<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN" "http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd"> <html> <head> <link rel="stylesheet" type="text/css" href="iphone.css" charset="utf-8" media="only screen and (max-device-width: 480px)" /> <link rel="stylesheet" type="text/css" href="desktop.css" charset="utf-8" media="screen and (min-width: 481px)" /> <meta name="viewport" content="user-scalable=no, width=device-width" /> <title>Patrick Ingram</title> </head> <body> <div id="picture"> <img src="me_eng.jpg" alt="Patrick Ingram"> </div> <div id="title"> <h1>Patrick Ingram</h1> <h2>Assistant Professor<br> York University </h2> </div> <div id="email"> <p>To e-mail me, type pingram and then @ and then yorku.ca (unless you're a bot!)</p> </div> <div id="research"> <h2>Research</h2> <p> My research is in number theory, and in particular diophantine geometry. My specific interests lie in the arithmetic of elliptic curves and surfaces, and in the theory of dynamical systems over global fields. </p> <h2>Publications</h2> <p>These are listed first by general topic, and then in approximate reverse chronological order. Please note that draft versions on the arXiv may differ from published versions, and only the journal versions are "official."</p> <h4>Arithmetic dynamics</h4> <ol> <li value="34"> <i>Critical orbits of polynomials with a periodic point of specified multiplier</i> <div class="indent">draft available on the <a class="paper" href="https://arxiv.org/abs/1706.05352">arxiv</a></div> <div class="indent">to appear in <a class="paper" href="https://link.springer.com/search?sortOrder=newestFirst&facet-content-type=Article&facet-journal-id=209"><i>Math. Zeitschrift</i></a></div> <li value="33"> <i>The critical height is a moduli height</i> <div class="indent">draft available on the <a class="paper" href="https://arxiv.org/abs/1610.07904">arXiv</a></div> <div class="indent"><a class="paper" href="https://projecteuclid.org/euclid.dmj/1520046165"><i>Duke Math. J.</i></a>, Volume 167, Number 7 (2018), pp. 1311-1346.</div> </li> <li value="32"> <i>p-adic uniformization and the action of Galois on certain affine correspondences</i> <div class="indent">draft available on the <a class="paper" href="https://arxiv.org/abs/1604.05197">arXiv</a></div> <div class="indent"><a class="paper" href="https://cms.math.ca/10.4153/CMB-2017-082-7"><i>Canadian Math. Bull.</i></a>, <a href="https://doi.org/10.4153/CMB-2017-082-7">https://doi.org/10.4153/CMB-2017-082-7</a> Volume 61 (2018), pp. 531-542</div> </li> <li value="31"> <i>Canonical heights and preperiodic points for weighted homogeneous families of polynomials</i> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/1510.08807">arXiv</a></div> <div class="indent"><a class="paper" href="https://academic.oup.com/imrn/advance-article/doi/10.1093/imrn/rnx291/4782491?guestAccessKey=52754711-b85e-4fff-9b71-ab0a1997eb62"><i>Int. Math. Res. Not.</i></a>, <a href="https://doi.org/10.1093/imrn/rnx291">https://doi.org/10.1093/imrn/rnx291</a>, Published: 12 January 2018</div> </li> <li value="30"> <i>Finite ramification for preimage fields of postcritically finite morphisms</i> <div class="indent">with <a href="http://www.math.rochester.edu/people/faculty/abridy/">Andrew Bridy</a>, <a href="http://www.people.carleton.edu/~rfjones/">Rafe Jones</a>, <a href="https://www.amherst.edu/people/facstaff/jjuul">Jamie Juul</a>, <a href="https://people.kth.se/~alonlevy/">Alon Levy</a>, <a href="http://www.math.hawaii.edu/~mmanes/">Michelle Manes</a>, <a href="http://math.stanford.edu/~simonr/"> Simon Rubinstein-Salzedo</a>, and <a href="http://www.math.brown.edu/~jhs/">Joseph H. Silverman</a> </div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/1511.00194">arXiv</a></div> <div class="indent"><a href="https://intlpress.com/site/pub/pages/journals/items/mrl/content/vols/0024/0006/a003/index.html"><i>Math. Research Letters</i></a>, Volume 24 (2017), Number 6</div> </li> <li value="29"> <i>Critical dynamics of variable-separated affine correspondences</i> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/1411.6954">arXiv</a></div> <div class="indent"><a class="paper" href="https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/jlms.12045"><i>J. London Math. Soc.</i></a>, Volume 95, Issue 3, June 2017, pp. 1011-1034</div> </li> <li value="28"> <i>Canonical heights for correspondences</i> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/1411.1041">arXiv</a></div> <div class="indent"><a class="paper" href=""><i>Trans. Amer. Math. Soc.</a>, DOI: <a href="https://doi.org/10.1090/tran/7288">https://doi.org/10.1090/tran/7288</a>, Published electronically: May 30, 2018</div> </li> <li value="27"> <i>Rigidity and height bounds for certain post-critically finite endomorphisms of projective space</i> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/1310.4114">arXiv</a></div> <div class="indent"><a href="http://cms.math.ca/10.4153/CJM-2015-045-x"><i>Canadian Journal of Mathematics</i></a>, Volume 68 (2016), pp. 625-654 <a href="https://cms.math.ca/MediaReleases/2018/GdeBRobinson18">(see also!)</a></div> </li> <li value="25"> <i>Variation of the canonical height for polynomials in several variables</i> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/1408.5416">arXiv</a></div> <div class="indent"><a href="http://imrn.oxfordjournals.org/content/early/2015/04/29/imrn.rnv121.full.pdf?ijkey=B9o3tzqoKcBN4za&keytype=ref"><i>International Mathematics Research Notices</i></a>, Vol. 2015, No. 24, pp. 13545-13562</div> </li> <li value="22"> <i>Attracting cycles in p-adic dynamics and height bounds for post-critically finite maps</i> <div class="indent">with <a href="http://www.cs.amherst.edu/~rlb/">Rob Benedetto</a>, <a href="http://www.people.carleton.edu/~rfjones/">Rafe Jones</a>, and <a href="https://people.kth.se/~alonlevy/">Alon Levy</a></div> <div class="indent"><a href="http://projecteuclid.org/euclid.dmj/1412168847"><i>Duke Mathematical Journal</i></a>, Volume 163, Number 13 (2014), pp. 2325-2356.</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/1201.1605">arXiv</a></div> </li> <li value="21"> <i>Canonical heights for Hnon maps</i> <div class="indent"><a href="http://plms.oxfordjournals.org/content/early/2013/07/22/plms.pdt026.abstract?sid=a7c3b67d-1cef-4aa0-8288-3336ca6e0a84"><i>Proceedings of the London Mathematical Society</i></a>, Volume 108 (2014), no. 3, pp. 780-808.</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/1111.3609">arXiv</a></div> </li> <li value="19"> <i>Arboreal Galois representations and uniformization of polynomial dynamics</i> <div class="indent"><a href="http://blms.oxfordjournals.org/content/45/2/301.abstract?sid=54da9b9f-551e-45b1-8e32-c755cc6399ad"><i>Bulletin of the London Mathematical Society</i></a>, Volume 45 (2013), no. 2, pp. 301-308.</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/1111.3607">arXiv</a></div> </li> <li value="18"> <i>A finiteness result for post-critically finite polynomials</i> <div class="indent"><a href="http://imrn.oxfordjournals.org/content/2012/3/524.abstract?sid=8c6f391b-1998-4d2a-9480-1372ead59072"><i>International Mathematics Research Notices</i></a>, issue 3 (2012), pp. 524-543.</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/1010.3393">arXiv</a></div> </li> <li value="17"> <i>Variation of the canonical height for a family of polynomials</i> <div class="indent"><a href="http://www.degruyter.com/view/j/crelle.ahead-of-print/crelle-2012-0017/crelle-2012-0017.xml?format=INT"><i>Journal fur die reine und angewandte Mathematik</i></a>, Volume 685 (2013), pp. 73-97. </div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/1003.4225">arXiv</a></div> </li> <li value="16"> <i>Cubic polynomials with periodic cycles of a specified multiplier</i> <div class="indent"><a href="http://cms.math.ca/10.4153/CJM-2011-093-8"><i> Canadian Journal of Mathematics</i></a>, <b>64</b> no. 2 (2012), pp. 318-345</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/0909.5408">arXiv</a></div> </li> <li value="14"> <i>On Poonen's conjecture concerning rational preperiodic points of quadratic maps</i> <div class="indent">with <a href="http://my.fit.edu/~bhutz/">B. Hutz</a></div> <div class="indent"><a href="http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.rmjm/1370267185"><i>Rocky Mountain Journal of Mathematics</i></a>, Volume 43, Number 1 (2013), pp. 193-204.</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/0909.5050">arXiv</a> </div> </li> <li value="13"> <i>Uniform bounds on pre-images under quadratic dynamical systems</i> <div class="indent">with <a href="http://www.math.hawaii.edu/~xander/">X. W. C. Faber</a>, <a href="http://my.fit.edu/~bhutz/">B. Hutz</a>, <a href="http://www.people.carleton.edu/~rfjones/">R. Jones</a>, <a href="http://www.math.hawaii.edu/~mmanes/">M. Manes</a>, <a href="http://www.math.rochester.edu/people/faculty/ttucker/">T. J. Tucker</a>, and <a href="http://www.math.rutgers.edu/~zieve/">M. E. Zieve</a></div> <div class="indent"><a href="http://intlpress.com/site/pub/pages/journals/items/mrl/content/vols/0016/0001/00020407/index.html"><i>Mathematical Research Letters</i></a> <b>16</b> number 1 (2009), pp. 87-101</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/0805.0441">arXiv</a></div> </li> <li value="8"> <i>Lower bounds on the canonical height associated to the morphism f(z) = z^d + c</i> <div class="indent"><a href="http://link.springer.com/article/10.1007/s00605-008-0018-6"><i>Monatshefte f&#252;r Mathematik</i></a> <b>157</b> (2009), pp. 69-89</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/0709.4154">arXiv</a></div> </li> <li value="7"> <i>Primitive divisors in arithmetic dynamics</i> <div class="indent"> with <a href="http://www.math.brown.edu/~jhs">J. H. Silverman</a></div> <div class="indent"><a href="http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=3823104&fulltextType=RA&fileId=S0305004108001795"><i>Mathematical Proceedings of the Cambridge Philosophical Society</i></a> <b>146</b> issue 2 (2009), pp. 289-302</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/0707.2505">arXiv</a></div> </li> </ol> <h4>Drinfeld modules</h4> <ol> <li value="26"> <i>The torsion submodule of an abelian t-module</i> <div class="indent">in preparation</div> </li> <li value="24"> <i>The filled Julia set of a Drinfeld module and uniform bounds for torsion</i> <div class="indent">submitted, <a href="http://arxiv.org/abs/1210.3059">arXiv</a></div> </li> <li value="23"> <i>A lower bound for the canonical height associated to a Drinfeld module</i> <div class="indent"><a href="http://imrn.oxfordjournals.org/content/early/2013/05/24/imrn.rnt104.abstract?sid=ce62fe05-d550-4ba0-8859-94b795420a1f"><i>International Mathematics Research Notices</i></a>, to appear</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/1210.2340">arXiv</a></div> </li> </ol> <h4>Elliptic curves and surfaces</h4> <ol> <li value="15"> <i>Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group</i> <div class="indent"><a href="http://msp.org/ant/2011/5-4/p02.xhtml"><i>Algebra and Number Theory</i></a> <b>5</b> no. 4 (2011), pp. 465-493</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/0811.3109">arXiv</a></div> </li> <li value="10"> <i>Multiples of integral points on elliptic curves</i> <div class="indent"><a href="http://www.sciencedirect.com/science/article/pii/S0022314X08001492"><i>Journal of Number Theory</i></a> <b>129</b> issue 1 (2009), pp. 182-208</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/0802.2651">arXiv</a></div> </li> <li value="5"> <i>Approximating algebraic numbers by j-invariants of elliptic curves</i> <div class="indent"><i>Acta Arithmetica</i> <b>131</b> (2008), pp. 57-68</div> <div class="indent">draft <a class="paper" href="oldpapers/j_approx.pdf">available</a></div> </li> <li value="3"> <i>Diophantine analysis and torsion on elliptic curves</i> <div class="indent"><a class="paper" href="http://plms.oxfordjournals.org/cgi/reprint/pdl008?ijkey=zQYcGM7rG4FsBg5&keytype=ref"><i> Proceedings of the London Mathematical Society</i></a> <b>94</b> no. 1 (2007), pp. 137-154.</div> </li> <li value="1"> <i>Torsion subgroups of elliptic curves in short Weierstrass form</i> <div class="indent">with <a href="http://www.math.ubc.ca/~bennett">M. A. Bennett</a></div> <div class="indent"><a class="paper" href="http://www.ams.org/journals/tran/2005-357-08/S0002-9947-05-03629-9/home.html?pagingLink=%3Ca+href%3D%22%2Fepubsearch%2Fservlet%2FPubSearch%3Fco1%3Dand%26co2%3Dand%26co3%3Dand%26endmo%3D00%26f1%3Dmsc%26f2%3Dtitle%26f3%3Danywhere%26f4%3Dauthor%26pubname%3Dall%26sendit22%3DSearch%26sperpage%3D30%26ssort%3Dd%26startmo%3D00%26v4%3Dingram%26startRec%3D1%22%3Ehttps://www.facebook.com/ShiftDelivery"><i>Transactions of the American Mathematical Society</i></a> <b>357</b> no. 8 (2005), pp. 3325-3337</div> </li> </ol> <h4>Algebraic divisibility sequences</h4> <ol> <li value="20"> <i>Algebraic divisibility sequences over function fields</i> <div class="indent">with <a href=http://lmb.univ-fcomte.fr/rubrique.php3?id_rubrique=159">V. Mah</a>, <a href ="http://www.math.brown.edu/~jhs">J. H. Silverman</a>, <a href="http://math.colorado.edu/~kstange/">K. E. Stange</a>, <a href="http://www.warwick.ac.uk/~masjap/">M. Streng</a></div> <div class="indent"><a href="http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8610690&fulltextType=RA&fileId=S1446788712000092"><i>Journal of the Australian Mathematical Society</i></a><b>92</b> (2012), pp. 99-126</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/1105.5633">arXiv</a></div> </li> <li value="12"> <i>A quantitative primitive divisor result for elliptic divisibility sequences</i> <div class="indent"><a href="http://jtnb.cedram.org/jtnb-bin/item?id=JTNB_2009__21_3_609_0"><i>Journal de Thorie des Nombres de Bordeaux</i></a> <b>21</b> fascicule 3 (2009), pp. 609-634</div> </li> <li value="11"> <i>Primitive divisors on twists of the Fermat cubic</i> <div class="indent">with G. Everest and <a href="http://www.mth.uea.ac.uk/~h008/">S. Stevens</a></div> <div class="indent"><a href="http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=6559864&fulltextType=RA&fileId=S1461157000000024"><i>LMS Journal of Computation and Mathematics</i></a> <b>12</b> (2009), pp. 54-81</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/math/0703553">arXiv</a></div> </li> <li value="9"> <i>The uniform primality conjecture for elliptic curves</i> <div class="indent">with G. Everest, <a href=http://lmb.univ-fcomte.fr/rubrique.php3?id_rubrique=159">V. Mah</a>, and <a href="http://www.mth.uea.ac.uk/~h008/">S. Stevens</a></div> <div class="indent"><i>Acta Arithmetica</i> <b> 134</b> (2008), pp. 157-181</div> <div class="indent">draft available on the <a class="paper" href="http://arxiv.org/abs/0712.2696">arXiv</a></div> </li> <li value="6"> <i>Uniform estimates for primitive divisors in elliptic divisibility sequences</i> <div class="indent">with <a href ="http://www.math.brown.edu/~jhs">J. H. Silverman</a></div> <div class="indent"><a class="paper" href="http://www.springerlink.com/content/r1g6341070536723/"><i>Number Theory, Analysis and Geometry</i></a> Springer-Verlag, 2012</div> </li> <li value="4"> <i>Elliptic divisibility sequences over certain curves</i> <div class="indent"><a href="http://www.sciencedirect.com/science/article/pii/S0022314X06001910"><i>Journal of Number Theory</i></a> <b>123</b> issue 2 (2007), pp. 473-486</div> <div class="indent">Received one of twenty "Top Cited Article 2007 - 2011" awards from JNT</div> <div class="indent">a draft, fraught with errors, is <a class="paper" href="oldpapers/eds.pdf">available</a></div> </li> </ol> <h4>Solving diophantine equations</h4> <ol> <li value="2"> <i>On <i>k</i>-th power numerical centres</i> <div class="indent"><i>Comptes rendus mathematiques de l'Academie des sciences</i> (2006)</div> <div class="indent">a draft is <a class="paper" href="oldpapers/house.pdf">available</a></div> </li> </ol> </div> <div id="teaching"> <h2>Teaching</h2> <p>This winter (2018) I am teaching Math 1013 (Calculus) and Math 4161 (Cryptography). Information for both is on Moodle. </div> </body> </html>