20 May 2026. Talk by Filip Moučka at the West University of Timișoara.
Abstract: The 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–Jordan algebras.