Madeleine Jotz Lean (University of Sheffield)
m.jotz-lean@sheffield.ac.uk
I will sketch how $N$-manifolds of degree $2$ are equivalent to double vector bundles endowed with a linear metric. Then I will explain the correspondence of VB-Courant algebroids with Lie $2$-algebroids. In order to do this, I will define the notion of Dorfman 2-representation, the "dual" of a Lie $2$-algebroid. I will then describe how this correspondence gives rise to several new classes of examples of Lie $2$-algebroids, such as the bicrossproducts of representations up to homotopy.