We prove results about orbit closures and equidistribution for the SL (2, ℝ) action on the
moduli space of compact Riemann surfaces, which are analogous to the theory of unipotent …

We prove some ergodic-theoretic rigidity properties of the action of on moduli space. In
particular, we show that any ergodic measure invariant under the action of the upper …

For almost all Riemannian metrics (in the C^ ∞ C∞ Baire sense) on a closed manifold M^
n+ 1 M n+ 1, 3 ≤ (n+ 1) ≤ 7 3≤(n+ 1)≤ 7, we prove that there is a sequence of closed …

Writing long books is a laborious and impoverishing act of foolishness: expanding in five
hundred pages an idea that could be perfectly explained in a few minutes. A better …

Unipotent Flows and Counting Lattice Points on Homogeneous Varieties Page 1 Annals of
Mathematics, 143 (1996), 253-299 Unipotent flows and counting lattice points on homogeneous …

Let L be a Lie group and λ a lattice in L. Suppose G is a non-compact simple Lie group
realized as a Lie subgroup of L and GA= L. Let aεG be such that Ada is semisimple and not …

Publisher Summary This chapter presents an exposition of homogeneous dynamics—that is,
the dynamical and ergodic properties of actions on the homogeneous spaces of Lie groups …

Let G be a real Lie group, Λ be a lattice in G and Γ be a compactly generated closed
subgroup of G. If the Zariski closure of the group Ad (Γ) is semisimple with no compact factor …

Under explicit diophantine conditions on, we prove that the local two-point correlations of the
sequence given by the values, with (m, n)∈ Z2, are those of a Poisson process. This partly …

We prove effective equidistribution, with polynomial rate, for large closed orbits of
semisimple groups on homogeneous spaces, under certain technical restrictions (notably …