Cohomological equation and cocycle rigidity for algebraic parabolic actions
Time and place
1 PM on Monday, March 11th, 2013; Artino lab
Zhenqi Wang (Yale)
Abstract
In the past two decades one of the main themes in dynamics is the study of various smooth rigidity phenomena for higher-rank abelian algebraic actions. This is in contrast to the C^0-stability for rank-one situation. For (partially)-hyperbolic actions, the cohomological equation and cocycle rigidity have been well understood. For parabolic actions, the horocycle flow on SL(2,R)/\gamma where \gamma is a lattice has been studied by using representation theory. The natural difficulty in extending the results to higher rank simple Lie groups is related to the complexity of the representation theory tool. Even for SL(3,R) the problem remained open for a long time.
In the first part of the talk, I will give a short review of the important results concerning higher-rank abelian algebraic actions of the rigidity phenomena in a broad context. In the second part of the talk, I will discuss the recent progress on how to apply representation theory to study cohomological equation and cocycle rigidity for algebraic parabolic actions on homogeneous space obtained from some higher-rank simple algebraic groups.
