Non-left-orderability of lattices in higher-rank semisimple Lie groups (after Deroin and Hurtado)

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.