### Infinite sumsets in sets of positive density

Combinatorics Seminar

9th May 2023, 11:00 am – 12:00 pm

Fry Building, 2.04

In the 1970’s Erdos asked several questions about what kind of infinite arithmetic structures can be found in every set of natural numbers with positive density. In recent joint work with Kra, Richter and Robertson we answered some of those questions using ergodic theory, showing for instance that any set A with positive density contains, up to a shift, a (restricted) sumset B+B for some infinite subset B of A. I will discuss this and related questions, most of which are still open, and present some of the ideas of the proof.

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