{"id":112,"date":"2015-02-08T17:20:03","date_gmt":"2015-02-09T01:20:03","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=112"},"modified":"2015-02-08T17:20:03","modified_gmt":"2015-02-09T01:20:03","slug":"andrew-lawrie-february-9th","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2015\/02\/08\/andrew-lawrie-february-9th\/","title":{"rendered":"Andrew Lawrie (February 9th)"},"content":{"rendered":"<div>\n<div>Speaker: Andrew Lawrie (UC Berkeley)<\/div>\n<div><\/div>\n<div><\/div>\n<div>Title: A refined threshold theorem for &nbsp;$(1+2)$-dimensional wave maps into surfaces. (joint with Sung-Jin Oh)<\/div>\n<div><\/div>\n<div><\/div>\n<div>Abstract:<\/div>\n<div>The recently established threshold theorem of Sterbenz and Tataru for energy critical wave maps states that wave maps with energy less than that of the ground state (i.e., a minimal energy nontrivial harmonic map) are globally regular and scattering on $\\mathbb{R}^{1+2}$. In this talk we give a refinement of this theorem when the target is a closed orientable surface by taking into account an additional &nbsp;invariant of the problem, namely the topological degree. We show that the sharp energy threshold for global regularity and scattering is in fact \\emph{twice} the energy of the ground state for wave maps with degree zero, whereas wave maps with nonzero degree necessarily have at least the energy of the ground state.<\/div>\n<\/div>\n<div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Speaker: Andrew Lawrie (UC Berkeley) Title: A refined threshold theorem for &nbsp;$(1+2)$-dimensional wave maps into surfaces. (joint with Sung-Jin Oh) Abstract: The recently established threshold theorem of Sterbenz and Tataru for energy critical wave maps states that wave maps with energy less than that of the ground state (i.e., a minimal energy nontrivial harmonic map) [&hellip;]<\/p>\n","protected":false},"author":105,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-112","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/112","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\/105"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=112"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/112\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=112"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=112"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}