{"id":4,"date":"2023-06-16T09:28:10","date_gmt":"2023-06-16T13:28:10","guid":{"rendered":"https:\/\/sites.temple.edu\/lang\/?page_id=4"},"modified":"2025-07-23T17:05:26","modified_gmt":"2025-07-23T21:05:26","slug":"papers","status":"publish","type":"page","link":"https:\/\/sites.temple.edu\/lang\/papers\/","title":{"rendered":"Papers"},"content":{"rendered":"\n<ul class=\"wp-block-list\">\n<li>The Eisenstein ideal at prime-square level has constant rank, with <a href=\"https:\/\/sites.google.com\/msu.edu\/prestonwake\" data-type=\"link\" data-id=\"https:\/\/sites.google.com\/msu.edu\/prestonwake\">P. Wake<\/a>, <em>Proceedings of the National Academy of Sciences<\/em>, 2025  (<a href=\"https:\/\/arxiv.org\/abs\/2501.04162\" data-type=\"link\" data-id=\"https:\/\/arxiv.org\/abs\/2501.04162\">arXiv<\/a>, <a href=\"https:\/\/www.pnas.org\/doi\/10.1073\/pnas.2500729122\">journal<\/a>)<\/li>\n\n\n\n<li>Big images of two-dimensional pseudorepresentations, with <a href=\"https:\/\/sites.google.com\/site\/andreacontimath\/\">A. Conti<\/a>, <a href=\"https:\/\/math.bu.edu\/people\/medved\/\">A. Medvedovsky<\/a>, <em>Mathematische Annalen<\/em>, 2023 (<a href=\"https:\/\/arxiv.org\/abs\/1904.10519\">arXiv<\/a>, <a href=\"https:\/\/link.springer.com\/article\/10.1007\/s00208-021-02345-w\">journal<\/a>, <a href=\"https:\/\/sites.temple.edu\/lang\/files\/2023\/06\/Lang_algebraische_zahlentheorie.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Oberwolfach report<\/a>, <a href=\"https:\/\/sites.temple.edu\/lang\/files\/2023\/06\/CNTAtalk.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">slides<\/a>)<\/li>\n\n\n\n<li>A modular construction of unramified p-extensions of <strong>Q<\/strong>(N<sup>1\/p<\/sup>), with <a href=\"https:\/\/sites.google.com\/msu.edu\/prestonwake\/home\">P. Wake<\/a>, <em>Proceedings of the AMS, Series B<\/em>, 2022 (<a href=\"https:\/\/arxiv.org\/abs\/2109.04308\">arXiv<\/a>, <a href=\"https:\/\/www.ams.org\/journals\/bproc\/2022-09-39\/S2330-1511-2022-00141-X\/\">journal<\/a>)<\/li>\n\n\n\n<li><strong>A<\/strong><sub>inf<\/sub> is infinite dimensional, with <a href=\"https:\/\/www.judith-ludwig.com\">J. Ludwig<\/a>, <em>Journal of the Institute of Mathematics of Jussieu<\/em>, 2021 (<a href=\"https:\/\/arxiv.org\/abs\/1906.03583\">arXiv<\/a>, <a href=\"https:\/\/www.cambridge.org\/core\/journals\/journal-of-the-institute-of-mathematics-of-jussieu\/article\/mathbbatextinf-is-infinite-dimensional\/41E4C7B898226B0CE567A17590B18BB8\">journal<\/a>)<\/li>\n\n\n\n<li>Chow motives associated to certain algebraic Hecke characters, with <a href=\"https:\/\/sites.google.com\/view\/laureflapan\/home\">L. Flapan<\/a>, <em>Transactions of the AMS, Series B<\/em>, 2018 (<a href=\"https:\/\/arxiv.org\/abs\/1708.03145\">arXiv<\/a>, <a href=\"https:\/\/www.ams.org\/journals\/btran\/2018-05-05\/S2330-0000-2018-00027-9\/?active=current\">journal<\/a>)<\/li>\n\n\n\n<li>On the image of the Galois representation associated to a non-CM Hida family, <em>Algebra and Number Theory<\/em>, 2016 (<a href=\"https:\/\/arxiv.org\/abs\/1409.8651\">arXiv<\/a>, <a href=\"https:\/\/msp.org\/ant\/2016\/10-1\/p06.xhtml\">journal<\/a>, <a href=\"https:\/\/sites.temple.edu\/lang\/files\/2023\/06\/BU2015.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">slides<\/a>, <a href=\"https:\/\/sites.temple.edu\/lang\/files\/2023\/06\/BUposter.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">poster<\/a>)<\/li>\n\n\n\n<li>Shadow lines in the arithmetic of elliptic curves, with <a href=\"http:\/\/math.bu.edu\/people\/jbala\/\">J. Balakrishnan<\/a>, <a href=\"https:\/\/web.ma.utexas.edu\/users\/mirela\/\">M. \u00c7iperiani<\/a>, B. Mirza, <a href=\"https:\/\/racheldominica.wordpress.com\">R. Newton<\/a>, <em>Directions in Number Theory<\/em>, 2016 (<a href=\"https:\/\/arxiv.org\/abs\/1610.08729\">arXiv<\/a>, <a href=\"https:\/\/link.springer.com\/chapter\/10.1007\/978-3-319-30976-7_2\">article<\/a>)<\/li>\n\n\n\n<li>Functions with class number indivisible by a prime l, with M. Daub, <a href=\"https:\/\/www2.math.upenn.edu\/~mmerling\/\">M. Merling<\/a>, N. Pitiwan, <a href=\"https:\/\/web.williams.edu\/Mathematics\/apacelli\/\">A. Pacelli<\/a>, <a href=\"https:\/\/www.brown.edu\/academics\/math\/people\/michael-rosen\">M. Rosen<\/a>, <em>Acta Arithmetica<\/em>, 2011 (<a href=\"https:\/\/arxiv.org\/abs\/0906.3728\">arXiv<\/a>, <a href=\"https:\/\/www.impan.pl\/en\/publishing-house\/journals-and-series\/acta-arithmetica\/all\/150\/4\/83249\/function-fields-with-class-number-indivisible-by-a-prime-ell\">journal<\/a>)<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Other writings<\/h2>\n\n\n\n<p>Here are major papers I&#8217;ve written for various degrees.  I provide them only as encouragement for current students in similar programs; I do not recommend them as your primary source to learn any particular topic they cover!<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>Images of Galois representations associated to p-adic families of modular forms<\/em>, <a href=\"https:\/\/sites.temple.edu\/lang\/files\/2023\/06\/Lang_thesis.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">PhD thesis<\/a> at UCLA, 2016, supervised by <a href=\"https:\/\/www.math.ucla.edu\/~hida\/\">Haruzo Hida<\/a><\/li>\n\n\n\n<li><em>Two-descent on the Jacobians of <\/em><i>hyperelliptic<\/i><em> curves<\/em>, <a href=\"https:\/\/sites.temple.edu\/lang\/files\/2023\/06\/partiiiessay.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Part III essay<\/a> at Cambridge, 2010, supervised by <a href=\"https:\/\/www.dpmms.cam.ac.uk\/~taf1000\/\">Tom Fisher<\/a><\/li>\n\n\n\n<li><em>Properties of class groups of a family of cyclic cubic fields<\/em>, <a href=\"https:\/\/sites.temple.edu\/lang\/files\/2023\/06\/mathesis.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">MA thesis<\/a> at Bryn Mawr, 2009, supervised by <a href=\"https:\/\/www.brynmawr.edu\/inside\/people\/helen-g-grundman\">Helen Grundman<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Other writings Here are major papers I&#8217;ve written for various degrees. I provide them only as encouragement for current students in similar programs; I do not recommend them as your primary source to learn any particular topic they cover!<\/p>\n","protected":false},"author":32768,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.temple.edu\/lang\/wp-json\/wp\/v2\/pages\/4","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.temple.edu\/lang\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.temple.edu\/lang\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.temple.edu\/lang\/wp-json\/wp\/v2\/users\/32768"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.temple.edu\/lang\/wp-json\/wp\/v2\/comments?post=4"}],"version-history":[{"count":6,"href":"https:\/\/sites.temple.edu\/lang\/wp-json\/wp\/v2\/pages\/4\/revisions"}],"predecessor-version":[{"id":85,"href":"https:\/\/sites.temple.edu\/lang\/wp-json\/wp\/v2\/pages\/4\/revisions\/85"}],"wp:attachment":[{"href":"https:\/\/sites.temple.edu\/lang\/wp-json\/wp\/v2\/media?parent=4"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}