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Mark Levi : A connection between tire tracks, the stationary Schr\odingers equation and forced vibrations (Apr 28, 2014 4:25 PM)

I will describe a recently discovered equivalence between the first two objects mentioned in the title. The stationary Schr\"odinger's equation, a.k.a. Hill’s equation, is ubiquitous in mathematics, physics, engineering and chemistry. Just to mention one application, the main idea of the Paul trap (for which W. Paul earned the 1989 Nobel Prize in physics) amounts to a certain property of Hill's equation. I will show that Hill's equation is equivalent to a seemingly unrelated problem of “tire tracks”. There is, in addition, a yet another connection between the ``tire tracks” problem and the high frequency forced vibrations which I will also outline briefly.

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