Do we know any thing about cohomology of realization space of matroid (the space of all set of vectors in $\mathbb{C}^n$ which captures the independence structure of matroid $M$), more simple, for uniform matroid $U_{k,n}$? The realization space is totally determined by structure of matroid, so as the cohomology, can we write it? I found little paper about this thing, does people lost the interest to calculate it since the realization space can be vary complicated by Mnev's universal theorem?