Two recent examples will be given of how industrial stimulus can lead to new ways of thinking about problems in partial differential equations. The first shows how models for capacitor manufacturing can pose interesting new questions for the Laplace-Young equation; the second describes how the quest for more acute radar systems motivates the construction of a systematic theory of complex rays for the Helmholtz equation.

For various reasons, the academic mathematics community has been deluged with industrial problems in recent years. The talk will conclude with a transparency to demonstrate the current mismatch between supply and demand for mathematical expertise in this area.

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