GUANAJUATO, GTO., M E X I C O

The lectures will take place at the CIMAT, at the salon de seminarios Diego Bricio, on each of the five days Monday through Friday, 12:00-13:30. People from outside Guanajuato who are interested in staying in CIMATEL during this week should contact the CIMAT. A tentative program of the lectures follows.

**Lecture I.** Introduction. (A general lecture that serves as
an introduction to the subject. Samples of the
applications to be discussed in the remaining lectures
and an overview of what sorts of geometry one can
reasonably hope to attach to a PDE.)

**Lecture II. ** The Method of Equivalence. (An introduction to the method
with several examples computed so that the audience
can get a feel for how the computations are done. The
rest of the talks will use this method.)

**Lecture III. ** Control Theory and Pfaffian Systems. (Examples of problems
from control theory and differential equations where
the method of equivalence can be used to understand
basic phenomena. Rigid curves, rolling bodies,
parking problems, sub-Riemannian geometry.)

**Lecture IV.** The Geometry of Conservation Laws. (How the invariants of
a PDE can be used to calculate the space of conservation
laws, integrable extentions, and other important
PDE constructions.)

**Lecture V.** Natural PDEs on 3-manifolds. (An investigation, using
the above methods, of several geometrically natural
PDE problems, such as prescribed curvature problems,
both for metrics and connections, as well as the
problem of describing special families of metrics
in dimension 3 that are characterized by differential
equations on the curvature tensors.)

All lectures will be given at the Salon Diego Bricio, Cimat, from 12:00-13:30.

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