I will discuss a recent result on the sum-product problem in finite fields, showing that given a subset $A$ of a finite field of sufficiently large characteristic $p$, if $|A|< p^{26/51}$ then
$$\max\{|A+A|, |AA|\}> |A|^{16/13 - o(1)}.$$
This talk is based on a joint work with Sophie Stevens (RICAM).
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