An old conjecture of Erdos-Turan states that any set of positive integers whose reciprocals form a divergent series should contain arbitrarily long arithmetic progressions.  I will discuss connections between (almost) arithmetic progressions, weak tangents, and Assouad dimension and give a simple proof that sets of positive integers whose reciprocals form a divergent series contain arbitrarily long (almost) arithmetic progressions.

 

This is joint work with Han Yu (St Andrews).

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