{"id":3017,"date":"2025-10-30T15:49:50","date_gmt":"2025-10-30T13:49:50","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=3017"},"modified":"2025-11-05T19:39:42","modified_gmt":"2025-11-05T17:39:42","slug":"colloquium-tuesday-nov-4-2025-1400-room-614-speaker-alek-vainshtein-haifa-title-poisson-lie-groups-and-cluster-structures","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=3017","title":{"rendered":"Colloquium: Tuesday Nov. 4, 2025 (14:00, room 614). Speaker: Alek Vainshtein (Haifa). Title: &#8220;Poisson-Lie groups and cluster structures&#8221;."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">It is well known that cluster structures and Poisson structures in the algebra of regular functions on a quasi-affine variety are closely related. In this talk, I will discuss this connection for Poisson structures defined on a simple simply connected complex Lie group G by a pair of classical R-matrices. The key element of the construction is a rational Poisson map from the group with a bracket defined by a pair of suitably chosen standard R-matrices to the same group with an arbitrary pair of R-matrices. In the case of G=SL_n one can build explicitly the corresponding cluster structure and prove its regularity and completeness.<br><br>Based on joint work with Misha Gekhtman (Notre Dame) and Michael Shapiro (Michigan State University)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It is well known that cluster structures and Poisson structures in the algebra of regular functions on a quasi-affine variety are closely related. In this talk, I will discuss this connection for Poisson structures defined on a simple simply connected&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=3017\">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-3017","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\/3017","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=3017"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/3017\/revisions"}],"predecessor-version":[{"id":3018,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/3017\/revisions\/3018"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3017"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3017"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}