DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, November 6, 2002 Padelford C-36 3:45 pm

Local geometric invariants for 2nd-order ODE systems

Daniel Grossman (University of Chicago)

In this talk, I will describe the results of applying E. Cartan’s equivalence method to so-called ”path geometries”, which are geometric versions of 2ndorder ODE systems. The main outcome of the method is a collection of invariants that can be interpreted as the curvature of the system, in the sense that it locally measures deviation from the system whose solutions are straight lines. The most interesting result is the identification, in terms of these local invariants, of a special class of ODE systems with several beautiful properties. These “torsion-free” systems generically have many conservation laws (despite their lack of symmetry), and a solution space with a rich local geometry of its own.

For more information about this seminar, visit the DG/PDE Seminar Web page (from the Math Department home page, www.math.washington.edu, follow the link Seminars, Colloquia, and Conferences).

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