This talk begins with an introduction to Courant algebroids and Dirac structures. The direct sum of the tangent space and the cotangent space of a manifold carries the structure of a ``standard Courant algebroid'', which naturally extends the Lie algebroid structure of the tangent space.

Linear connections are useful for describing the tangent spaces of vector bundles, especially their Lie algebroid structure. Similarly, we introduce the notion of "Dorfman connection" and explain how the standard Courant algebroid structure over a vector bundle is encoded by a certain class of Dorfman connections. Then we explain how this is in fact a special case of a more general equivalence between Lie 2-algebroids and VB-Courant algebroids (its existence is due to Li-Bland).

The correspondence of Courant algebroids with symplectic Lie 2-algebroids is then explained as a special case of this result.

Meeting ID: 886 2178 7717