## Some uniform expansion properties of $SL_2$ over finite fields

#### Oren DinaiHebrew UniversityMath

In this talk we investigate the growth properties of generators of $SL_2$ over finite fields. From this we obtain uniform poly-logarithmic diameter bounds for all the (connected) Cayley graphs of this family. This work extends the result of Helfgott from the family $\{SL_2(p):p prime\}$ to the family $\{SL_2(p^n):p prime, n \geq 1 \}$

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