Nondivergence of reductive group actions on homogeneous spacesAbstractLet $G/\Gamma$ be the quotient of a semisimple Lie group $G$ by its arithmetic lattice. Let $H$ be a reductive algebraic subgroup of $G$ acting on $G/\Gamma$. The question we are interested in is whether there is a compact set of $G/\Gamma$ that intersects every H-orbit. We show that the failure of this can be explained by a ...
Effective joint equidistribution of primitive rational points on expanding horospheresAbstractIn this talk, we will discuss effective joint equidistribution of primitive rational points on expanding horospheres in the space of unimodular lattices in any dimension. (For 1-dimentional case, this is joint equidistribtion of {a/q,b/q} where ab=1 mod q, as q goes to infinity.) The proof uses Fourier...
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