{"id":15655,"date":"2026-03-29T08:12:06","date_gmt":"2026-03-29T12:12:06","guid":{"rendered":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=15655"},"modified":"2026-03-30T16:06:58","modified_gmt":"2026-03-30T20:06:58","slug":"langlands-program-2-0","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=15655","title":{"rendered":"Langlands Program 2.0"},"content":{"rendered":"

Yesterday I was at Peter Scholze’s Seminaire Bourbaki talk, his write-up is available here<\/a>. It was advertised as an exposition of the recent proof of the geometric Langlands conjecture, but Pierre Colmez accurately describes it<\/a> as something much more: the Langlands program 2.0.<\/p>\n

In his talk, Scholze described the situation of the geometric Langlands program as for many years getting further and further away from the original arithmetic Langlands program. Recently there has been a dramatic change, as things have turned around and geometric Langlands is having an impact on arithmetic Langlands. He gives a new version of the basic conjecture of the arithmetic Langlands program (Conjecture 1.5), in a form similar to that of geometric Langlands. He describes this conjecture though as merely a “template for a conjecture”, since some of the terms remain undefined.<\/p>\n

I learned from his references about something perhaps more accessible, David Ben-Zvi’s talk What is the Geometric Langlands Correspondence About?<\/a> at the AMS meeting this past January. The blurb for the talk is:<\/p>\n

Number theorists found the tusks. Physicists found the tail. Now geometric Langlands tells us it\u2019s an elephant.<\/p><\/blockquote>\n

Update<\/strong>: In a comment David Ben-Zvi explains that there’s a revised version of his talk write-up available at this website<\/a> (soon to be on the arxiv), and a video of the talk should soon appear on the AMS Joint Mathematics Meetings youtube playlist.<\/p>\n","protected":false},"excerpt":{"rendered":"

Yesterday I was at Peter Scholze’s Seminaire Bourbaki talk, his write-up is available here. It was advertised as an exposition of the recent proof of the geometric Langlands conjecture, but Pierre Colmez accurately describes it as something much more: the … Continue reading →<\/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-15655","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\/15655","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=15655"}],"version-history":[{"count":5,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/15655\/revisions"}],"predecessor-version":[{"id":15660,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/15655\/revisions\/15660"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=15655"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=15655"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=15655"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}