{"id":759,"date":"2026-05-12T22:41:58","date_gmt":"2026-05-12T20:41:58","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/gentle\/?p=759"},"modified":"2026-05-12T22:41:58","modified_gmt":"2026-05-12T20:41:58","slug":"from-the-patterson-walker-metric-to-symmetric-poisson-geometry","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/gentle\/2026\/05\/12\/from-the-patterson-walker-metric-to-symmetric-poisson-geometry\/","title":{"rendered":"From the Patterson-Walker metric to symmetric Poisson geometry"},"content":{"rendered":"<p>20 May 2026. Talk by Filip Mou\u010dka at the West University of Timi\u0219oara.<\/p>\n<p>Abstract:\u00a0The Patterson-Walker metric, introduced in 1952, is a split-signature metric on the total space of the cotangent bundle, and it can be viewed as a symmetric counterpart of the canonical symplectic form. In this talk, I will show that studying its gradient flow leads to the definition of symmetric Poisson structures. 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. 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>20 May 2026. Talk by Filip Mou\u010dka at the West University of Timi\u0219oara. Abstract:\u00a0The Patterson-Walker metric, introduced in 1952, is a split-signature metric on the total space of the cotangent bundle, and it can be viewed as a symmetric counterpart of the canonical symplectic form. In this talk, I will show that studying its gradient [&hellip;]<\/p>\n","protected":false},"author":54,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28,26],"tags":[],"class_list":["post-759","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\/759","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=759"}],"version-history":[{"count":1,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/759\/revisions"}],"predecessor-version":[{"id":760,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/759\/revisions\/760"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/media?parent=759"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/categories?post=759"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/tags?post=759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}