### Thursday, June 4

## IP8

Recent Results in Nonlinear Geometric Optics

1:30 PM-2:15 PM

*Chair: John Berger, Colorado School of Mines*

*Room 246*

Geometric optics is the study of high frequency solutions of hyperbolic partial differential equations. The solutions are described with rays and amplitudes which are the solutions of ordinary differential equations. This resolves the classical wave-particle controversy in optics. In recent years some of the ideas have been extended to nonlinear hyperbolic partial differential equations. The resulting approximations reveal new qualitative behaviors as well as justify a variety of ad hoc approximations in the scientific literature. The speaker will describe some of the central ideas in the theory and some striking consequences.

**Jeffrey Rauch**

*Department of Mathematics, University of Michigan, Ann Arbor*

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*tjf, 12/18/97*