### MATH 848I: Exterior Differential Systems

Spring 2020

This course will be an introduction to Cartan's method of moving frames and EDS. The latter is a method for encoding systems of partial differential equations on manifolds as differential ideals on associated manifolds, which is particularly adapted to the intrinsic geometry of the PDEs. The core of the course will be based on Ivey and Landsberg's *Cartan for Beginners* Chapters 1 and 4-7, which includes the Cartan-Kähler algorithm yielding a criterion for existence of solutions with given initial conditions, as well as applications to particular classes of PDEs such as Monge-Ampère systems.

Suggested Texts:
- T.A. Ivey and J.M. Landsberg:
*Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems* (2nd ed.), AMS Graduate Studies in Mathematics **175**, Providence, RI (2016).
- R. Bryant, P. Griffiths, D. Grossman:
*Exterior Differential Systems and Euler-Lagrange Partial Differential Equations*, Chicago Lectures in Mathematics, Chicago (2003).

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