I will introduce the notion of “Ramsey partition regularity,” a generalization of partition regularity involving infinite configurations.  This notion is characterized in terms of certain ultrafilters related to tensor products, and called Ramsey witnesses.  We use the properties of this characterization in the nonstandard context of hypernatural numbers to determine whether various patterns involving polynomials and exponentials are Ramsey partition regular.

(Joint work with L. Luperi Baglini, M. Mamino, R. Mennuni, and M. Ragosta.)