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In this article, we survey the the recent literature surrounding the geometryof complex polynomials. Specific areas surveyed are i) Generalizations of theGauss--Lucas Theorem, ii) Geometry of Polynomials Level Sets, and iii) ShapeAnalysis and Conformal Equivalence.

Some Recent Results on the Geometry of Complex Polynomials: The  Gauss--Lucas Theorem, Polynomial Lemniscates, Shape Analysis, and Conformal  Equivalence