Effective equidistribution for some unipotent flows in $PSL(2,   \mathbb{R})^k$ mod cocompact, irreducible lattice
  Let $d \geq 2$, and let $\Gamma \subset PSL(2, \mathbb{R})^d$ be an irreducible, cocompact lattice. We prove a sharp estimate up to a logarithmic factor on the rate of equidistribution of coordinate horocycle flows on $\Gamma \backslash PSL(2, \mathbb{R})^d$. 
James Tanis
math.DS