7 Mar 2024, 11h CET. Talk by M. Cueca.
Abstract: It is known that Courant algebroids are in correspondence with degree 2 symplectic dg-manifolds. The standard cochain complex of a Courant algebroid is, by definition, the complex consisting of functions on the corresponding dg-manifold. This definition has been difficult to work with directly, due to a lack of explicit ordinate-free formulas relating the Courant data (bracket, anchor, and pairing) to the standard complex. In this talk, I will give a description of the standard complex in terms of the Courant data, and I will explain how the differential satisfies a familiar-looking Cartan formula. As an application, I will explain how the classical theory of connections extends almost verbatim to Courant algebroids, leading to a construction of secondary characteristic classes that formally resembles the classical Chern-Simons construction. This is joint work with Rajan Mehta.