The celebrated sum-product conjecture of Erdos and Szemeredi asserts that a set cannot be additively and multiplicatively small at the same time. We will discuss a somewhat different approach to this phenomenon, namely what structural constraints are satisfied by an arbitrary sumset or product set. For example, the Erdos unit distance problem can be rephrased in this way. In general, one would expect that a sumset (product set) cannot be multiplicatively (additively) structured. Some partial results will be presented in this direction together with a few open questions.
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