Geometry of partial differential equations

This belongs to a longer term project which covers the basics on the "geometry of partial differential equations" (in the various senses that can be found in the literature, including the formal theory of differential equations, exterior differential systems, Cartan's equivalence method) and its applications to geometry. For the Fall we will probably concentrate on the formal theory of differential equations.

The intended level of these lectures is that of PhD students interested on the subject and researchers interested in Differential Geometry and Mathematical Physics.

Person in charge: Sergey Igonin, Marius Crainic.

Some literature:

lecture notes by Sergey Igonin.

Exterior differential systems by R. Bryant, etc, Mathematical Sciences Research Institute Publications, 18. Springer-Verlag, New York, 1991.

Lie's structural approach to PDE Systems by Olle Stormark, Encyclopedia of Mathematics and its Applications, 80. Cambridge University Press, Cambridge, 2000.

Basic ideas and concepts of differential geometry. Geometry I, by D. V. Alekseevskij, A. M. Vinogradov, and V. V. Lychagin. Encyclopaedia Math. Sci., 28, Springer, Berlin, 1991.

Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, I. S. Krasil'shchik and A. M. Vinogradov (eds.), Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, American Mathematical Society, Providence, RI, 1998.

Section 3 of this book.