The family of high rank arithmetic groups is class of groups which is playing\u00a0 an important role in various areas of mathematics. It includes SL(n,Z) for n>2, SL(n, Z[1\/p]) for n>1, their finite index subgroups and many more. A number of remarkable results on them have been proven, including: Mostow rigidity, Margulis super rigidity and the Quasi-isometric rigidity.<\/p>\n
We will talk about a new type of rigidity (which at this point we can prove only for many but not all): first order rigidity. Namely if G is such an arithmetic group and H a finitely generated group which is elementary equivalent to it (i.e., the same first order theory in the sense of model theory) then H is isomorphic to G. This stands in contrast with Zlil Sela’s remarkable work which implies that the free groups, surface groups and hyperbolic groups (many of whose are low-rank arithmetic groups) are far from having such a rigidity.<\/p>\n
Various questions and problems for further research will be discussed.<\/p>\n
Joint work (in progress) with Nir Avni and Chen Meiri.<\/p>\n","protected":false},"excerpt":{"rendered":"
The family of high rank arithmetic groups is class of groups which is playing\u00a0 an important role in various areas of mathematics. It includes SL(n,Z) for n>2, SL(n, Z[1\/p]) for n>1, their finite index subgroups and many more. A number…
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-764","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\/764","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=764"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/764\/revisions"}],"predecessor-version":[{"id":765,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/764\/revisions\/765"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=764"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=764"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}