Strong asymptotic of Cauchy biorthogonal polynomials and orthogonal polynomials with varying measure

In this talk we present some recent results on the strong asymptotic of Cauchy biorthogonal polynomials under the assumption that the defining measures are supported on non-intersecting intervals of the real line and satisfy Szegő's condition. These biorthogonal polynomials are connected with certain mixed type Hermite-Padé polynomials, which verify full orthogonality relations with respect to some varying measures. Thus, the strong asymptotic of orthogonal polynomials with respect to varying measures plays a key role in the study. This is a joint work with Luis Giraldo Gonzalez Ricardo.