{"id":19,"date":"2012-09-05T11:22:25","date_gmt":"2012-09-05T15:22:25","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/template\/?page_id=19"},"modified":"2026-09-14T11:34:55","modified_gmt":"2026-09-14T15:34:55","slug":"publications","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/mathguy\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"\n<section class=\"fullwidth-text-block\"><div class=\"container px-0\"><div class=\"row align-items-start\"><div class=\"col-12\">\n<h1 class=\"wp-block-heading\">Publications &amp; Scholarship<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\nMy scholarly work has included research in dynamical systems and topology as well as\nmore recent work growing out of undergraduate mentoring, computational mathematics,\nand applications of artificial intelligence.\n<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Refereed Research<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\nMy research in dynamical systems and topology has focused in part on the relationship\nbetween mapping classes, topological entropy, and mathematical models of fluid mixing.\n<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\n<strong>Philip L. Boyland and Jason C. Harrington.<\/strong>\n<a href=\"https:\/\/doi.org\/10.2140\/agt.2011.11.2265\">\n\u201cThe Entropy Efficiency of Point-Push Mapping Classes on the Punctured Disk.\u201d\n<\/a>\n<em>Algebraic &amp; Geometric Topology<\/em>,\n11(4), 2265\u20132296, 2011.\n<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\nThis work studies topological entropy and the efficiency of point-push mapping classes,\nmotivated by the problem of mixing a fluid using a moving stirrer among fixed obstacles.\n<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Undergraduate Research &amp; Educational Scholarship<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\nMore recently, my scholarly work has developed through undergraduate mentoring and\nprojects connecting mathematics, computer science, and artificial intelligence.\n<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\n<strong>Divij Goyal and Jason C. Harrington.<\/strong>\n\u201c<em>Navigating the Swamp: Enhancing Student Involvement at UF through AI-Driven Event Navigation.<\/em>\u201d\n<em>University of Florida Journal of Undergraduate Research<\/em>,\n<strong>in press<\/strong>.\n<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\nThis project grew out of the University of Florida AI Scholars Program and explored\nthe use of artificial intelligence to help students discover campus organizations,\nactivities, and events. I served as the faculty mentor for the project, working with\nundergraduate researcher Divij Goyal from project development through publication.\n<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Current Scholarly Interests<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Computational mathematics and numerical analysis<\/li>\n\n\n\n<li>Dynamical systems and topology<\/li>\n\n\n\n<li>Mathematical models of mixing<\/li>\n\n\n\n<li>Artificial intelligence in mathematics education<\/li>\n\n\n\n<li>Undergraduate research and interdisciplinary computing projects<\/li>\n<\/ul>\n<\/div><\/div><\/div><\/section>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":634,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-19","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/pages\/19","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/users\/634"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/comments?post=19"}],"version-history":[{"count":7,"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/pages\/19\/revisions"}],"predecessor-version":[{"id":483,"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/pages\/19\/revisions\/483"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/mathguy\/wp-json\/wp\/v2\/media?parent=19"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}