Daniel Palacin - On sums of infinite sets

jeudi 15 janv. 2026, 15:00 → 16:00 Europe/Paris

Salle 112 (ICJ)

In 2019, Moreira, Richter and Robertson showed that every subset A of the natural numbers with positive density contains a set of the form B+C for some infinite subsets B and C of natural numbers, settling a longstanding conjecture of Erdős. This result was later extended to higher order sumsets B_1+...+B_k (for a fixed k) by the same authors in collaboration with Kra.

 

Kra et al. asked whether the same is true for countable abelian groups, and proposed as well several variants of the problem. In this talk I will present a model-theoretic proof that addresses this question for a class of definably amenable groups that includes all countable amenable groups. This is joint work with Amador Martin-Pizarro.