Julia Lange --- Introduction to Courant algebroids

This talk is general introduction to the structure of Courant algebroids, which are a generalization of Lie algebroids, arising naturally in the study of Poisson geometry. These structures are defined by a vector bundle equipped with a skew-symmetric bracket, a non-degenerate symmetric pairing, and an anchor map, all satisfying a set of compatibility conditions. In this talk, I will introduce the fundamental properties of Courant algebroids, emphasizing their geometric and algebraic roles. Key examples, such as the standard Courant algebroid over a smooth manifold and its connection to Dirac structures, will illustrate their versatility. I will also explore several applications, emphasizing their role in Poisson geometry.