Department of

November 2018 December 2018 January 2019 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 1 1 2 3 4 5 4 5 6 7 8 9 10 2 3 4 5 6 7 8 6 7 8 9 10 11 12 11 12 13 14 15 16 17 9 10 11 12 13 14 15 13 14 15 16 17 18 19 18 19 20 21 22 23 24 16 17 18 19 20 21 22 20 21 22 23 24 25 26 25 26 27 28 29 30 23 24 25 26 27 28 29 27 28 29 30 31 30 31

Monday, December 3, 2018

**Abstract:** Courant algebroids originated over 20 years ago motivated by constrained mechanics but now play an important role in Poisson geometry and related areas. Courant algebroids have an associated cohomology, which is hard to describe concretely. Building on work of Keller and Waldmann, I will show an explicit description of the complex of a Courant algebroid where the differential satisfies a Cartan-type formula. This leads to a new viewpoint on connections and representations of Courant algebroids and allows us to define new invariants as secondary charcateristic classes, analogous to what Crainic and Fernandes did for Lie algebroids. This is joint work with R. Mehta.