  We establish the strong asymptotics for Bergman orthogonal polynomials
defined over Jordan domains with corners. This complements an investigation
started in 1923 by T. Carleman, who derived the strong asymptotics for domains
bounded by analytic curves, and carried over by P.K. Suetin in the 1960's, who
established them for domains with smooth boundaries. In order to do so, we use
a new approach based on tools from quasiconformal mapping theory. The impact of
the resulting theory is demonstrated in a number of applications, varying from
coefficient estimates in the well-known class Sigma of univalent functions and
a connection with operator theory, to the computation of capacities and a
reconstruction algorithm from moments.
