{"id":10108,"date":"2018-03-13T10:36:09","date_gmt":"2018-03-13T14:36:09","guid":{"rendered":"http:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=10108"},"modified":"2018-03-15T12:02:13","modified_gmt":"2018-03-15T16:02:13","slug":"recent-developments-in-constructive-field-theory","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=10108","title":{"rendered":"Recent Developments in Constructive Field Theory"},"content":{"rendered":"<p>This week there&#8217;s a mini-workshop here at Columbia organized by the probabilists, on <a href=\"http:\/\/www.math.columbia.edu\/department\/probability\/CFT18\/CFT18.html\">Recent Developments in Constructive Field Theory<\/a>.  I&#8217;ll be attending some of the talks, will write more here if I can come up with something constructive to say.<\/p>\n<p><strong>Update<\/strong>: One of the talks today was Sourav Chatterjee on Yang-Mills for Probabilists, explaining what Yang-Mills and lattice gauge theory are, along the lines of <a href=\"https:\/\/arxiv.org\/abs\/1803.01950\">this preprint<\/a>.  The discussion brought back memories of my grad school days and early research, but I fear didn&#8217;t give much cause for optimism that there will be much progress anytime soon on a rigorous understanding of 4d Yang-Mills theory.<\/p>\n<p><strong>Update<\/strong>:  Today Scott Sheffield gave a talk on <em>Gauge theory and the three barriers<\/em>.  He started with the initial motivation of finding a continuum theory of random surfaces giving an alternative representation of gauge theory in 4d (this goes back to Polyakov and others around 1980).  There&#8217;s not much progress on this, but the question has inspired a wealth of results involving in some sense random surfaces.  For some details of all of this, one place to look is the <a href=\"http:\/\/math.mit.edu\/~sheffield\/fall2017math177.html\">website of Sheffield&#8217;s recent graduate course<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This week there&#8217;s a mini-workshop here at Columbia organized by the probabilists, on Recent Developments in Constructive Field Theory. I&#8217;ll be attending some of the talks, will write more here if I can come up with something constructive to say. &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=10108\">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":[1],"tags":[],"class_list":["post-10108","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"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\/10108","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=10108"}],"version-history":[{"count":5,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/10108\/revisions"}],"predecessor-version":[{"id":10122,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/10108\/revisions\/10122"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10108"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10108"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10108"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}