{"id":729,"date":"2026-04-12T19:44:20","date_gmt":"2026-04-12T17:44:20","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/gentle\/?p=729"},"modified":"2026-04-12T19:44:23","modified_gmt":"2026-04-12T17:44:23","slug":"a-symmetric-cousin-of-poisson-geometry-2","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/gentle\/2026\/04\/12\/a-symmetric-cousin-of-poisson-geometry-2\/","title":{"rendered":"A symmetric cousin of Poisson geometry"},"content":{"rendered":"<p>16 Apr 2026. Talk by Filip Mou\u010dka at the Prague Mathematical Physics Seminar, Charles University, Prague.<\/p>\n<p>Abstract: Poisson geometry is a natural extension of symplectic geometry that encodes Hamiltonian dynamics, Lie algebras, and singular foliations via skew-symmetric bivector fields. In this talk, I will explore a symmetric counterpart of this framework by introducing symmetric Poisson structures, defined as pairs consisting of a symmetric bivector field and a torsion-free connection satisfying a natural compatibility condition. These new geometric structures extend (pseudo-)Riemannian geometry and describe locally geodesically invariant distributions endowed with a metric along them. In particular, they include totally geodesic foliations equipped with a metric and a compatible connection on each leaf. I will explain how symmetric Poisson geometry is closely related to the Patterson\u2013Walker metric, a split-signature metric on the cotangent bundle that is analogous to the canonical symplectic form. Finally, I will present several examples of symmetric Poisson structures, with special emphasis on the linear case, which is in one-to-one correspondence with real finite-dimensional Jacobi\u2013Jordan algebras.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>16 Apr 2026. Talk by Filip Mou\u010dka at the Prague Mathematical Physics Seminar, Charles University, Prague. Abstract: Poisson geometry is a natural extension of symplectic geometry that encodes Hamiltonian dynamics, Lie algebras, and singular foliations via skew-symmetric bivector fields. In this talk, I will explore a symmetric counterpart of this framework by introducing symmetric Poisson [&hellip;]<\/p>\n","protected":false},"author":54,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28,26],"tags":[],"class_list":["post-729","post","type-post","status-publish","format-standard","hentry","category-moucka","category-talks"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/729","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/users\/54"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/comments?post=729"}],"version-history":[{"count":1,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/729\/revisions"}],"predecessor-version":[{"id":730,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/729\/revisions\/730"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/media?parent=729"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/categories?post=729"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/tags?post=729"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}