{"id":48,"date":"2018-11-27T12:43:54","date_gmt":"2018-11-27T17:43:54","guid":{"rendered":"http:\/\/sites.williams.edu\/csilva\/?page_id=48"},"modified":"2023-02-05T21:33:01","modified_gmt":"2023-02-06T02:33:01","slug":"publications","status":"publish","type":"page","link":"https:\/\/sites.williams.edu\/csilva\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"<ul>\n<li>&#8220;Rank-one transformations, odometers, and finite factors,&#8221;\u00a0 with Matthew Foreman, Su Gao, Aaron Hill, Benjamin Weiss, <i>Isr. J. Math.<\/i> (2022). https:\/\/doi.org\/10.1007\/s11856-022-2451-y.<\/li>\n<li>&#8220;Nonsingular transformations that are ergodic with isometric coefficients and not weakly doubly ergodic,&#8221; with Beatrix Haddock, James Leng, <a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/journaldoc.html?id=3713\"><em>Indag. Math. (N.S.)<\/em><\/a> <a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=463290\">33 <\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=463290\">(2022), <\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=463290\">no. 6,<\/a> 1297\u20131311.<\/li>\n<li>&#8220;W-measurable sensitivity of semigroup actions,&#8221; with Francisc Bozgan, Anthony Sanchez, Jack Spielberg, David Stevens, Jane Wang, <a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/journaldoc.html?id=4247\"><em>Colloq. Math.<\/em><\/a> <a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=444742\">163 <\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=444742\">(2021), <\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=444742\">no. 1,<\/a> 113\u2013129.<\/li>\n<li>&#8220;Partially bounded transformations have trivial centralizers,&#8221; with Johan Gaebler, Alexander Kastner, Xiaoyu Xu, Zirui Zhou,\u00a0 <em>Proc. Amer. Math. Soc.<\/em> 146 (2018), no. 12, 5113\u20135127.<\/li>\n<li>&#8220;Weak mixing for infinite measure invertible transformations,&#8221; with Terrence Adams,\u00a0<em>Ergodic theory and dynamical systems in their interactions with arithmetics and combinatorics, <\/em>327\u2013349, Lecture Notes in Math., 2213, <em>Springer, Cham,<\/em> 2018.<\/li>\n<li>&#8220;Infinite symmetric ergodic index and related examples in infinite measure,&#8221; with Isaac Loh,\u00a0 <em>Studia Math.<\/em> 243 (2018), no. 1, 101\u2013115.<\/li>\n<li>&#8220;<span class=\"title\">On conservative sequences and their application to ergodic multiplier problems,&#8221; with\u00a0Madeleine Elyze; Alexander Kastner; Juan Ortiz Rhoton;\u00a0Vadim Semenov,\u00a0<\/span><em>Colloq. Math.<\/em> 151 (2018), no. 1, 123\u2013145.<\/li>\n<li>&#8220;Strict doubly ergodic infinite transformations,&#8221; with Isaac Loh,\u00a0 <a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/journaldoc.html?id=5674\"><em>Dyn. Syst.<\/em><\/a> 32 (2017), no. 4, 519\u2013543.<\/li>\n<li>&#8220;On mixing-like notions in infinite measure,&#8221;\u00a0<em>Amer. Math. Monthly<\/em> 124 (2017), no. 9, 807\u2013825.<\/li>\n<li>&#8221; <span class=\"title\">If a prime divides a product<span id=\"MathJax-Element-1-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mo\">\u2026<\/span><\/span><\/span><\/span>.,&#8221; with Steven J. Miller,\u00a0<em>College Math. J.<\/em> 48 (2017), no. 2, 123\u2013128.<\/span><\/li>\n<li>&#8220;The mathematical work of John C. Oxtoby,&#8221; with Steve Alpern, Joseph Auslander, <em>Ergodic theory, dynamical systems, and the continuing influence of John C. Oxtoby, <\/em>43\u201351, <a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/series.html?id=1059\">Contemp. Math., 678,<\/a> <em>Amer. Math. Soc., Providence, RI,<\/em> 2016.<\/li>\n<li>&#8220;Weak Rational Ergodicity Does Not Imply Rational Ergodicity,&#8221; with Terrence M. Adams, Israel Journal of Mathematics, 2144 (2016), no. 1, 491-506.\u00a0\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1502.06566\" target=\"_blank\" rel=\"noopener\">http:\/\/arxiv.org\/abs\/1502.06566<\/a><\/li>\n<li>&#8220;Ergodicity and Conservativity of products of infinite transformations and their inverses,&#8221; with Julien Clancy, Rina Friedberg, Isaac Loh, Indraneel Kalsmarka, Sahana Vasudevan, Colloq. Math. 143 (2016), no. 2, 271-291.\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1408.2445\" target=\"_blank\" rel=\"noopener\">http:\/\/arxiv.org\/abs\/1408.2445<\/a><\/li>\n<li>&#8220;<span class=\"title\">What is <span id=\"MathJax-Element-2-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-4\" class=\"math\"><span id=\"MathJax-Span-5\" class=\"mrow\"><span id=\"MathJax-Span-6\" class=\"mo\">\u2026<\/span><\/span><\/span><\/span> an ergodic transformation?&#8221;\u00a0<a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/journaldoc.html?id=400\"><em>Notices Amer. Math. Soc.<\/em><\/a> <a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=338499\">63 <\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=338499\">(2016), <\/a><a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/search\/publications.html?pg1=ISSI&amp;s1=338499\">no. 1,<\/a> 26\u201327.<\/span><\/li>\n<li>&#8220;On Infinite Transformations with Maximal Control of Ergodic Two-fold Product Powers,&#8221; with Terrence M. Adams, Israel Journal of Mathematics, 209 (2015), no. 2, 929-948.\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1402.1818\" target=\"_blank\" rel=\"noopener\">http:\/\/arxiv.org\/abs\/1402.1818<\/a><\/li>\n<li>\u201cSubsequence Bounded Rational Ergodicity of Rank-One Transformations,\u201d with Francisc Bozgan, Anthony Sanchez, David Stevens and Jane Wang, Dynamical Systems, 30 (2015), no. 1, 70&#8211;84.\u00a0<a href=\"https:\/\/web.williams.edu\/Mathematics\/csilva\/SubsequenceRatErgRankOne.pdf\" target=\"_blank\" rel=\"noopener\">SubsequenceRatErgRankOne.pdf\u00a0<\/a><br \/>\nFor an older more extensive version:\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1310.5084\" target=\"_blank\" rel=\"noopener\">http:\/\/arxiv.org\/abs\/1310.5084<\/a><\/li>\n<li>&#8220;On $v$-Positive Type Transformations in Infinite Measure,&#8221; with Tudor Padurariu and Evangelie Zachos, Colloq. Math. 140 (2015), 149\u2014170.\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1309.6257\" target=\"_blank\" rel=\"noopener\">On $v$-Positive Type Transformations in Infinite Measure<\/a><\/li>\n<li>&#8220;On Rationally Ergodic and Rationally Weakly Mixing Rank-One Transformations,&#8221; with Irving Dai, Xavier Garcia, and Tudor Padurariu, Ergodic Theory &amp; Dynamical Systems 35 (2015), no. 4, 1141&#8211;1164.\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1309.6257\" target=\"_blank\" rel=\"noopener\">On Rationally Ergodic and Rationally Weakly Mixing Rank-One Transformations<\/a><\/li>\n<li>&#8220;On Li-Yorke Measurable Sensitivity,&#8221; with Jared Hallett and Lucas Manuelli, Proc. Amer. Math. Soc. 143 (2015), no. 6, 2411&#8211;2426.\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1207.3575\" target=\"_blank\" rel=\"noopener\">On Li-Yorke Measurable Sensitivity<\/a><\/li>\n<li>&#8220;Measurable Time-Restricted Sensitivity,&#8221; with Domenico Aiello, Hansheng Diao, Zhou Fan, Daniel O. King, and Jessica Lin, Nonlinearity 25 (2012), 3313&#8211;3325.<a href=\"http:\/\/arxiv.org\/abs\/1105.1493\" target=\"_blank\" rel=\"noopener\">Measurable Time-Restricted Sensitivity<\/a><\/li>\n<li>&#8220;On $mu$-Compatible Metrics and Measurable Sensitivity,&#8221; with Ilya Grigoriev, Nathaniel Ince, Marius Catalin Iordan, Amos Lubin, Colloquium Math. 126 (2012), 53&#8211;72.\u00a0<a href=\"http:\/\/arxiv.org\/abs\/0910.1958\" target=\"_blank\" rel=\"noopener\">On $mu$-Compatible Metrics\u00a0<\/a><\/li>\n<li>&#8220;Digraph Representations of Rational Functions over $p$-adic Numbers,&#8221; with Hansheng Diao, P-adic Numbers, Ultrametric Analysis, and Applications, Vol. 3, No. 1, (2011) 23&#8211;38.\u00a0<a href=\"http:\/\/arxiv.org\/abs\/0909.4130\" target=\"_blank\" rel=\"noopener\">Digraph Representations\u00a0<\/a><\/li>\n<li>&#8220;Dynamics of the $p$-adic shift and Applications,&#8221; with J. Kingsbery, A. Levin, and A. Preygel, Discrete and Continuous Dynamical Systems, 30, (2011), no. 1, 209&#8211;218.\u00a0<a href=\"http:\/\/arxiv.org\/abs\/0903.4226\" target=\"_blank\" rel=\"noopener\">Dynamics of the $p$-adic shift and Applications\u00a0<\/a><\/li>\n<li>&#8220;Mixing on Rank-One Transformations,&#8221; with D. Creutz, Studia Math. 199 (2010), no. 1, 43\u201372.\u00a0<a href=\"https:\/\/web.williams.edu\/Mathematics\/csilva\/MixingRankOne_123009.pdf\" target=\"_blank\" rel=\"noopener\">MixingRankOne.pdf\u00a0<\/a><\/li>\n<li>&#8220;Ergodic Properties of a Class of Discrete Abelian Group Extensions of Rank-One Transformations,&#8221; P. Jeasakul, A. Jirapattanakul, D. Kane, B. Robinson, and N. Stein, Colloq. Math., 119 (2010), 1-22.\u00a0<a href=\"https:\/\/web.williams.edu\/Mathematics\/csilva\/Small04May_5_2009%20copy.pdf\" target=\"_blank\" rel=\"noopener\">Small04May_5_2009.pdf\u00a0<\/a><\/li>\n<li>&#8220;On ergodic transformations that are both weakly mixing and uniformly rigid,&#8221; with J. James, T. Koberda, K. Lindsey, and P. Speh, New York Journal of Math. 15 (2009), 393&#8211;403.\u00a0<a href=\"http:\/\/nyjm.albany.edu\/j\/2009\/15-20.html\" target=\"_blank\" rel=\"noopener\">Weakly mixing and uniformly rigid\u00a0<\/a><\/li>\n<li>&#8220;Ergodic Theory: Nonsingular Transformations,&#8221; with A. Danilenko, Encyclopedia of Complexity and Systems Science, Springer, (2009), Part 5, 3055-3083.<a href=\"https:\/\/web.williams.edu\/Mathematics\/csilva\/NonsingularET_Apr.pdf\" target=\"_blank\" rel=\"noopener\">NonsingularTransformations.pdf\u00a0<\/a><\/li>\n<li>&#8220;Measurable Sensitivity,&#8221; with J. James, T. Koberda, K. Lindsey, and P. Speh, Proc. Amer. Math. Soc. 136 (2008), no. 10, 3549&#8211;3559.\u00a0<a href=\"http:\/\/arxiv.org\/abs\/math\/0612480\" target=\"_blank\" rel=\"noopener\">MeasurableSensitivity\u00a0<\/a><\/li>\n<li>&#8220;Measurable Dynamics of Maps on Profinite Groups,&#8221; with J. Kingsbery, A. Levin, and A. Preygel, Indag. Math. (N.S.) 18 (2007), no. 4, 561&#8211;581.\u00a0<a href=\"https:\/\/web.williams.edu\/Mathematics\/csilva\/ProfiniteKLPS.pdf\" target=\"_blank\" rel=\"noopener\">ProfiniteGroups.pdf\u00a0<\/a><\/li>\n<li>&#8220;On measure-preserving C^1 transformations of compact-open subsets of non-archimedean local fields,&#8221; with J. Kingsbery, A. Levin, and A. Preygel, Tran. Amer Math. Soc. 361 (2009), 61-85. Early version:\u00a0<a href=\"https:\/\/web.williams.edu\/Mathematics\/csilva\/LocallyScalingKLPS\" target=\"_blank\" rel=\"noopener\">LocallyScaling.pdf\u00a0<\/a><\/li>\n<li>&#8220;Mixing rank-one actions of locally compact abelian groups,&#8221; with A. Danilenko, Ann. Inst. H. Poincar\u00e9 Probab. Statist. 43 (2007), no. 4, 375&#8211;398.<a href=\"https:\/\/web.williams.edu\/Mathematics\/csilva\/GmixingMar05.pdf\" target=\"_blank\" rel=\"noopener\">MixingAbelianGroups.pdf\u00a0<\/a><\/li>\n<li>&#8220;Weakly Mixing and Doubly Ergodic Infinite Measure-Preserving R^d actions,&#8221; with S. Iams, B. Katz, B. Street, and K. Wickelgren, Colloq. Math. 103 (2005), 247-264.\u00a0<a href=\"https:\/\/web.williams.edu\/Mathematics\/csilva\/NonSingDoubleErgV032505.pdf\" target=\"_blank\" rel=\"noopener\">WeaklyMixingRd.pdf\u00a0<\/a><\/li>\n<li>&#8220;Measurable Dynamics of Simple p-adic Polynomials,&#8221; with J. Bryk, Amer. Math. Monthly, Vol. 112 (2005), no. 3, 212-232.\u00a0<a href=\"https:\/\/web.williams.edu\/Mathematics\/csilva\/BrykSilvaMonthly2005.pdf\" target=\"_blank\" rel=\"noopener\">pAdicMeasurableSystems.pdf\u00a0<\/a><\/li>\n<li>&#8220;Multiple and Polynomial Recurrence for Abelian Actions in Infinite Measure,&#8221; with A. Danilenko, Journal London Math. Soc. (2) 69 (2004), no. 1, 183-200.\u00a0<a href=\"https:\/\/web.williams.edu\/Mathematics\/csilva\/mult_rec3.pdf\" target=\"_blank\" rel=\"noopener\">AbelianMultRec.pdf\u00a0<\/a><\/li>\n<li>&#8220;Power Weak Mixing does not imply Multiple Recurrence in Infinite Measure and other Counterexamples,&#8221; with K. Gruher, F. Hines, D. Patel, and R. Waelder, New York Journal of Mathematics 9 (2003), 1-22.<a href=\"http:\/\/nyjm.albany.edu:8000\/j\/2003\/Vol9.htm\" target=\"_blank\" rel=\"noopener\">http:\/\/nyjm.albany.edu:8000\/j\/2003\/Vol9.htm\u00a0<\/a><\/li>\n<li>&#8220;Mixing on a class of rank one transformations,&#8221; with D. Creutz, Ergodic Theory and Dynam. Sys. 24 (2004), no. 2, 407-440.\u00a0<a href=\"http:\/\/journals.cambridge.org\/action\/displayAbstract?fromPage=online&amp;aid=208351\" target=\"_blank\" rel=\"noopener\">RankOneMixingClass.pdf<\/a><\/li>\n<li>&#8220;Genericity of Rigid and Multiply Recurrent Infinite Measure Preserving and Nonsingular Transformations,&#8221; with O. N. Ageev, Topology Proceedings 26 No. 2 (2001-2002), pp. 357-365.\u00a0<a href=\"https:\/\/web.williams.edu\/Mathematics\/csilva\/Ageev-Silva.pdf\" target=\"_blank\" rel=\"noopener\">GenMultRec.pdf<\/a><\/li>\n<li>&#8220;Double Ergodicity of Nonsingular Transformations and Infinite Measure Preserving Staircase Transformations,&#8221; with A. Bowels, L. Fidkowski, and A.E. Marinello, Illinois J. Math., Vol. 45, No. 3, (2001), 999-1019.<\/li>\n<li>&#8220;Factors of Cartesian products of nonsingular Chacon transformations,&#8221; with A. del Junco, Ergodic Theory and Dynam. Sys. 23 (2003), 1445-1465.\u00a0<a href=\"https:\/\/web.williams.edu\/Mathematics\/csilva\/FactorsTxSV5.pdf\" target=\"_blank\" rel=\"noopener\">FactorsTxS.pdf<\/a><\/li>\n<li>&#8220;On nonsingular Chacon transformations,&#8221; with T. Hamachi, Illinois J. Math., Vol. 44, No. 4, (2000), 868-883.<\/li>\n<li>&#8220;Rank one power weakly mixing nonsingular transformations,&#8221; with T. Adams and N. Friedman, Ergodic Theory and Dyn. Sys. 21 (2001), no. 5, 1321&#8211;1332.<\/li>\n<li>&#8220;Power weakly mixing infinite transformations,&#8221; with S.L. Day, B.R. Grivna, and E.P. McCartney, New York J. of Math., 5 (1999), 17-24.\u00a0<a href=\"http:\/\/nyjm.albany.edu:8000\/j\/1999\/5-2.html\" target=\"_blank\" rel=\"noopener\">http:\/\/nyjm.albany.edu:8000\/j\/1999\/5-2.html<\/a><\/li>\n<li>&#8220;Lightly mixing on dense algebras,&#8221; with E. Muehlegger, A. Raich, and W. Zhao, Real Analysis Exchange, Vol. 23, No. 1, (1998), 259-266. [MR 99c:28052].<\/li>\n<li>&#8220;Zd staircase actions,&#8221; with T. Adams, Ergodic Theory and Dyn. Sys., (1999), 19, 837-850. May be downloaded from\u00a0<a href=\"http:\/\/journals.cambridge.org\/action\/displayAbstract?fromPage=online&amp;aid=69921\" target=\"_blank\" rel=\"noopener\">http:\/\/www.journals.cup.org\/<\/a><\/li>\n<li>&#8220;Infinite ergodic index Zd actions in infinite measure,&#8221; with E. Muehlegger &#8217;97, B. Narasimhan &#8217;97, A. Raich &#8217;98, M.Touloumtzis &#8216; 96, and W. Zhao, Colloq. Math., vol. 82, No. 2 (1999), 167-190.<\/li>\n<li>&#8220;Characterizing mildly mixing group actions using orbit equivalence,&#8221; with J. Hawkins, New York J. of Math., 3A (1998), 99-115. [MR 99b:28019].\u00a0<a href=\"http:\/\/nyjm.albany.edu:8000\/j\/1998\/3A-8.html\" target=\"_blank\" rel=\"noopener\">http:\/\/nyjm.albany.edu:8000\/j\/1998\/3A-8.html<\/a><\/li>\n<li>&#8220;Rank-one weak-mixing for nonsingular transformations,&#8221; with T. Adams and N. Friedman, Israel J. Math, vol. 102, (1997), 269-282. [MR 98j:28013].<\/li>\n<li>&#8220;Prime type IIIl automorphisms: An instance of coding techniques applied to nonsingular maps,&#8221; with A. del Junco, in Algorithms, Fractals and Dynamics (Okayama\/Kyoto, 1992), 101-115, Plenum, New York, 1995. [MR 98f:28026].<\/li>\n<li>&#8220;Quotients of ergodic actions with quasi-invariant measure whose self-joinings are graphs,&#8221; with D. Witte, Inter. J. Math. 5 (2) (1994), 219-237. [MR: 95k:28042].<\/li>\n<li>&#8220;A skew product entropy for nonsingular transformations,&#8221; with P. Thieullen, J. London Math. Soc. (2) 52 (1995), 497-516. [MR 97a: 28015].<\/li>\n<li>&#8220;Noninvertible transformations admitting no absolutely continuous s-finite invariant measure,&#8221; with J.M Hawkins, Proc. Amer. Math. Soc. 111 (2) (1991), 455-463. [MR 92h:58115].<\/li>\n<li>&#8220;Minimal self-joinings for nonsingular transformations,&#8221; with D.J. Rudolph, Ergodic Theory and Dyn. Sys. 9 (1989), 759-800. [MR 91c: 28017].<\/li>\n<li>&#8220;The subadditive ergodic theorem and recurrence properties of Markovian transformations,&#8221; with P. Thieullen, J. Math. Analysis and App. 154 (1) (1991), 83-99. [MR 92a: 47009].<\/li>\n<li>&#8220;Finite Full Sets in 2-stack Structures,&#8221; with S. Eigen, Contemporary Math. 94 (1989), 131-140. [MR 90h: 28018].<\/li>\n<li>&#8220;Remarks on recurrence and orbit equivalence of nonsingular transformations,&#8221; with J. Hawkins, Dynamical Systems (College Park, MD, 1986-87), 281-290, Lecture Notes in Math., 1342, Springer, Berlin-New York, 1988. [MR 90i: 28031].<\/li>\n<li>&#8220;A structure theorem for n-to-1 nonsingular endomorphisms and existence of non-recurrent measures,&#8221; with S. Eigen, J. London Math. Soc. (2) 40 (1989), 441-451. [MR 91e:28013].<\/li>\n<li>&#8220;On \u00b5-recurrent nonsingular endomorphisms,&#8221; Israel J. Math. 61 (1988), 1-13. [MR 89f:28042].<\/li>\n<li>&#8220;Truncated ergodic theorems for nonsingular transformations,&#8221; Rocky Mountain J. Math. 20 (1) (1990), 223-241. [Mathematical Reviews 91f:28011].<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&#8220;Rank-one transformations, odometers, and finite factors,&#8221;\u00a0 with Matthew Foreman, Su Gao, Aaron Hill, Benjamin Weiss, Isr. J. Math. (2022). https:\/\/doi.org\/10.1007\/s11856-022-2451-y. &#8220;Nonsingular transformations that are ergodic with isometric coefficients and not weakly doubly ergodic,&#8221; with Beatrix Haddock, James Leng, Indag. Math. &hellip; <a href=\"https:\/\/sites.williams.edu\/csilva\/publications\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2001,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-48","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.williams.edu\/csilva\/wp-json\/wp\/v2\/pages\/48","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.williams.edu\/csilva\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.williams.edu\/csilva\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/csilva\/wp-json\/wp\/v2\/users\/2001"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/csilva\/wp-json\/wp\/v2\/comments?post=48"}],"version-history":[{"count":10,"href":"https:\/\/sites.williams.edu\/csilva\/wp-json\/wp\/v2\/pages\/48\/revisions"}],"predecessor-version":[{"id":115,"href":"https:\/\/sites.williams.edu\/csilva\/wp-json\/wp\/v2\/pages\/48\/revisions\/115"}],"wp:attachment":[{"href":"https:\/\/sites.williams.edu\/csilva\/wp-json\/wp\/v2\/media?parent=48"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}