Zeroes of orthogonal polynomials of Szegő class

The talk is based on joint work with S. A. Denisov. In the first part, we will discuss a new version of Szegő formula that allows us to control oscillations of Schur functions of a measure from Szegő class. In the second part, some properties of Schur functions will be used in the study of zeroes of orthogonal polynomials. We obtain an equivalent reformulation of a well-known conjecture on asymptotic behaviour of orthogonal polynomials on the unit circle in terms of distribution of their zeroes.