 1999;150(2):729-741. doi:<a href=\"https://doi.org/10.2307/121093\">10.2307/121093</a>","apa":"Kaloshin, V. (1999). An extension of the Artin-Mazur theorem. <i>The Annals of Mathematics</i>. JSTOR. <a href=\"https://doi.org/10.2307/121093\">https://doi.org/10.2307/121093</a>","chicago":"Kaloshin, Vadim. “An Extension of the Artin-Mazur Theorem.” <i>The Annals of Mathematics</i>. JSTOR, 1999. <a href=\"https://doi.org/10.2307/121093\">https://doi.org/10.2307/121093</a>."},"volume":150,"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"day":"01","article_processing_charge":"No","oa_version":"None","type":"journal_article","_id":"8526","article_type":"original","intvolume":"       150"}]