Title: Infinite sumsets in sets with positive density
Speaker: Joel Moreira
Speaker Info: University of Warwick
Brief Description:
Special Note:
Abstract:
Answering a question raised by Erdos we show that any set of natural numbers with positive upper density contains (up to a shift) all sums $b_i+b_j$ with $i\neq j$ from some strictly increasing sequence $b_1, b_2,...$ of natural numbers. The proof begins with a version of Furstenberg's correspondence principle to translate the combinatorial statement into a dynamical one. The dynamical problem we are left to solve involves a delicate understanding of the ergodic decomposition of the cartesian product of a certain measure preserving system. This talk is based on joint work with Bryna Kra, Florian Richter and Donald Robertson.Date: Tuesday, February 07, 2023