{"id":1019,"date":"2021-10-13T18:16:53","date_gmt":"2021-10-14T01:16:53","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=1019"},"modified":"2021-10-13T18:16:53","modified_gmt":"2021-10-14T01:16:53","slug":"michael-christ-uc-berkeley","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2021\/10\/13\/michael-christ-uc-berkeley\/","title":{"rendered":"Michael Christ (UC Berkeley)"},"content":{"rendered":"\n\t\t\t\t\n<p>The APDE seminar on Monday, 10\/18, will be given by our own Michael Christ online via Zoom from <strong>4:10pm to 5:00pm PST<\/strong>. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu).<\/p>\n\n\n\n<p><strong>Title<\/strong>: On quadrilinear implicitly oscillatory integrals<\/p>\n\n\n\n<p><strong>Abstract<\/strong>: Multilinear oscillatory integrals arise<br>in various contexts in harmonic analysis,<br>in partial differential equations, in ergodic theory,<br>and in additive combinatorics.\u00a0 We discuss the majorization of integrals<br>$\\int \\prod_{j} (f_j\\circ\\varphi_j)$ of finite products<br>by negative order norms of the factors,<br>where integration is over a ball in Euclidean space and $\\varphi_j$ are smooth<br>mappings to a space of strictly lower dimension. The talk focuses<br>on the quadrilinear case, after work on the trilinear case of Bourgain (1988),<br>of Joly, M\\&#8217;etivier, and Rauch (1995), and of the speaker (2019).<br>Sublevel set inequalities, which quantify the nonsolvability of certain systems<br>of linear equations, are a central element of the analysis.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 10\/18, will be given by our own Michael Christ online via Zoom from 4:10pm to 5:00pm PST. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu). Title: On quadrilinear implicitly oscillatory integrals Abstract: Multilinear oscillatory integrals arisein various contexts in harmonic analysis,in partial differential equations, in ergodic theory,and in additive combinatorics.\u00a0 We discuss [&hellip;]<\/p>\n","protected":false},"author":106,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1019","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1019","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/users\/106"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1019"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1019\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1019"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1019"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1019"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}