Spherical buildings of type A can be modeled as the flag complex of F_q^n, which is the complex where each partial flag represents a simplex. The object of interest of this talk is the upper Laplacian (delta o d) which is used to define the Hodge Laplace decomposition and popular object of study when discussing expansion phenomena. I will give a gentle introduction to buildings, their description as BN-pairs and in particular retractions. Using this framework, I will first explain how to bound the number of distinct eigenvalues of the upper Laplacians and then show how to determine the asymptotic spectrum of the upper Laplacians for q -> infinity.