### A solution to the Burr-Erdos problems on Ramsey completeness

- Series
- School of Mathematics Colloquium
- Time
- Thursday, November 21, 2019 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Jacob Fox – Stanford University

A sequence A of positive integers is r-Ramsey complete if for every r-coloring of A, every sufficiently large integer can be written as a sum of the elements of a monochromatic subsequence. Burr and Erdos proposed several open problems in 1985 on how sparse can an r-Ramsey complete sequence be and which polynomial sequences are r-Ramsey complete. Erdos later offered cash prizes for two of these problems. We prove a result which solves the problems of Burr and Erdos on Ramsey complete sequences. The proof uses tools from probability, combinatorics, and number theory.

Joint work with David Conlon.