Greg Smith: Sums of Squares on Real Projective Varieties

How does classical algebraic geometry help one recognize sums of squares? After sampling some of the geometric aspects of sums of squares, we will look at new bounds on the number of terms in a sum-of-squares expression for a quadratic form on a real projective variety. This talk is based on joint work with G. Blekherman, R. Sinn, and M. Velasco.