Seminar

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The determination of the collection of polynomials with real coefficients that are nonnegative on a subset X of R^n is an interesting foundational problem having a wealth of applications ranging from nonconvex optimization to stochastic control theory. In this talk I will describe some recent characterizations of nonnegative polynomials when the set X has the structure of a real algebraic variety.

These characterizations arise from the interaction between convex geometry and classical algebraic geometry. In the talk I will first describe these ideas in detail in their simplest setting, namely the case when X is a finite set, and then discuss how they can be used to solve the problem on real algebraic curves and some real algebraic surfaces. These results are joint work with G. Blekherman (GA Tech), R. Sinn (U. Lepizig) and G.G. Smith (Queen's U).