{"id":2826,"date":"2011-09-22T20:09:44","date_gmt":"2011-09-22T18:09:44","guid":{"rendered":"https:\/\/wpethzprd.ethz.ch\/kowalski\/?p=2826"},"modified":"2024-02-20T13:40:36","modified_gmt":"2024-02-20T11:40:36","slug":"expanders-course","status":"publish","type":"post","link":"https:\/\/blogs.ethz.ch\/kowalski\/2011\/09\/22\/expanders-course\/","title":{"rendered":"Expanders course"},"content":{"rendered":"<p>I am teaching a class on expander graphs this semester, and as usual there is <a href=\"http:\/\/www.math.ethz.ch\/~kowalski\/expanders.html\">a web page<\/a> about it. For the moment, do not be fooled by the link to &#8220;lecture notes&#8221;, since I haven&#8217;t put up anything yet (I am trying to learn the easiest way to incorporate nice pictures of graphs in LaTeX; <a href=\"http:\/\/altermundus.com\/pages\/tkz\/index.html\">tkz-graph and tkz-berge<\/a> seem to be the best way to do that&#8230;) <\/p>\n<p>The course meets only 2 hours per week (and those are ETH hours, which means 1h30 really), so it will necessarily be very restricted in what I can cover. I have decided on the content of the first two parts: a general discussion of elementary material (of course), and then a full account of the combination of the results of Helfgott and Bourgain&#8211;Gamburd, which together imply that the family of Cayley graphs of $latex \\mathrm{SL}_2(\\mathbf{F}_{p})$, with respect to the projections modulo primes $latex p$ of a subset $latex S\\subset \\mathrm{SL}_2(\\mathbf{Z})$ which generates a Zariski-dense subgroup of $latex \\mathrm{SL}_2$, is an expander family. <\/p>\n<p>If there is time after this, which I hope, I haven&#8217;t quite decided what to do. One possibility would be an account of the &#8220;expander philosophy&#8221; discussed at the end of <a href=\"https:\/\/blogs.ethz.ch\/kowalski\/2010\/09\/01\/esperantism-expands-but-not-so-quickly\/\">this post<\/a>, another would be to discuss some applications to theoretical computer science (admittedly, this would be because I would learn about them much more than I know at the current time&#8230;)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I am teaching a class on expander graphs this semester, and as usual there is a web page about it. For the moment, do not be fooled by the link to &#8220;lecture notes&#8221;, since I haven&#8217;t put up anything yet (I am trying to learn the easiest way to incorporate nice pictures of graphs in &hellip; <a href=\"https:\/\/blogs.ethz.ch\/kowalski\/2011\/09\/22\/expanders-course\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Expanders course<\/span><\/a><\/p>\n","protected":false},"author":625,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[157,2],"tags":[],"class_list":["post-2826","post","type-post","status-publish","format-standard","hentry","category-eth","category-blogroll"],"_links":{"self":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts\/2826","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/users\/625"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/comments?post=2826"}],"version-history":[{"count":0,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/posts\/2826\/revisions"}],"wp:attachment":[{"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/media?parent=2826"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/categories?post=2826"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ethz.ch\/kowalski\/wp-json\/wp\/v2\/tags?post=2826"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}