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Friday, December 7, 2018

**Abstract:** In 1957 a ground-breaking three-page paper in the Annals marked the birth of CR geometry. There, Hans Lewy gave the first example of a locally non-solvable first-order linear partial differential equation. In this talk I will present a Lewy-type phenomenon for flat functions. That is, smooth functions whose derivatives are all equal to zero at a point. The result is elementary in nature, and no deep analytic background is required to understand this talk. I will describe some of the consequences of the result, with special attention to complex analysis. The talk is based on joint work with Yifei Pan.