Sala Seminari (Dip. Matematica).
In this talk I will outline some of the basics of nonstandard analysis and discuss how nonstandard methods can be applied to obtain new results in combinatorial number theory. We will look at a recent result obtained jointly with Di Nasso, Goldbring, Jin, Lupini and Mahlburg, where nonstandard methods are used to show that any subset of the natural numbers with Banach density greater than 1/2 contains a set of the form B+C where B and C are in\x85nite. This provides a partial answer to an old question posed by Erdoes, who conjectured that this conclusion holds for any set of positive lower density.