Bounded orbits of Diagonalizable Flows on finite volume quotients of   products of $SL_2(\mathbb{R})$
  We prove a number field analogue of W. M. Schmidt's conjecture on the intersection of weighted badly approximable vectors and use this to prove an instance of a conjecture of An, Guan and Kleinbock. Namely, let $G := SL_2(\mathbb{R}) \times \dots \times SL_2(\mathbb{R}) $ and $\Gamma$ be a lattice in $G$. We show that the set of points on $G/\Gamma$ whose forward orbits under a one parameter Ad-semisimple subsemigroup of $G$ are bounded, form a hyperplane absolute winning set. 
Jinpeng An, Anish Ghosh, Lifan Guan, Tue Ly
math.DS math.NT