Michele Ancona: Random sections of line bundles over a real Riemann surface

Abstract: The number of real roots of a degree d real polynomial depends on the choice of the coefficients. This raises a natural question.
How many real roots does a degree d real polynomial have, if we pick it at random?
The goal of the talk is to answer this question. More generally, given an ample line bundle L over a real projective curve, we will study the number of real zeros of a random section of L.