An Erdős problem on additive Sidon bases: perverse sheaves in action

In 1993, Erdős, Sárközy and Sós posed the question of whether there exists a set S of positive integers that is both a Sidon set and an asymptotic basis of order 3. This means that the sums of two elements of S are all distinct, while the sums of three elements of S cover all sufficiently large integers. In this talk, I will present a construction of such a set, building on ideas of Ruzsa and Cilleruelo. The proof uses a powerful number-theoretic result of Sawin, which is established using cutting-edge algebraic geometry techniques.