Miklós Laczkovich: On the disproof of the sum-product conjecture

The sum-product problem, asked by Erdős in 1976, is the following. Is it true that for every $\varepsilon >0$, if $A$ is a finite set on numbers with $|A|>N(\varepsilon )$, then $\max (|A+A|, |A\cdot A|)> |A|^{2-varepsilon}$? The question may be asked for integers, real, or complex numbers.

Recently T.F. Bloom, W. Sawin, C. Schildkraut and D. Zhelezov proved, using some tools in algebraic number theory, that for real numbers the answer is negative. In the talk we give the details of their counterexample, explaining also the necessary background material.