Rigidity of some rank two partially hyperbolic abelian actions: restrictions of Weyl chamber flow

In the first part of the talk I will discuss a proof of
cocycle rigidity for rank-two generic restrictions of the Weyl
chamber flow on SL(n, R)/L, where n>3 and L is a cocompact lattice in
SL(n, R). The proof relies on the structure of Lyapunov foliations
for the action. In the second part of the talk I will discuss
robustness of this approach and its consequence to the local rigidity
problem for such actions.