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Effective equidistribution and property $(\tau )$


Authors: M. Einsiedler, G. Margulis, A. Mohammadi and A. Venkatesh
Journal: J. Amer. Math. Soc. 33 (2020), 223-289
MSC (2010): Primary 11E99, 37A17, 37A45; Secondary 22E55
DOI: https://doi.org/10.1090/jams/930
Published electronically: October 2, 2019
MathSciNet review: 4066475
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Abstract:

We prove a quantitative equidistribution statement for adelic homogeneous subsets whose stabilizer is maximal and semisimple. Fixing the ambient space, the statement is uniform in all parameters.

We explain how this implies certain equidistribution theorems which, even in a qualitative form, are not accessible to measure-classification theorems. As another application, we describe another proof of property $(\tau )$ for arithmetic groups.


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Additional Information

M. Einsiedler
Affiliation: Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland
MR Author ID: 636562
Email: manfred.einsiedler@math.ethz.ch

G. Margulis
Affiliation: Department of Mathematics, Yale University, P.O. Box 208283, New Haven, Connecticut 06520-8283
MR Author ID: 196455
Email: margulis@math.yale.edu

A. Mohammadi
Affiliation: Department of Mathematics, UC San Diego, 9500 Gilman Drive, La Jolla, California 92093
MR Author ID: 886399
Email: ammohammadi@ucsd.edu

A. Venkatesh
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
MR Author ID: 693009
Email: akshay@math.stanford.edu

Received by editor(s): March 31, 2015
Received by editor(s) in revised form: August 28, 2017, October 21, 2018, and June 21, 2019
Published electronically: October 2, 2019
Additional Notes: The first author acknowledges support from the SNF (Grant 200021-127145 and 200021-152819)
The second author acknowledges support from the NSF (Grant 1265695)
The third author acknowledges support from the NSF and Alfred P. Sloan Research Fellowship
The fourth author acknowledges support from the NSF and the Packard foundation
Article copyright: © Copyright 2019 American Mathematical Society