Let $T$ be a positive closed current of bidegree $(1,1)$ on a multiprojective space $X={\mathbb P}^{n_1}\times\ldots\times{\mathbb P}^{n_k}$. In this talk we look at the geometric properties of sets of points where a current $T$ has ``large" Lelong numbers, where how large they need to be depends on the cohomology class of the current $T$, and see that they have certain geometric properties. Before hand, however, we will go over analogues of these results in the setting of $\mathbb{P}^n$. This talk is based on joint work with Dan Coman. Speaker(s): James Heffers (University of Michigan)