Let $G$ be a perfect Lie group, $\Gamma$ be a lattice in G and $U$ be a unipotent subgroup of $G$. A celebrated theorem of Ratner says that for any $x$ in $G/\Gamma$ the orbit $U.x$ is equidistributed in a periodic orbit of some subgroup $U \leq L \leq G$. Establishing a quantitative version of Ratner's theorem has been long sought after. If $U$ is a horospherical subgroup of $G$, the question is well-studied. If $U$ is not a horospherical subgroup, this question is far less understood. Recently, Lindenstrauss, Mohammadi, Wang and Yang established fully quantitative and effective equidistribution results for orbits of one-parameter (non-horospherical) unipotent groups in a wide variety of cases. In this talk, we will discuss a recent equidistribution theorem for some higher dimensional unipotent subgroups. Our results in particular provide effective equidistribution theorems for orbits of maximal unipotent subgroups of $\mathrm{SO}(p,q)$ in $\mathrm{SL}_n(\mathbb{R})/\mathrm{SL}_n(\mathbb{Z})$ for all $n=p+q$. If time permits, we will also discuss a submodularity inequality in irreducible representations, which is a key ingredient of the proof and is of independent interest.