We will analyze the basin \Omega of a superattracting fixed point in C^n and show that it is a circled pseudoconvex domain and that the smooth locus of the boundary of \Omega is Levy-flat, meaning foliated by complex (n-1)-manifolds. When n=2 we will parametrize this foliation, describe it topologically and give an expression for the holonomy. Speaker(s): Benjamin Krakoff (UM)