{"id":6,"date":"2018-08-22T00:41:27","date_gmt":"2018-08-22T00:41:27","guid":{"rendered":"https:\/\/my.vanderbilt.edu\/alexcameron\/publications\/"},"modified":"2018-08-22T15:18:24","modified_gmt":"2018-08-22T20:18:24","slug":"publications","status":"publish","type":"page","link":"https:\/\/my.vanderbilt.edu\/alexcameron\/publications\/","title":{"rendered":"Research"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-31\" src=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/2889\/2018\/08\/mathstuff.jpg\" alt=\"math stuff\" width=\"300\" height=\"232\" \/><\/p>\n<p>My research interests are primarily in graph theory and combinatorics. In particular, I work on Ramsey theory and extremal problems for graphs, hypergraphs, and other combinatorial structures. I am also interested in working on open problems from finite model theory, complexity theory, and the developing area of graph limits. Feel free to read my <a href=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/2889\/2018\/08\/CameronResearch.pdf\">research statement<\/a> for more information.<\/p>\n<p>Here is a list of my papers. The papers have links to pdf versions where available. Any comments or ideas are welcome!<\/p>\n<p><strong>Published Papers<\/strong><\/p>\n<ul>\n<li><strong>A (5,5)-colouring of the complete graph with few colours\u00a0<\/strong> (with <a href=\"https:\/\/math.illinois.edu\/directory\/profile\/eheath3\">Emily Heath<\/a>), <em>Combinatorics, Probability and Computing<\/em>, Cambridge University Press (2018).\u00a0<a href=\"https:\/\/doi.org\/10.1017\/S0963548318000172\">Published version<\/a>\u00a0and early\u00a0<a href=\"https:\/\/arxiv.org\/pdf\/1702.06227.pdf\">arXiv version<\/a>.<\/li>\n<li><strong>Extremal numbers for directed hypergraphs with two edges<\/strong>, <em>The Electronic Journal of Combinatorics<\/em>, 25(1), P1.56 (2018). <a href=\"http:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p56\">Published version<\/a> (Free, but requires account) and\u00a0early arXiv version: <a href=\"http:\/\/arxiv.org\/pdf\/1607.04930v1.pdf\">part 1<\/a>,\u00a0<a href=\"http:\/\/arxiv.org\/pdf\/1607.04932v1.pdf\">part 2<\/a>.<\/li>\n<li><strong>Counting ring homomorphisms<\/strong>, <em>The Pi Mu Epsilon Journal<\/em>, 13:2(Spring 2010), 65\u201367.<\/li>\n<\/ul>\n<p><strong>Other Papers<\/strong><\/p>\n<ul>\n<li><strong>An explicit edge-coloring of the complete graph with six colors on every 5-clique<\/strong>, submitted (2018). <a href=\"https:\/\/arxiv.org\/pdf\/1704.01156.pdf\">arXiv version<\/a>.<\/li>\n<li><strong>Extremal problems on generalized directed hypergraphs<\/strong>, a set of research notes (2016). <a href=\"http:\/\/arxiv.org\/pdf\/1607.04927v1.pdf\">arXiv version<\/a>.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>My research interests are primarily in graph theory and combinatorics. In particular, I work on Ramsey theory and extremal problems for graphs, hypergraphs, and other combinatorial structures. I am also interested in working on open problems from finite model theory, complexity theory, and the developing area of graph limits. Feel free to read my research&#8230;<\/p>\n","protected":false},"author":7665,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[],"class_list":["post-6","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/my.vanderbilt.edu\/alexcameron\/wp-json\/wp\/v2\/pages\/6","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/my.vanderbilt.edu\/alexcameron\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/my.vanderbilt.edu\/alexcameron\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/alexcameron\/wp-json\/wp\/v2\/users\/7665"}],"replies":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/alexcameron\/wp-json\/wp\/v2\/comments?post=6"}],"version-history":[{"count":8,"href":"https:\/\/my.vanderbilt.edu\/alexcameron\/wp-json\/wp\/v2\/pages\/6\/revisions"}],"predecessor-version":[{"id":49,"href":"https:\/\/my.vanderbilt.edu\/alexcameron\/wp-json\/wp\/v2\/pages\/6\/revisions\/49"}],"wp:attachment":[{"href":"https:\/\/my.vanderbilt.edu\/alexcameron\/wp-json\/wp\/v2\/media?parent=6"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/alexcameron\/wp-json\/wp\/v2\/tags?post=6"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}