Mihai Putinar: Hermitian algebra along the ellipse

When not a circle, the ellipse barely fails a Riesz-Fejer theorem stating that a positive polynomial on the curve is a sum of moduli squares of complex polynomials. An analysis of the phenomenon, focused on the subtle difference between sums of squares of real polynomials and sums of hermitian squares will bring in the front line some recent results in several complex variables, real algebra and operator theory.