{"id":2364,"date":"2022-04-07T10:39:49","date_gmt":"2022-04-07T07:39:49","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=2364"},"modified":"2022-04-24T10:53:35","modified_gmt":"2022-04-24T07:53:35","slug":"colloquium-tuesday-april-12-2022-speaker-speaker-ariel-yadin-ben-gurion-title-abundance-of-subgroups-via-random-walk-entropy","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=2364","title":{"rendered":"Colloquium: Tuesday, April 12, 2022. Speaker:  Ariel Yadin (Ben-Gurion). Title: &#8220;Abundance of subgroups via random walk entropy&#8221;."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">The talk (given in person in room (614) will also be broadcasted on zoom, and the link for the meetings is:<br><a rel=\"noreferrer noopener\" href=\"https:\/\/us02web.zoom.us\/j\/83337601824\" target=\"_blank\">https:\/\/us02web.zoom.us\/j\/83337601824<\/a><\/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\">Abstract: Given a (finitely generated) group, we are interested in investigating whether the group has a rich family of subgroups or not.&nbsp; This question is not precise enough, as stated.&nbsp; What we will focus on for this talk, is whether a group has many normal subgroups, or whether it has many invariant random subgroups (IRS), which are a probabilistic generalization of a normal subgroup.&nbsp;&nbsp;For example, a simple group does not have any non-trivial normal subgroups. A famous theorem of Margulis tells us that SL(3,Z) has &#8220;few&#8221; normal subgroups. Stuck &amp; Zimmer extend this also to IRSs.<br>Contrary to the high rank SL(n,Z) case, we believe&nbsp;that SL(2,Z) should have many many normal subgroups and IRSs.&nbsp; Since SL(2,Z) contains a free group&nbsp; on 2 elements with finite index, this leads one to consider subgroups of finitely generated free groups.<br>Indeed, extending results of Bowen, in joint works with Y. Hartman and L. Ron-George, we show that finitely generated free groups and SL(2,Z) have an abundance of ergodic IRSs, where &#8220;abundant&#8221; here is measured using random walk entropy.&nbsp; Specifically, all a-priori random walk entropy values can be realized by some ergodic IRS. The question whether entropy values can be realized with normal subgroups is still open.<br>Our methods involve a new construction&nbsp;of IRSs, by gluing together Schreier graphs, and we combine algebraic constructions with geometric and random walk considerations.&nbsp;<br>No prior knowledge of the notions of IRS, random walk entropy, etc. is assumed.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The talk (given in person in room (614) will also be broadcasted on zoom, and the link for the meetings is:https:\/\/us02web.zoom.us\/j\/83337601824 Time:&nbsp;14:00 Abstract: Given a (finitely generated) group, we are interested in investigating whether the group has a rich family&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=2364\">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-2364","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\/2364","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=2364"}],"version-history":[{"count":2,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2364\/revisions"}],"predecessor-version":[{"id":2366,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2364\/revisions\/2366"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2364"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2364"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}