Hindman’s theorem and uncountable groups

In the early 1970’s, Hindman proved a beautiful theorem in additive Ramsey theory asserting that for any partition of the set of natural numbers into finitely many cells, there exists some infinite set such that all of its finite sums belong to a single cell.

In this talk, we shall address generalizations of this statement to the realm of the uncountable. Among others, we shall present a new theorem concerning the real line which simultaneously generalizes a recent theorem of Hindman, Leader and Strauss, and a classic theorem of Galvin and Shelah.

This is joint work with David Fernandez-Breton.