19 Jan 2026. Talk by Filip Moučka at the 46th Winter school on geometry and physics, Srní, Czech Republic.
Abstract: Given a Courant algebroid on a bundle of the form TM+E, we describe a natural construction of a pairing, an anchor, and a bracket on TE using a vector bundle connection on E. In general, this resulting structure on TE fails to satisfy all Courant algebroid axioms, which leads us to introduce the notion of a curved Courant algebroid. We identify the precise obstruction to obtaining an actual Courant algebroid and provide several illustrative examples related to the Patterson-Walker metric, special complex geometry, and Poisson geometry. This talk is based on joint work with Roberto Rubio, arXiv:2511.04743.