**Nora Frankl**

London School of Economics and Political Science

#### Thursday, May 17 at 2:30 PM

**Abstract**

A finite subset A of R^d is called diameter-Ramsey if for every r there exists some n and a finite set B in R^n with diam(A)=diam(B) such that whenever B is coloured with r colours, there is a monochromatic subset A’ of B which is congruent to A. We prove that sets of diameter 1 with circumradius larger than 1/sqrt(2) are not diameter-Ramsey. In particular, we obtain that triangles with an angle larger than 135° are not diameter-Ramsey, improving a result of Frankl, Pach, Reiher and Rödl. Furthermore, we deduce that there are simplices which are almost regular but not diameter-Ramsey. Joint work with Jan Corsten.

We prove that sets of diametern 1 with circumradius larger than 1/sqrt(2) are not diameter-Ramsey. In particular, we obtain that triangles with an angle larger than 135° are not diameter-Ramsey, improving a result of Frankl, Pach, Reiher and Rödl. Furthermore, we deduce that there are simplices which are almost regular but not diameter-Ramsey.