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Nonnegative Polynomials and Sums of Squares

4:00 pm Thursday, October 23, 2014
Greg Blekherman (Georgia Tech)

A polynomial with real coefficients is nonnegative if it takes only nonnegative values. For example, any sum of squares is obviously nonnegative. The study of the relationship between nonnegative polynomial and sums of squares is a classical area in real algebraic geometry. After reviewing the history of the problem I will explain how this topic is inextricably linked to classical topics in complex algebraic geometry (varieties of minimal degree, dimension of secant varieties). Surprisingly these connections come via convex geometry. The talk is based on joint work with Sadik Iliman, Martina Kubitzke, Greg Smith and Mauricio Velasco.

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