Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces

Abstract

We prove effective equidistribution, with polynomial rate, for large closed orbits of semisimple groups on homogeneous spaces, under certain technical restrictions (notably, the acting group should have finite centralizer in the ambient group). The proofs make extensive use of spectral gaps, and also of a closing lemma for such actions.

References in corpus (5)

• Local-global principles for representations of quadratic forms
• Sparse equidistribution problems, period bounds, and subconvexity
• Ratner's theorem on SL(2,R)-invariant measures
• Effective equidistribution of S-integral points on symmetric varieties
• On one class of unipotent subgroups of semisimple algebraic groups