{"id":10,"date":"2023-04-17T14:16:06","date_gmt":"2023-04-17T14:16:06","guid":{"rendered":"https:\/\/commons.mtholyoke.edu\/toriday\/?page_id=10"},"modified":"2026-08-07T14:06:21","modified_gmt":"2026-08-07T14:06:21","slug":"teaching","status":"publish","type":"page","link":"https:\/\/commons.mtholyoke.edu\/toriday\/teaching\/","title":{"rendered":"Research"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><span style=\"text-decoration: underline\">Mathematics Research:<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">I am a number theorist and enjoy studying Galois representations, modular forms, and elliptic curves. I really enjoy problems that blend computation and theory. More specifically, I am currently studying entanglement fields of elliptic curves. Recently, I have also become interested in arithmetic dynamics.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Papers<\/strong>: <br><em><a href=\"https:\/\/arxiv.org\/pdf\/2403.03073\">Entanglement  of elliptic curves upon base extension<\/a> <\/em>(with <a href=\"https:\/\/www.math.union.edu\/~gajekler\/?_gl=1*173voqd*_ga*MTI0MDMzNDcwLjE2ODEyMjQ4MjE.*_ga_QDTJMT872K*MTY4MzQwNTY5MS4yLjAuMTY4MzQwNTY5MS4wLjAuMA..&amp;_ga=2.98259867.5079043.1683405692-124033470.1681224821\">R. Gajek-Leonard<\/a>) &#8211; <em>International Journal of Number Theory<\/em>, 21(06), 1297\u20131315. https:\/\/doi.org\/10.1142\/S1793042125500678 (2025)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em><a href=\"https:\/\/arxiv.org\/pdf\/2409.10467\">Dynamical Irreducibility of Certain Polynomials Over Finite Fields<\/a> <\/em>(with <a href=\"https:\/\/math.colorado.edu\/~rede4151\/index.html\">R. DeLand<\/a>, <a href=\"https:\/\/sites.google.com\/view\/jamiejuul\">J. Juul<\/a> , <a href=\"https:\/\/cigole.github.io\/\">C. Thomas<\/a> , <a href=\"https:\/\/biancasmath.wordpress.com\/\">B. Thompson<\/a> , and <a href=\"https:\/\/www.bellatobin.com\/\">B. Tobin<\/a>) [project from <a href=\"https:\/\/sites.google.com\/view\/rethinkingnumbertheory\/home\">RNT 4 <\/a> ] &#8211; <em>Finite Fields and Their Applications<\/em>, 108, 102666. https:\/\/doi.org\/10.1016\/j.ffa.2025.102666 (2025)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"text-decoration: underline\">Scholarship of Teaching and Learning (SOTL)<\/span>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">As a mathematics educator, I enjoy learning about how students learn and developing innovative pedagogy (especially when that pedagogy lets me collaborate with other campus partners). I am also interested in applying queer theory and queer pedagogy to the higher ed math classroom. Most recently, I&#8217;ve been participating in workshops through <a href=\"https:\/\/www.mtholyoke.edu\/academics\/centers-and-facilities\/intergroup-dialogue-center\">MHC&#8217;s IGD Center<\/a> to learn more about integroup dialogue pedagogy. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Papers:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em><a href=\"https:\/\/digitaleditions.walsworthprintgroup.com\/publication\/?i=863612&amp;p=1&amp;view=issueViewer\">How can your writing center make your math students better mathematicians?<\/a><\/em>  (with <a href=\"https:\/\/www.mtholyoke.edu\/directory\/faculty-staff\/jordan-lassonde-16\">J.E.Lassonde<\/a> ) <em>MAA Focus<\/em>, 46(2), 54\u201356.&nbsp;(2026)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"text-decoration: underline\">With Students<\/span>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">I love working with students on research problems! If you are interested in learning more about number theory or getting involved in a research project with me, please reach out. Here is a short list of students I have worked and their project topics:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Anita Chiragia &#8217;28: worked on writing and using Sage code to compute the cartographic group of a given bipartite graph (alternatively, monodromy group of a given dessin d&#8217;enfant) [Summer 2026]<\/li>\n\n\n\n<li>Namuuna Negi &#8217;27: worked on constructing trees given a partition of 2n and computing their cartographic groups [Summer 2026]<\/li>\n\n\n\n<li>Minh Le &#8217;28: worked on generalizing an algorithm to look for dynamically irreducible cubics over finite fields and collecting data with that algorithm [Summer 2025]<\/li>\n\n\n\n<li>Tram Nguyen &#8217;28: worked on looking for dynamically irreducible quartic polynomials over finite fields [Summer 2025]<br><br><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><br><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><br><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mathematics Research: I am a number theorist and enjoy studying Galois representations, modular forms, and elliptic curves. I really enjoy problems that blend computation and theory. More specifically, I am currently studying entanglement fields of elliptic curves. Recently, I have also become interested in arithmetic dynamics. Papers: Entanglement of elliptic curves upon base extension (with [&hellip;]<\/p>\n","protected":false},"author":2098,"featured_media":0,"parent":0,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"footnotes":""},"class_list":["post-10","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/commons.mtholyoke.edu\/toriday\/wp-json\/wp\/v2\/pages\/10","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/commons.mtholyoke.edu\/toriday\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/commons.mtholyoke.edu\/toriday\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/commons.mtholyoke.edu\/toriday\/wp-json\/wp\/v2\/users\/2098"}],"replies":[{"embeddable":true,"href":"https:\/\/commons.mtholyoke.edu\/toriday\/wp-json\/wp\/v2\/comments?post=10"}],"version-history":[{"count":14,"href":"https:\/\/commons.mtholyoke.edu\/toriday\/wp-json\/wp\/v2\/pages\/10\/revisions"}],"predecessor-version":[{"id":103,"href":"https:\/\/commons.mtholyoke.edu\/toriday\/wp-json\/wp\/v2\/pages\/10\/revisions\/103"}],"wp:attachment":[{"href":"https:\/\/commons.mtholyoke.edu\/toriday\/wp-json\/wp\/v2\/media?parent=10"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}