  Let $\text{Homeo}_+(D^2_n)$ be the group of orientation-preserving
homeomorphisms of $D^2$ fixing the boundary pointwise and $n$ marked points as
a set. Nielsen realization problem for the braid group asks whether the natural
projection $p_n:\text{Homeo}_+(D^2_n)\to B_n:=\pi_0(\text{Homeo}_+(D^2_n))$ has
a section over subgroups of $B_n$. All of the previous methods either use
torsions or Thurston stability, which do not apply to the pure braid group
$PB_n$, the subgroup of $B_n$ that fixes $n$ marked points pointwise. In this
paper, we show that the pure braid group has no realization inside the
area-preserving homeomorphisms using rotation numbers.
