**Papers Published**

- with Bryant, RL; Griffiths, PA,
*Characteristic cohomology of differential systems. I. General theory*, The Journal of the American Mathematical Society, vol. 8 no. 3 (1995), pp. 507-507

(last updated on 2018/05/23)**Author's Comments:**

This paper is the first of a series in which we explore the relationship between the geometry of a PDE (in the sense of differential invariant theory) and its so-called 'characteristic cohomology', a generalization of the notion of conservation laws that is largely due to Vinogradov. Rather than work directly with a PDE system, we work with the associated exterior differential system and formulate the theory in a way that is natural in this context. We develop some new commutative algebra tools to help deal with the computations that arise in our treatment of the spectral sequences involved, and explore the relationship between the characteristic variety of the system and various vanishing theorems that generalize the famous Vinogradov 2-line theorem.