## Expansion properties of linear groups and affine sieve

#### Alireza Salehi GolsefidyUniversity of California, San Diego (UCSD)Mathematics

In the first part of this talk, we will see what affine sieve is and see the best possible basic result on the subject. In particular, the connection with random walk on $\prod_{p}{\rm GL}_n(\mathfrak{f}_p)$ will be explain (sometimes called super-strong approximation). In the second part I will report on the new results on random walks on $\prod_{p}{\rm GL}_n(\mathbb{Z}_p)$.

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