Effective equidistribution and property (𝜏)

Einsiedler, M.; Margulis, G.; Mohammadi, A.; Venkatesh, A.

doi:10.1090/jams/930

Effective equidistribution and property $(\tau )$
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by M. Einsiedler, G. Margulis, A. Mohammadi and A. Venkatesh

J. Amer. Math. Soc. 33 (2020), 223-289

DOI: https://doi.org/10.1090/jams/930

Published electronically: October 2, 2019

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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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