  Let $G$ be a connected, semisimple, real Lie group with finite centre, with
real rank at least two. B.Deroin and S.Hurtado recently proved the 30-year-old
conjecture that no irreducible lattice in $G$ has a left-invariant total order.
(Equivalently, they proved that no such lattice has a nontrivial,
orientation-preserving action on the real line.) We will explain many of the
main ideas of the proof, by using them to prove the analogous result for
lattices in $p$-adic semisimple groups. The $p$-adic case is easier, because
some of the technical issues do not arise.
