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Title: SDP representation of convex sets Abstract: A set S is SDP representable if it is the projection of a set in higher dimensional space that can be described by linear matrix inequality (LMI). Clearly, the necessary conditions are that S should be convex and semialgbraic. In this talk, we will give sufficient conditions for SDP representability. We show that if the boundary of a convex set has positive curvature or is sos-convex shaped, then that set is SDP representable.