Title: Polar convexity and a refinement of the Gauss-Lucas theorem

Hristo Sendov

Abstract: We will introduce the notion of polar convexity, which extends the
usual notion of convexity. 
We will give examples and explain its basic properties. Then, we will use it
to give a new refinement of the 
classical Gauss-Lucas theorem for complex polynomials. The Gauss-Lucas
theorem
states that the critical points of a polynomial are in the convex hull of
its zeros.