Actions of higher rank, irreducible lattices on $\CAT(0)$ cubical   complexes
  Let $\Gamma$ be an irreducible lattice of $\Q$-rank $\geq 2$ in a semisimple Lie group of noncompact type. We prove that any action of $\Gamma$ on a $\CAT(0)$ cubical complex has a global fixed point. 
T. Tam Nguyen Phan
math.GT