A classical subject in complex dynamics is the linearization problem, which asks when an analytic function is locally conjugate to its local linearization. This problem has been studied since the 19th century, but it took until the '90s to completely resolve the simplest case: quadratic polynomials. In the first part of this talk we will discuss the solution in the quadratic case. In the second part of part of this talk we will examine properties of the Yoccoz function, a remarkable function defined by Yoccoz to study the linearization problem. Speaker(s): Alex Kapiamba (U(M))