Nonstandard methods in the partition regularity of equations

Lorenzo Luperi Baglini (Università di Milano-Statale)

Abstract: In the recent past, several problems regarding the partition regularity of nonlinear configurations have been solved. Non-Archimedean mathematics has played an important role in many of these developments, through nonstandard analysis. In this talk, we will present the key ideas behind this nonstandard approach to Ramsey theory, which is based on an identification of ultrafilters with hypernatural numbers. We will discuss some limits of this approach, as well as some ideas to try to solve a few important open problems in the area.