{"id":1750,"date":"2009-03-24T20:07:22","date_gmt":"2009-03-25T01:07:22","guid":{"rendered":"http:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=1750"},"modified":"2009-03-24T20:07:22","modified_gmt":"2009-03-25T01:07:22","slug":"latest-langlands","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=1750","title":{"rendered":"Latest Langlands"},"content":{"rendered":"<p>The <a href=\"http:\/\/sunsite.ubc.ca\/DigitalMathArchive\/Langlands\/\">site at UBC<\/a> collecting the work of Robert Langlands is now no longer being maintained. There&#8217;s a <a href=\"http:\/\/publications.ias.edu\/rpl\/\">new site<\/a> now at the IAS.  It includes some interesting recent short articles of various kinds that I hadn&#8217;t seen before, including a <a href=\"http:\/\/publications.ias.edu\/rpl_works\/L12\/shaw\/photoshell.pdf\">short autobiographical memoir<\/a>, an <a href=\"http:\/\/publications.ias.edu\/rpl_works\/L12\/pls\/pls-ps.pdf\">expository piece<\/a> written for <em>Pour La Science<\/em>, and <a href=\"http:\/\/publications.ias.edu\/rpl_works\/L12\/shaw\/reflexionsshell.pdf\">another piece<\/a> which includes extensive speculative remarks about his current thinking on the topic of the &#8220;Langlands Program&#8221;.<\/p>\n<p>The expository piece includes remarks about the remarkable centrality of representation theory both in number theory and quantum theory:<\/p>\n<blockquote><p>La le&ccedil;on que nous voulons tirer de ce dicton, \u201cil se trouve derri&egrave;re tout nombre quantique une representation d\u2019un groupe\u201d, c\u2019est que tomber en math&eacute;matiques ou en physique sur les repr&eacute;sentations d\u2019un groupe, c\u2019est souvent tomber sur une veine d\u2019or &agrave; laquelle il faut tenir corps et &acirc;me.<\/p><\/blockquote>\n<p>(&#8220;The lesson we would like to draw from this motto [due to Weyl] &#8216;behind every quantum number is a group representation&#8217;, is that when one comes upon group representations in mathematics or physics, one has often come upon a vein of gold, which one must pursue body and soul.&#8221;)<\/p>\n<p>On the geometric Langlands front, earlier this month the Clay Mathematics Institute organized a <a href=\"http:\/\/www.claymath.org\/programs\/claylecturesmath\/2009CLM\/\">series of talks<\/a> at RIMS in Kyoto by Bezrukavnikov, Gaitsgory and Nakajima about various aspects of the subject.  Unfortunately notes from the lectures don&#8217;t seem to be available anywhere that I have looked.<\/p>\n<p>Last week the KITP in Santa Barbara hosted a mini-conference on <a href=\"http:\/\/online.kitp.ucsb.edu\/online\/duality09\/\">Dualities in Physics and Mathematics<\/a>, with some of the talks devoted to topics relating geometric Langlands and quantum field theory. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>The site at UBC collecting the work of Robert Langlands is now no longer being maintained. There&#8217;s a new site now at the IAS. It includes some interesting recent short articles of various kinds that I hadn&#8217;t seen before, including &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=1750\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1750","post","type-post","status-publish","format-standard","hentry","category-langlands"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/1750","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1750"}],"version-history":[{"count":8,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/1750\/revisions"}],"predecessor-version":[{"id":1758,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/1750\/revisions\/1758"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1750"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1750"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}