Yves Benoist

The 2011 Clay Research Award has been made to Yves Benoist and Jean-François Quint for their spectacular work on stationary measures and orbit closures for actions of non-abelian groups on homogeneous spaces.

This work is a major breakthrough in homogeneous dynamics and related areas of mathematics. In particular, Benoist and Quint proved the following conjecture of Furstenberg. Let H be a Zariski dense semisimple subgroup of a Lie group which acts by left translations on the quotient of G by a discrete subgroup with finite covolume. Consider a probability measure m on H whose support generates H. Then any m-stationary probability measure for such an action is H-invariant.