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Tuesday, March 11, 2014

**Abstract:** I will describe a newly discovered equivalence between the first two objects mentioned in the title. The stationary Schrodinger'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. As it turns out, Hill's equation is equivalent to a seemingly completely unrelated problem of “tire tracks”. In addition to this equivalence, I will describe a yet another connection between the ``tire tracks” problem and the high frequency forced vibrations.