9 Apr 2025. Talk by Roberto Rubio at the IMPA Symplectic geometry seminar.
Abstract: The canonical symmetric pairing on TM+T*M is key to Dirac structures and generalized complex geometry. Not only is it used to define lagrangian subbundles, but also is at the core of the Clifford module structure, from which the Dorfman bracket can be recovered as a derived bracket. However, there is an equally canonical skew-symmetric pairing which has remained largely unexplored. In this talk, I will showcase an ongoing joint project with Filip Moucka to develop the geometry behind it, known as Cn-generalized geometry. On the way, we will present symmetric analogues of Cartan calculus and Poisson structures and will see how we reach a different realm of geometries, such as anti-Kählerian structures.