{"id":2,"date":"2024-04-16T18:04:13","date_gmt":"2024-04-16T18:04:13","guid":{"rendered":"https:\/\/math.hmc.edu\/arvm\/?page_id=2"},"modified":"2025-01-22T23:39:56","modified_gmt":"2025-01-22T23:39:56","slug":"research","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/arvm\/research\/","title":{"rendered":"Research &amp; Writing"},"content":{"rendered":"\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>Research Interests:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Algebraic, enumerative, and geometric combinatorics.<\/li>\n\n\n\n<li>Scholarship of teaching and learning.<\/li>\n\n\n\n<li>Quantitative justice.<\/li>\n<\/ul>\n<\/blockquote>\n\n\n\n<p>Please use the navigation menu or click on the following for my scholarly works:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/math.hmc.edu\/arvm\/math-articles\/\" data-type=\"page\" data-id=\"165\">Mathematics Articles &amp; Theses<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/math.hmc.edu\/arvm\/interdisciplinary\/\" data-type=\"page\" data-id=\"128\">Writing on Mathematics, Education, Culture, and Society<\/a><\/li>\n\n\n\n\n<p><br><\/p>\n\n\n\n<p><strong>Keywords of Mathematical Interests:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Triangulations, subdivisions, and volume of lattice and rational polytopes and cones.<\/li>\n\n\n\n<li>Ehrhart theory: (local) h*-polynomials, quasi-polynomials, Equivariant Ehrhart theory, Ehrhart positivity.<\/li>\n\n\n\n<li>Catalan Combinatorics: generating functions, trees, standard Young tableaux, integer partitions, q-analogs, Dyck paths, generalizations of parking functions, Narayana numbers.<\/li>\n\n\n\n<li>Combinatorics of Posets: lattices, chains, order ideals, rank generating functions, meet-irreducibles.<\/li>\n\n\n\n<li>Geometric combinatorics: matroids, hyperplane arrangements, symmetry.<\/li>\n\n\n\n<li>Polynomial properties: real-rootedness, gamma-positivity, symmetric decompositions.<\/li>\n\n\n\n<li>Symmetric functions: chromatic symmetric functions, q- and q,t-analogs.&nbsp;<\/li>\n\n\n\n<li>Critical group of graphs and chip-firing.<\/li>\n\n\n\n<li>Data science and mathematics for social justice: data analysis, interdisciplinary study (e.g., social science, history, economics), and racial\/social issues.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Please use the navigation menu or click on the following for my scholarly works:<\/p>\n","protected":false},"author":29,"featured_media":341,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"tags":[],"class_list":["post-2","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/arvm\/wp-json\/wp\/v2\/pages\/2","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/arvm\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/arvm\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/arvm\/wp-json\/wp\/v2\/users\/29"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/arvm\/wp-json\/wp\/v2\/comments?post=2"}],"version-history":[{"count":67,"href":"https:\/\/math.hmc.edu\/arvm\/wp-json\/wp\/v2\/pages\/2\/revisions"}],"predecessor-version":[{"id":687,"href":"https:\/\/math.hmc.edu\/arvm\/wp-json\/wp\/v2\/pages\/2\/revisions\/687"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/arvm\/wp-json\/wp\/v2\/media\/341"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/arvm\/wp-json\/wp\/v2\/media?parent=2"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/arvm\/wp-json\/wp\/v2\/tags?post=2"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}