{"id":502,"date":"2016-05-12T10:10:37","date_gmt":"2016-05-12T07:10:37","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=502"},"modified":"2016-05-19T15:02:34","modified_gmt":"2016-05-19T12:02:34","slug":"colloquium-tuesday-may-17-2-pm-speaker-gidi-amir-bar-ilan-title-liouville-groups-with-very-slowly-growing-harmonic-functions","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=502","title":{"rendered":"Colloquium: Tuesday, May 17, 2 pm. Speaker: Gidi Amir (Bar Ilan). Title: &#8220;Liouville groups with very slowly growing harmonic functions&#8221;."},"content":{"rendered":"<p>A group G has the Liouville property with respect to some generating set S if the only bounded\u00a0harmonic\u00a0functions on the Cayley graph of (G,S) are the constant functions. On such Cayley graphs it is interesting to ask how slowly can a non-constant\u00a0harmonic\u00a0function grow?<\/p>\n<p>We construct groups with arbitrary slowly growing\u00a0harmonic\u00a0functions. More precisely, for any &#8220;nice&#8221; function f growing slower than log n, we construct a group and a generating set so that there is a non-constant\u00a0harmonic\u00a0function growing like f, but any\u00a0harmonic\u00a0function asymptotically slower than f must be constant. This is joint work with\u00a0Gady\u00a0Kozma.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A group G has the Liouville property with respect to some generating set S if the only bounded\u00a0harmonic\u00a0functions on the Cayley graph of (G,S) are the constant functions. On such Cayley graphs it is interesting to ask how slowly can&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=502\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-502","post","type-post","status-publish","format-standard","hentry","category-colloquium"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/502","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=502"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/502\/revisions"}],"predecessor-version":[{"id":503,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/502\/revisions\/503"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=502"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=502"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=502"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}