Roman Prosanov: Upper bounds for the chromatic numbers of Euclidean spaces with forbidden Ramsey sets

Let C be a finite set in R^d. Our central question is how many colors do we need to paint R^n (n >= d) so that there is no monochromatic set congruent to C. We call this quantity the chromatic number of R^n with forbidden set C. When C consists of two points at distance one, then this is the usual chromatic number of R^n. In my talk I will discuss how we can obtain upper bounds for these quantities. Additionally I will explain how we can get better bounds if we replace R^n with a Euclidean ball of radius r.