In 2011, Yves Benoist and Jean-François Quint received the Clay Research Award for their collaborative research (and Jonathan Pila also received the 2011 Clay Research Award for unrelated research).
According to the citations, Benoist and Quint were honored "for their spectacular work on stationary measures and orbit closures for actions of nonabelian 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 m measure on H whose support generates H. Then any m-stationary probability measure for such an action is H-invariant."[3]
with Benoist: Mesures stationnaires et fermés invariants des espaces homogènes, Parts 1,2, Comptes Rendus Mathématiques, vol. 347, 2009, pp. 9–13, vol. 349, 2011, pp. 341–345; and Annals of Mathematics, vol. 174, 2011, pp. 1111–1162 doi:10.4007/annals.2011.174.2.8
with Benoist: Random walks on finite volume homogeneous spaces, Inventiones Mathematicae, vol. 187, 2012, pp. 37–59 doi:10.1007/s00222-011-0328-5
with Benoist: Stationary measures and invariant subsets of homogeneous spaces (II). J. Amer. Math. Soc. 26 (2013), no. 3, 659–734. MR3037785
with Benoist: Stationary measures and invariant subsets of homogeneous spaces (III). Ann. of Math. (2) 178 (2013), no. 3, 1017–1059. MR3092475
