Abstract]
In this talk we will analyze how the interplay between additive and multiplicative structures in βN can be used to extend several well known results in Ramsey theory. In particular, we will sketch proofs that any finite coloring of N contains monochromatic solutions to the equation a+b=xy and arbitrarily long monochromatic polynomial progressions of the form (a+p_i(b))c^j, and discuss some related results and conjectures.