Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces

By Manfred Einsiedler, Gregory Margulis, Akshay Venkatesh. 2007

107 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2d001ef4268860c22a1e63605769268f43a3525e

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In Discrete Mathematics and Combinatorics

1. Jonathan Pila
2. Andreas Strombergsson
3. Jacob Tsimerman
4. Manjul Bhargava

In Mathematical Physics

1. Jonathan Pila
2. Jacob Tsimerman
3. Andreas Strombergsson
4. Ziyang Gao
5. Bruno Klingler
6. E. Ullmo
7. Manjul Bhargava

Citations in the corpus

• The André–Oort conjecture for the moduli space of abelian surfaces (2011, background): “1 in [3] these come in finitely many sets of conjugacy classes, so we can assume wlog that there is a fixed semisimple lie group H ⊂ Sp4(R) and elements ti ∈ Sp4(R) with Hi = tiHt −1 i .”
• ON THE DEVIATION OF ERGODIC AVERAGES FOR HOROCYCLE FLOWS (2013, result): “Also for Γ\G compact, Venkatesh [37, Thm. 3.1] has proved an effective equidistribution result for discrete orbits of the horocycle flow.”
• Ax-Lindemann for $\mathcal{A}_g$ (2014, background): “There are only finitely many semi-simple real groups that embed into Sp 2 g, R , and the embeddings come in finitely many families up to conjugacy by ([13, A.1]).”