{"id":2413,"date":"2022-06-05T11:41:52","date_gmt":"2022-06-05T08:41:52","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=2413"},"modified":"2022-06-12T10:42:00","modified_gmt":"2022-06-12T07:42:00","slug":"colloquium-tuesday-june-7-2022-speaker-eran-nevo-hebrew-university-title-directions-in-graph-rigidity","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=2413","title":{"rendered":"Colloquium: Tuesday, June 7, 2022. Speaker:  Eran Nevo (Hebrew University). Title: &#8220;Directions in graph rigidity&#8221;."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The talk will be on Zoom. The link for the meetings is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/us02web.zoom.us\/j\/83337601824\">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\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Abstract: Given a graph G and an embedding of its vertices in R^d, what continuous motions of the vertices preserve all edge lengths?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Clearly all motions induced by an isometry of R^d do, these are the trivial motions; are there any others? If the answer is NO for all (equivalently, for one) generic embedding, G is called d-rigid. What are the d-rigid graphs?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This problem has been extensively studied since the 70s, and is still widely open for d&gt;=3.&nbsp;It is studied mainly from algebraic geometry, linear algebra, and combinatorics points of view. Variants of it, especially in dimensions 2 and 3, are of importance also beyond mathematics, e.g. in structural engineering, computational biology and more.<br><br>I will discuss various directions and open problems in graph rigidity, including:<br>combinatorial characterization, numerical consequences, non-generic rigid embeddings, rigidity of random graphs, and a quantitative version of rigidity via spectral analysis of the related stiffness matrix.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The talk will be on Zoom. The link for the meetings is: https:\/\/us02web.zoom.us\/j\/83337601824 Time:&nbsp;14:00 Abstract: Given a graph G and an embedding of its vertices in R^d, what continuous motions of the vertices preserve all edge lengths? Clearly all motions&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=2413\">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-2413","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\/2413","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=2413"}],"version-history":[{"count":2,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2413\/revisions"}],"predecessor-version":[{"id":2416,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2413\/revisions\/2416"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2413"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2413"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}