A conjecture of Erdős, Graham, Montgomery, Rothschild, Spencer and Straus states that, with the exception of equilateral triangles, any two-coloring of the plane will have a monochromatic congruent copy of every three-point configuration. In this presentation, we will discuss the recent proof of one of the most natural open cases, namely that any two-colouring of the plane admits a monochromatic congruent copy of every 3-term arithmetic progression.
This talk is based on a joint work with Gabriel Currier and Chi Hoi Yip.