{"id":1616,"date":"2026-04-10T00:58:59","date_gmt":"2026-04-10T07:58:59","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1616"},"modified":"2026-04-14T20:05:08","modified_gmt":"2026-04-15T03:05:08","slug":"inverse-theorems-in-additive-combinatorics","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2026\/04\/10\/inverse-theorems-in-additive-combinatorics\/","title":{"rendered":"Inverse theorems in additive combinatorics"},"content":{"rendered":"<p>The HADES seminar on Tuesday, <strong>April 14t<\/strong><strong>h<\/strong>, will be at\u00a0<strong>3:30pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<\/p>\n<p><strong>Speaker:\u00a0<\/strong>James Leng<\/p>\n<p><strong>Abstract: <\/strong>Let $r_k(N)$ denote the largest subset of the integers from $1$ to $N$ without a $k$-term arithmetic progression. A famous open problem is to find optimal upper bounds on $r_k(N)$. In this talk, I will survey work leading up to the current best upper bounds. Of particular note is the inverse theory of Gowers norms, which I will motivate through both finitary combinatorics and ergodic theory. Time permitting, I will end off by describing my favorite open problem in this area.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, April 14th, will be at\u00a03:30pm\u00a0in\u00a0Room 740. Speaker:\u00a0James Leng Abstract: Let $r_k(N)$ denote the largest subset of the integers from $1$ to $N$ without a $k$-term arithmetic progression. A famous open problem is to find optimal upper bounds on $r_k(N)$. In this talk, I will survey work leading up to the [&hellip;]<\/p>\n","protected":false},"author":95,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26,1],"tags":[],"class_list":["post-1616","post","type-post","status-publish","format-standard","hentry","category-spring-2026","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1616","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/95"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1616"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1616\/revisions"}],"predecessor-version":[{"id":1617,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1616\/revisions\/1617"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1616"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1616"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1616"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}