{"id":1645,"date":"2020-01-23T15:43:59","date_gmt":"2020-01-23T13:43:59","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=1645"},"modified":"2020-02-09T10:37:31","modified_gmt":"2020-02-09T08:37:31","slug":"colloquium-tuesday-january-28-2020-speaker-yair-hartman-bgu-title-which-groups-have-bounded-harmonic-functions","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=1645","title":{"rendered":"Colloquium: Tuesday, January 28, 2020. Speaker: Yair Hartman (BGU). Title: &#8220;Which groups have bounded harmonic functions?&#8221;."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Place:&nbsp;Room \n614 in the Education &amp; Sciences Building<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Time:&nbsp;<strong>14:00<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<strong>Abstract<\/strong><strong>:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bounded \nharmonic functions on groups are closely related to random walks on groups. It \nhas long been known that all virtually nilpotent groups are &#8220;Choquet-Deny \ngroups&#8221;: these groups cannot support non-trivial bounded harmonic functions. \nEquivalently, their Furstenberg-Poisson boundary is trivial, for any random \nwalk. I will present a recent result where we complete the classification of \ndiscrete countable Choquet-Deny groups, proving a conjecture of \nKaimanovich-Vershik. We show that any finitely generated group which is not \nvirtually nilpotent, is not Choquet-Deny. Surprisingly, the key here is not the \ngrowth rate, but rather the algebraic infinite conjugacy class property (ICC). \nThis is joint work with Joshua Frisch, Omer Tamuz and Pooya Vahidi \nFerdowsi.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tea \nwill be served before the talk (at <strong>13:50<\/strong>).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Place:&nbsp;Room 614 in the Education &amp; Sciences Building Time:&nbsp;14:00 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Abstract: Bounded harmonic functions on groups are closely related to random walks on groups. It has long been known that all virtually nilpotent groups are &#8220;Choquet-Deny groups&#8221;: these groups cannot support&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=1645\">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-1645","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\/1645","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=1645"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1645\/revisions"}],"predecessor-version":[{"id":1646,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1645\/revisions\/1646"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1645"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1645"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1645"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}