Daniel T. Soukup (Universität Wien): Monochromatic sumsets for colouring of the real numbers

Abstract: The aim of this talk is to review certain additive Ramsey-theoretic results on colouring the set of natural, rational and real numbers. In particular, we will prove that, under certain set theoretic assumptions, for any finite colouring f of the real number R there is an infinite X so that f is constant on X+X (where repetitions are allowed in the sumset). This work is joint with P. Komjáth, I. Leader, P. A. Russell, S. Shelah, Z. Vidnyánszky.