MATH 378.2

MATH 378.2: Exterior Differential Systems

Description: This is an introduction to exterior differential systems, a collection of techniques used to analyze systems of partial differential equations that arise in differential geometry. We will begin by discussing the basic idea of partial differential equations recast as exterior differential systems, exterior algebra, the elementary examples of Frobenius, Pfaff, and Darboux. We will then move on to a discussion of the infinitesimal picture, discussing the geometry of integral elements, polar spaces, extensions, etc. The basic existence theorem of Cartan and Kahler will be introduced and motivated and the course will finish with a series of applications to problems of interest in differential geometry and pde.

Prerequisites: Manifolds, differential forms, exterior algebra

Instructor: Robert L. Bryant

Instructor

Text:

• None, but lecture notes will be provided.