In the first part of this talk, we shall discuss some basic properties of the parameter space M_d of unicritical degree d polynomials for d >=2. We then focus on the case d=3, and establish a relationship between quadratic polynomials with a periodic critical point, and cubic polynomials with a periodic critical point whose kneading sequence contains only two symbols out of three. We shall deduce some properties of M_3 that follow directly by this relationship, and end by discussing the implications of the same and further questions that can be posed. Speaker(s): Malavika Mukundan (U(M))