{"id":13851,"date":"2024-02-28T16:44:21","date_gmt":"2024-02-28T21:44:21","guid":{"rendered":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=13851"},"modified":"2024-03-04T17:38:26","modified_gmt":"2024-03-04T22:38:26","slug":"a-new-approach-to-modularity","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=13851","title":{"rendered":"A New Approach to Modularity"},"content":{"rendered":"<p>I was assuming that Peter Scholze&#8217;s <a href=\"https:\/\/www.ias.edu\/event-series\/emmy-noether-lecture-series\">Emmy Noether lectures<\/a> at the IAS would be the big news about advances in the Langlands program this coming week, but an anonymous correspondent just sent me <a href=\"https:\/\/www.maths.ox.ac.uk\/node\/66503\">this link<\/a>.  Tomorrow Andrew Wiles will be giving a talk in Oxford on &#8220;A New Approach to Modularity&#8221;, with abstract:<\/p>\n<blockquote><p>In the 1960&#8217;s Langlands proposed a generalisation of Class Field Theory. I will review this and describe a new approach using the trace formua as well as some analytic arguments reminiscent of those used in the classical case. In more concrete terms the problem is to prove general modularity theorems, and I will explain the progress I have made on this problem.<\/p><\/blockquote>\n<p>I&#8217;m curious to hear from anyone who knows what this is about or can report tomorrow after the talk. Wiles does have a certain track record of unveiling unexpected huge progress in a talk like this&#8230;<\/p>\n<p><strong>Update<\/strong>:  Well, the talk should be over now. Sure someone who was there can let us know what happened?<\/p>\n<p><strong>Update:<\/strong>  There&#8217;s a <a href=\"https:\/\/twitter.com\/mOmobservatory\/status\/1763259550793076791\">tweet with some photos<\/a>.<\/p>\n<p><strong><br \/>\nUpdate<\/strong>:  The <a href=\"https:\/\/www.youtube.com\/watch?v=xqbdkxEhByo\">first of Scholze&#8217;s talks<\/a> is available at the IAS youtube channel.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I was assuming that Peter Scholze&#8217;s Emmy Noether lectures at the IAS would be the big news about advances in the Langlands program this coming week, but an anonymous correspondent just sent me this link. Tomorrow Andrew Wiles will be &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=13851\">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_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":"","jetpack_post_was_ever_published":false},"categories":[11],"tags":[],"class_list":["post-13851","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\/13851","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=13851"}],"version-history":[{"count":6,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/13851\/revisions"}],"predecessor-version":[{"id":13861,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/13851\/revisions\/13861"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13851"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13851"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13851"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}